problem solving methods framework

40 problem-solving techniques and processes

All teams and organizations encounter challenges. Approaching those challenges without a structured problem solving process can end up making things worse.

Proven problem solving techniques such as those outlined below can guide your group through a process of identifying problems and challenges , ideating on possible solutions , and then evaluating and implementing the most suitable .

In this post, you'll find problem-solving tools you can use to develop effective solutions. You'll also find some tips for facilitating the problem solving process and solving complex problems.

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What is problem solving?

Problem solving is a process of finding and implementing a solution to a challenge or obstacle. In most contexts, this means going through a problem solving process that begins with identifying the issue, exploring its root causes, ideating and refining possible solutions before implementing and measuring the impact of that solution.

For simple or small problems, it can be tempting to skip straight to implementing what you believe is the right solution. The danger with this approach is that without exploring the true causes of the issue, it might just occur again or your chosen solution may cause other issues.

Particularly in the world of work, good problem solving means using data to back up each step of the process, bringing in new perspectives and effectively measuring the impact of your solution.

Effective problem solving can help ensure that your team or organization is well positioned to overcome challenges, be resilient to change and create innovation. In my experience, problem solving is a combination of skillset, mindset and process, and it’s especially vital for leaders to cultivate this skill.

A group of people looking at a poster with notes on it

What is the seven step problem solving process?

A problem solving process is a step-by-step framework from going from discovering a problem all the way through to implementing a solution.

With practice, this framework can become intuitive, and innovative companies tend to have a consistent and ongoing ability to discover and tackle challenges when they come up.

You might see everything from a four step problem solving process through to seven steps. While all these processes cover roughly the same ground, I’ve found a seven step problem solving process is helpful for making all key steps legible.

We’ll outline that process here and then follow with techniques you can use to explore and work on that step of the problem solving process with a group.

The seven-step problem solving process is:

1. Problem identification

The first stage of any problem solving process is to identify the problem(s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they’re facing and wish to resolve.

Be sure to align with your team on the exact definition and nature of the problem you’re solving. An effective process is one where everyone is pulling in the same direction – ensure clarity and alignment now to help avoid misunderstandings later.

2. Problem analysis and refinement

The process of problem analysis means ensuring that the problem you are seeking to solve is the right problem . Choosing the right problem to solve means you are on the right path to creating the right solution.

At this stage, you may look deeper at the problem you identified to try and discover the root cause at the level of people or process. You may also spend some time sourcing data, consulting relevant parties and creating and refining a problem statement.

Problem refinement means adjusting scope or focus of the problem you will be aiming to solve based on what comes up during your analysis. As you analyze data sources, you might discover that the root cause means you need to adjust your problem statement. Alternatively, you might find that your original problem statement is too big to be meaningful approached within your current project.

Remember that the goal of any problem refinement is to help set the stage for effective solution development and deployment. Set the right focus and get buy-in from your team here and you’ll be well positioned to move forward with confidence.

3. Solution generation

Once your group has nailed down the particulars of the problem you wish to solve, you want to encourage a free flow of ideas connecting to solving that problem. This can take the form of problem solving games that encourage creative thinking or techniquess designed to produce working prototypes of possible solutions.

The key to ensuring the success of this stage of the problem solving process is to encourage quick, creative thinking and create an open space where all ideas are considered. The best solutions can often come from unlikely places and by using problem solving techniques that celebrate invention, you might come up with solution gold.

4. Solution development

No solution is perfect right out of the gate. It’s important to discuss and develop the solutions your group has come up with over the course of following the previous problem solving steps in order to arrive at the best possible solution. Problem solving games used in this stage involve lots of critical thinking, measuring potential effort and impact, and looking at possible solutions analytically.

During this stage, you will often ask your team to iterate and improve upon your front-running solutions and develop them further. Remember that problem solving strategies always benefit from a multitude of voices and opinions, and not to let ego get involved when it comes to choosing which solutions to develop and take further.

Finding the best solution is the goal of all problem solving workshops and here is the place to ensure that your solution is well thought out, sufficiently robust and fit for purpose.

5. Decision making and planning

Nearly there! Once you’ve got a set of possible, you’ll need to make a decision on which to implement. This can be a consensus-based group decision or it might be for a leader or major stakeholder to decide. You’ll find a set of effective decision making methods below.

Once your group has reached consensus and selected a solution, there are some additional actions that also need to be decided upon. You’ll want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

Set clear accountabilities, actions, timeframes, and follow-ups for your chosen solution. Make these decisions and set clear next-steps in the problem solving workshop so that everyone is aligned and you can move forward effectively as a group.

Ensuring that you plan for the roll-out of a solution is one of the most important problem solving steps. Without adequate planning or oversight, it can prove impossible to measure success or iterate further if the problem was not solved.

6. Solution implementation

This is what we were waiting for! All problem solving processes have the end goal of implementing an effective and impactful solution that your group has confidence in.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way. For some solutions, you might also implement a test with a small group and monitor results before rolling it out to an entire company.

You should have a clear owner for your solution who will oversee the plans you made together and help ensure they’re put into place. This person will often coordinate the implementation team and set-up processes to measure the efficacy of your solution too.

7. Solution evaluation

So you and your team developed a great solution to a problem and have a gut feeling it’s been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback.

You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives.

None of that is possible without taking the time to evaluate the success of the solution you developed in your problem solving model and adjust if necessary.

Remember that the problem solving process is often iterative and it can be common to not solve complex issues on the first try. Even when this is the case, you and your team will have generated learning that will be important for future problem solving workshops or in other parts of the organization.

It’s also worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time.

What does an effective problem solving process look like?

Every effective problem solving process begins with an agenda . In our experience, a well-structured problem solving workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

The format of a workshop ensures that you can get buy-in from your group, encourage free-thinking and solution exploration before making a decision on what to implement following the session.

This Design Sprint 2.0 template is an effective problem solving process from top agency AJ&Smart. It’s a great format for the entire problem solving process, with four-days of workshops designed to surface issues, explore solutions and even test a solution.

Check it for an example of how you might structure and run a problem solving process and feel free to copy and adjust it your needs!

For a shorter process you can run in a single afternoon, this remote problem solving agenda will guide you effectively in just a couple of hours.

Whatever the length of your workshop, by using SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Complete problem-solving methods

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

The Six Thinking Hats #creative thinking #meeting facilitation #problem solving #issue resolution #idea generation #conflict resolution The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly It doesn’t matter where you work and what your job role is, if you work with other people together as a team, you will always encounter the same challenges: Unclear goals and miscommunication that cause busy work and overtime Unstructured meetings that leave attendants tired, confused and without clear outcomes. Frustration builds up because internal challenges to productivity are not addressed Sudden changes in priorities lead to a loss of focus and momentum Muddled compromise takes the place of clear decision- making, leaving everybody to come up with their own interpretation. In short, a lack of structure leads to a waste of time and effort, projects that drag on for too long and frustrated, burnt out teams. AJ&Smart has worked with some of the most innovative, productive companies in the world. What sets their teams apart from others is not better tools, bigger talent or more beautiful offices. The secret sauce to becoming a more productive, more creative and happier team is simple: Replace all open discussion or brainstorming with a structured process that leads to more ideas, clearer decisions and better outcomes. When a good process provides guardrails and a clear path to follow, it becomes easier to come up with ideas, make decisions and solve problems. This is why AJ&Smart created Lightning Decision Jam (LDJ). It’s a simple and short, but powerful group exercise that can be run either in-person, in the same room, or remotely with distributed teams.

Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for brainstorming solutions

Now you have the context and background of the problem you are trying to solving, now comes the time to start ideating and thinking about how you’ll solve the issue.

Here, you’ll want to encourage creative, free thinking and speed. Get as many ideas out as possible and explore different perspectives so you have the raw material for the next step.

Looking at a problem from a new angle can be one of the most effective ways of creating an effective solution. TRIZ is a problem-solving tool that asks the group to consider what they must not do in order to solve a challenge.

By reversing the discussion, new topics and taboo subjects often emerge, allowing the group to think more deeply and create ideas that confront the status quo in a safe and meaningful way. If you’re working on a problem that you’ve tried to solve before, TRIZ is a great problem-solving method to help your team get unblocked.

Making Space with TRIZ #issue analysis #liberating structures #issue resolution You can clear space for innovation by helping a group let go of what it knows (but rarely admits) limits its success and by inviting creative destruction. TRIZ makes it possible to challenge sacred cows safely and encourages heretical thinking. The question “What must we stop doing to make progress on our deepest purpose?” induces seriously fun yet very courageous conversations. Since laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. Whoosh!

Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

Idea and Concept Development

Brainstorming without structure can quickly become chaotic or frustrating. In a problem-solving context, having an ideation framework to follow can help ensure your team is both creative and disciplined.

In this method, you’ll find an idea generation process that encourages your group to brainstorm effectively before developing their ideas and begin clustering them together. By using concepts such as Yes and…, more is more and postponing judgement, you can create the ideal conditions for brainstorming with ease.

Idea & Concept Development #hyperisland #innovation #idea generation Ideation and Concept Development is a process for groups to work creatively and collaboratively to generate creative ideas. It’s a general approach that can be adapted and customized to suit many different scenarios. It includes basic principles for idea generation and several steps for groups to work with. It also includes steps for idea selection and development.

Problem-solving techniques for developing and refining solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to develop and refine your ideas in order to bring them closer to a solution that actually solves the problem.

Use these problem-solving techniques when you want to help your team think through their ideas and refine them as part of your problem solving process.

Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

Ensuring that everyone in a group is able to contribute to a discussion is vital during any problem solving process. Not only does this ensure all bases are covered, but its then easier to get buy-in and accountability when people have been able to contribute to the process.

1-2-4-All is a tried and tested facilitation technique where participants are asked to first brainstorm on a topic on their own. Next, they discuss and share ideas in a pair before moving into a small group. Those groups are then asked to present the best idea from their discussion to the rest of the team.

This method can be used in many different contexts effectively, though I find it particularly shines in the idea development stage of the process. Giving each participant time to concretize their ideas and develop them in progressively larger groups can create a great space for both innovation and psychological safety.

1-2-4-All #idea generation #liberating structures #issue analysis With this facilitation technique you can immediately include everyone regardless of how large the group is. You can generate better ideas and more of them faster than ever before. You can tap the know-how and imagination that is distributed widely in places not known in advance. Open, generative conversation unfolds. Ideas and solutions are sifted in rapid fashion. Most importantly, participants own the ideas, so follow-up and implementation is simplified. No buy-in strategies needed! Simple and elegant!

15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Problem-solving techniques for making decisions and planning

After your group is happy with the possible solutions you’ve developed, now comes the time to choose which to implement. There’s more than one way to make a decision and the best option is often dependant on the needs and set-up of your group.

Sometimes, it’s the case that you’ll want to vote as a group on what is likely to be the most impactful solution. Other times, it might be down to a decision maker or major stakeholder to make the final decision. Whatever your process, here’s some techniques you can use to help you make a decision during your problem solving process.

How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

Straddling the gap between decision making and planning, MoSCoW is a simple and effective method that allows a group team to easily prioritize a set of possible options.

Use this method in a problem solving process by collecting and summarizing all your possible solutions and then categorize them into 4 sections: “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”.

This method is particularly useful when its less about choosing one possible solution and more about prioritorizing which to do first and which may not fit in the scope of your project. In my experience, complex challenges often require multiple small fixes, and this method can be a great way to move from a pile of things you’d all like to do to a structured plan.

MoSCoW #define intentions #create #design #action #remote-friendly MoSCoW is a method that allows the team to prioritize the different features that they will work on. Features are then categorized into “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”. To be used at the beginning of a timeslot (for example during Sprint planning) and when planning is needed.

When it comes to managing the rollout of a solution, clarity and accountability are key factors in ensuring the success of the project. The RAACI chart is a simple but effective model for setting roles and responsibilities as part of a planning session.

Start by listing each person involved in the project and put them into the following groups in order to make it clear who is responsible for what during the rollout of your solution.

Responsibility (Which person and/or team will be taking action?)
Authority (At what “point” must the responsible person check in before going further?)
Accountability (Who must the responsible person check in with?)
Consultation (Who must be consulted by the responsible person before decisions are made?)
Information (Who must be informed of decisions, once made?)

Ensure this information is easily accessible and use it to inform who does what and who is looped into discussions and kept up to date.

RAACI #roles and responsibility #teamwork #project management Clarifying roles and responsibilities, levels of autonomy/latitude in decision making, and levels of engagement among diverse stakeholders.

Problem-solving warm-up activities

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process. Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Closing activities for a problem-solving process

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Tips for effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Create psychologically safe spaces for discussion

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner.

It can be tough for people to stand up and contribute if the problems or challenges are emotive or personal in nature. Try and create a psychologically safe space for these kinds of discussions and where possible, create regular opportunities for challenges to be brought up organically.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

Save time and effort creating an effective problem solving process

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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A guide to problem-solving techniques, steps, and skills

You might associate problem-solving with the math exercises that a seven-year-old would do at school. But problem-solving isn’t just about math — it’s a crucial skill that helps everyone make better decisions in everyday life or work.

A guide to problem-solving techniques, steps, and skills

Problem-solving involves finding effective solutions to address complex challenges, in any context they may arise.

Unfortunately, structured and systematic problem-solving methods aren’t commonly taught. Instead, when solving a problem, PMs tend to rely heavily on intuition. While for simple issues this might work well, solving a complex problem with a straightforward solution is often ineffective and can even create more problems.

In this article, you’ll learn a framework for approaching problem-solving, alongside how you can improve your problem-solving skills.

The 7 steps to problem-solving

When it comes to problem-solving there are seven key steps that you should follow: define the problem, disaggregate, prioritize problem branches, create an analysis plan, conduct analysis, synthesis, and communication.

1. Define the problem

Problem-solving begins with a clear understanding of the issue at hand. Without a well-defined problem statement, confusion and misunderstandings can hinder progress. It’s crucial to ensure that the problem statement is outcome-focused, specific, measurable whenever possible, and time-bound.

Additionally, aligning the problem definition with relevant stakeholders and decision-makers is essential to ensure efforts are directed towards addressing the actual problem rather than side issues.

2. Disaggregate

Complex issues often require deeper analysis. Instead of tackling the entire problem at once, the next step is to break it down into smaller, more manageable components.

Various types of logic trees (also known as issue trees or decision trees) can be used to break down the problem. At each stage where new branches are created, it’s important for them to be “MECE” – mutually exclusive and collectively exhaustive. This process of breaking down continues until manageable components are identified, allowing for individual examination.

The decomposition of the problem demands looking at the problem from various perspectives. That is why collaboration within a team often yields more valuable results, as diverse viewpoints lead to a richer pool of ideas and solutions.

3. Prioritize problem branches

The next step involves prioritization. Not all branches of the problem tree have the same impact, so it’s important to understand the significance of each and focus attention on the most impactful areas. Prioritizing helps streamline efforts and minimize the time required to solve the problem.

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4. Create an analysis plan

For prioritized components, you may need to conduct in-depth analysis. Before proceeding, a work plan is created for data gathering and analysis. If work is conducted within a team, having a plan provides guidance on what needs to be achieved, who is responsible for which tasks, and the timelines involved.

5. Conduct analysis

Data gathering and analysis are central to the problem-solving process. It’s a good practice to set time limits for this phase to prevent excessive time spent on perfecting details. You can employ heuristics and rule-of-thumb reasoning to improve efficiency and direct efforts towards the most impactful work.

6. Synthesis

After each individual branch component has been researched, the problem isn’t solved yet. The next step is synthesizing the data logically to address the initial question. The synthesis process and the logical relationship between the individual branch results depend on the logic tree used.

7. Communication

The last step is communicating the story and the solution of the problem to the stakeholders and decision-makers. Clear effective communication is necessary to build trust in the solution and facilitates understanding among all parties involved. It ensures that stakeholders grasp the intricacies of the problem and the proposed solution, leading to informed decision-making.

Exploring problem-solving in various contexts

While problem-solving has traditionally been associated with fields like engineering and science, today it has become a fundamental skill for individuals across all professions. In fact, problem-solving consistently ranks as one of the top skills required by employers.

Problem-solving techniques can be applied in diverse contexts:

Individuals — What career path should I choose? Where should I live? These are examples of simple and common personal challenges that require effective problem-solving skills
Organizations — Businesses also face many decisions that are not trivial to answer. Should we expand into new markets this year? How can we enhance the quality of our product development? Will our office accommodate the upcoming year’s growth in terms of capacity?
Societal issues — The biggest world challenges are also complex problems that can be addressed with the same technique. How can we minimize the impact of climate change? How do we fight cancer?

Despite the variation in domains and contexts, the fundamental approach to solving these questions remains the same. It starts with gaining a clear understanding of the problem, followed by decomposition, conducting analysis of the decomposed branches, and synthesizing it into a result that answers the initial problem.

Real-world examples of problem-solving

Let’s now explore some examples where we can apply the problem solving framework.

Problem: In the production of electronic devices, you observe an increasing number of defects. How can you reduce the error rate and improve the quality?

Before delving into analysis, you can deprioritize branches that you already have information for or ones you deem less important. For instance, while transportation delays may occur, the resulting material degradation is likely negligible. For other branches, additional research and data gathering may be necessary.

Once results are obtained, synthesis is crucial to address the core question: How can you decrease the defect rate?

While all factors listed may play a role, their significance varies. Your task is to prioritize effectively. Through data analysis, you may discover that altering the equipment would bring the most substantial positive outcome. However, executing a solution isn’t always straightforward. In prioritizing, you should consider both the potential impact and the level of effort needed for implementation.

By evaluating impact and effort, you can systematically prioritize areas for improvement, focusing on those with high impact and requiring minimal effort to address. This approach ensures efficient allocation of resources towards improvements that offer the greatest return on investment.

Problem : What should be my next job role?

When breaking down this problem, you need to consider various factors that are important for your future happiness in the role. This includes aspects like the company culture, our interest in the work itself, and the lifestyle that you can afford with the role.

However, not all factors carry the same weight for us. To make sense of the results, we can assign a weight factor to each branch. For instance, passion for the job role may have a weight factor of 1, while interest in the industry may have a weight factor of 0.5, because that is less important for you.

By applying these weights to a specific role and summing the values, you can have an estimate of how suitable that role is for you. Moreover, you can compare two roles and make an informed decision based on these weighted indicators.

Key problem-solving skills

This framework provides the foundation and guidance needed to effectively solve problems. However, successfully applying this framework requires the following:

Creativity — During the decomposition phase, it’s essential to approach the problem from various perspectives and think outside the box to generate innovative ideas for breaking down the problem tree
Decision-making — Throughout the process, decisions must be made, even when full confidence is lacking. Employing rules of thumb to simplify analysis or selecting one tree cut over another requires decisiveness and comfort with choices made
Analytical skills — Analytical and research skills are necessary for the phase following decomposition, involving data gathering and analysis on selected tree branches
Teamwork — Collaboration and teamwork are crucial when working within a team setting. Solving problems effectively often requires collective effort and shared responsibility
Communication — Clear and structured communication is essential to convey the problem solution to stakeholders and decision-makers and build trust

How to enhance your problem-solving skills

Problem-solving requires practice and a certain mindset. The more you practice, the easier it becomes. Here are some strategies to enhance your skills:

Practice structured thinking in your daily life — Break down problems or questions into manageable parts. You don’t need to go through the entire problem-solving process and conduct detailed analysis. When conveying a message, simplify the conversation by breaking the message into smaller, more understandable segments
Regularly challenging yourself with games and puzzles — Solving puzzles, riddles, or strategy games can boost your problem-solving skills and cognitive agility.
Engage with individuals from diverse backgrounds and viewpoints — Conversing with people who offer different perspectives provides fresh insights and alternative solutions to problems. This boosts creativity and helps in approaching challenges from new angles

Final thoughts

Problem-solving extends far beyond mathematics or scientific fields; it’s a critical skill for making informed decisions in every area of life and work. The seven-step framework presented here provides a systematic approach to problem-solving, relevant across various domains.

Now, consider this: What’s one question currently on your mind? Grab a piece of paper and try to apply the problem-solving framework. You might uncover fresh insights you hadn’t considered before.

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Framework for Problem-Solving: 5 Best Examples for Product Teams

What is a framework for problem-solving? And how can product managers use them to tackle the challenges they face?

If you are after the answers to these questions, we’ve got you covered! We also look at examples of different frameworks and the main steps in the problem-solving process.

Are you ready to dive in?

A framework for problem-solving allows product teams to find the causes of the problems and generate solutions in an organized way.
Root Cause Analysis enables problem solvers to get to the bottom of the problem and find the main reason why the problem occurs.
Many companies like Google use the CIRCLES framework for problem-solving. The process consists of 7 steps and helps the product manager to take stock of the situation, identify user needs, prioritize them, and produce and assess solutions.
The CIA created the Pheonix Checklist with a list of questions to help the problem solver dissect the issue and guide them through the process.
Lightning Decision Jam (LDJ) allows remote teams to come up with solutions quickly and within the constraints of the online working environment.
The acronym DMAIC stands for Define, Measure, Analyze, Implement and Control. They are stages in Six Sigma, a popular quality improvement methodology.
All the problem-solving frameworks share certain processes: identifying and understanding the problem or the needs of the customer, brainstorming solutions, choosing and implementing the solutions, and monitoring their effectiveness.
Userpilot can help you to collect user feedback and track usage data to understand the problems your users are facing or set the baseline. Once you implement the solutions, you can use them to collect more data to evaluate their impact .

What is a problem-solving framework?

The problem-solving framework is a set of tools and techniques to identify the causes of the problem and find adequate solutions.

Problem-solving frameworks rely on both data analysis and heuristics.

What are heuristics?

We use them every day. In short, it’s mental shortcuts that allow us to apply what we already know in a new situation. They are particularly useful when detailed research is not practical. An educated guess or generalization may be good enough but the solutions won’t be perfect or cover all the eventualities.

Problem-solving framework example

Let’s look at some of the best-known problem-solving frameworks.

Root Cause Analysis

Managers usually use Root Cause Analysis to deal with problems that have already occurred. It consists of six main steps.

The process starts by defining the problem, followed by data collection .

Based on the data, the team generates a list of possible causes. Next, they can use techniques like 5 Why’s or the Fishbone diagram for more in-depth analysis to identify the actual problem – the root cause.

Once they know it, they can move on to recommend and implement relevant solutions.

CIRCLES method for problem-solving

The CIRCLES method is a problem-solving framework that was created by Lewis C. Lin, who is known for his best-selling book Decode and Conquer.

The framework is particularly suitable for product management. That’s because it allows managers to solve any kind of problem, no matter where it comes from. As a result, it’s a go-to framework for companies like Google.

CIRCLES stands for the 7 steps it takes to solve a problem:

C omprehend the situation
I dentify the Customer
R eport the customer’s needs
C ut, through prioritization
L ist solutions
E valuate tradeoffs
S ummarize recommendation

Comprehend the situation

At this step, the team tries to understand the context of the problem.

The easiest way to do that is by asking Wh- questions, like ‘What is it?’, ‘Who is it for?’, ‘Why do they need it?’, ‘When is it available?’, ‘Where is it available?’ and ‘How does it work?’

Identify the customer

The who question is particularly important because you need to know who you are building the product for.

At this step, you focus on the user in more detail. You can do it by creating user personas and empathy maps which allow you to understand your users’ experiences, behaviors, and goals.

Report customer’s needs

Next, the focus shifts to specific user needs and requirements.

Teams often use user stories for this purpose. These look like this:

As a <type of user> , I want <output> so that <outcome>.

For example:

As a product manager, I want to be able to customize the dashboard so that I can easily track the performance of my KPIs.

Reporting user needs in this way forces you to look at the problem from a user perspective and express ideas in plain accessible language.

Cut through prioritization

Now that you have a list of use cases or user stories, it’s time to prioritize them.

This stage is very important as we never have enough resources to build all the possible features. As the Pareto rule states, users only use about 20 percent of the available functionality.

However, many teams fall into the build trap and create bloated products that have tons of features but are not particularly great at solving any of the customer problems.

There are a bunch of techniques that product managers or owners can use to prioritize the backlog items, like MoSCoW or Kano analysis.

Kano Analysis helps to organize solutions according to their priority

List solutions

Now, that you have the most urgent user needs, it’s time to generate possible solutions.

There are different ways of solving each problem, so resist the temptation to jump at the first idea your team comes up with. Instead, try to brainstorm at least 3 solutions to a particular problem.

It’s extremely important to be non-judgemental at this stage and refrain from dismissing any ideas. Just list them all and don’t worry about evaluating their suitability. There will be time for it in the next stages.

Evaluate tradeoffs

At this step, you assess the pros and cons of each potential solution.

To aid the process, you may want to create a checklist with criteria like cost or ease of implementation, or riskiness.

Summarize your recommendation

The last step is to summarize the solutions and provide a recommendation, based on what you’ve found out by this stage.

Ideally, the customer should be involved at every stage of the process but if for some reason this hasn’t been the case this is the time to ask them for their opinion about the solutions you’ve chosen.

The Phoenix Checklist

The Phoenix Checklist is another solid framework.

It was developed by the CIA and it consists of sets of questions grouped into different categories.

Going through the checklist allows the agent… I mean the product manager to break down the problem and come up with the best solution.

Here are some of the questions:

Why is it necessary to solve this particular problem?
What benefits will you receive by solving it?
What is the information you have?
Is the information you have sufficient?
What are the unknowns?
Can you describe the problem in a chart?
Where are the limits for the problem?
Can you distinguish the different parts of the problem?
What are the relationships between the different parts of the problem?
Have you seen this problem before?
Can you use solutions to similar problems to solve this problem?

Lightning Decision Jam – problem-solving framework for remote teams

Lightning Decision Jam (LDJ) is a very effective problem-solving framework for dispersed teams.

It consists of 9 steps that allow the team members to list and reframe the issues they face, choose the most pressing ones to address, generate, prioritize and select solutions, and turn them into actionable tasks.

Each of the steps is time-boxed so that the team moves through the process quickly and efficiently.

DMAIC – The Six Sigma’s Problem-Solving Method

Six Sigma was initially developed for the needs of the automotive industry in Japan to help it deal with high defect rates. It is now one of the best quality-improvement frameworks and it is used in different sectors.

There are 5 main stages of Six Sigma projects.

During the Definition stage, the team identifies the problem they would like to solve, prepares the project charter, brings the right people on board, and ensures there are adequate resources available.

One of the key tasks during this stage is capturing the Voice of the Customer . After all, the definition of good quality is very much dependent on the needs of the customers and what they are ready to pay for, so their input is essential.

During the Measure phase, the team describes the process and measures its current performance to establish the baseline.

At the Analyze stage, they use the data to identify the root causes and waste, or activities that don’t bring any value.

The Improve stage focuses on generating, evaluating, and optimizing solutions. This is also when the team tests the ideas. If they are successful, they plan how to implement them.

Finally, the project champion must ensure that people stick to the new ways of doing things. That’s what the Control phase is about. The team also uses this stage to assess the outcomes and benefits of the project.

Problem-solving process recurring steps

Now, that we have looked at a few of the most popular frameworks for solving problems, why don’t we look at the steps that they have in common?

Identify and understand the problem with user research

First, it’s necessary to identify and understand the problem.

To do that, your team should conduct solid user research and capture the Voice of the Customer (VoC) .

How to do that?

You can track user in-app behavior , run in-app surveys , conduct interviews and analyze user social media feedback and online reviews.

To get a complete picture, try to collect both quantitative and qualitative data.

Brainstorm solutions

There’s no problem-solving framework out there that wouldn’t include brainstorming of some sort. And there’s a good reason for that: it’s one of the most effective ways to generate a lot of different solutions in a short time.

To make the brainstorming sessions as effective as possible, make sure all your team members have a chance to contribute. Your software engineer may not be the most vocal team member but it doesn’t mean she has nothing to offer, and not recognizing it can be costly.

The Delphi method or silent brainstorming are good techniques that prevent groupthink and the less outspoken team members from being talked over.

No matter how ridiculous or outrageous some ideas may seem, don’t discard any unless they’re completely irrelevant. It’s not the time to evaluate ideas, just come up with as many of them as possible.

Decide on a solution and implement

Some of the solutions will be better than others, so it’s always necessary to assess them and choose the one solution that solves the problem better than others.

Even the best ideas are not worth much if you don’t manage to implement them, so pay attention to this stage.

Often big changes are necessary to solve difficult problems so you need to prepare your team or your customers. Take your time, and focus on explaining the rationale for change and the benefits that it brings.

Make sure to provide the right training to your staff and support your users with onboarding and product education to reduce friction once the new solution goes live.

Collect feedback and evaluate

Once you implement the solution, keep collecting feedback to assess its effectiveness.

Is it solving the problem? Does it help you achieve the objectives? If not, how can you modify it to improve its success? If yes, is there anything else that would provide even more value?

You can do this by actively asking your users for feedback, for example via a survey.

A survey to collect feedback to the new solution

In addition to asking for feedback actively, give your users a chance to submit passive feedback whenever they feel like it.

In case of organizational changes, it’s important to monitor whether the new processes or tools are used in the first place, because as creatures of habit we tend to relapse to our old ways quite easily, often without realizing it.

There are a few useful frameworks for problem-solving. They can guide a product manager through the process of defining the problem, identifying causes, generating and implementing solutions, and assessing their impact.

If you’d like to learn how Userpilot can help you capture the voice of the customer, analyze the data to identify root causes, help design user-centered solutions and collect both active and passive feedback to test their effectiveness, book a demo !

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Adopting the right problem-solving approach

May 4, 2023 You’ve defined your problem, ensured stakeholders are aligned, and are ready to bring the right problem-solving approach and focus to the situation to find an optimal solution. But what is the right problem-solving approach? And what if there is no single ideal course of action? In our 2013 classic from the Quarterly , senior partner Olivier Leclerc highlights the value of taking a number of different approaches simultaneously to solve difficult problems. Read on to discover the five flexons, or problem-solving languages, that can be applied to the same problem to generate richer insights and more innovative solutions. Then check out more insights on problem-solving approaches, and dive into examples of pressing challenges organizations are contending with now.

Five routes to more innovative problem solving

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How to master the seven-step problem-solving process

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Take the McKinsey Problem Solving Test

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How to Solve Problems

Laura Amico

To bring the best ideas forward, teams must build psychological safety.

Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.

Laura Amico is a former senior editor at Harvard Business Review.

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At the core of our methodology is the Foresight Framework, a proven and proprietary methodology to find future innovation opportunities and to create forward-looking organizations. The methodology began at Stanford University and has been tested with various teams and companies since 2004. Comprised of 15 core methods for problem scoping and problem solving, the Foresight Framework is designed to address complex problems and future planning as systematically, creatively, and efficiently as possible.

By using this framework, participants prepare successfully for the future by answering three fundamental questions:

How do I begin looking for future opportunities?
How can I create a path to these opportunities that anticipates the inevitable changes along the way?
What can I start doing today that will help me get there first?

Playbook for Strategic Foresight and Innovation

Looking for practical foresight methods? Download a free PDF of our playbook (or buy a print version ) as your in-house guide.

Phase I: Perspective

Methods in the Perspective phase give you a broad frame of reference, holding up a mirror to the past so you may better anticipate the future.

METHOD	GOAL	OUTCOME
	Retain complexity of topic, while beginning to converge on priority areas	A visual map of the top 8 dimensions in a problem
	Connect multiple related events and highlights precedents	A set of related timelines showing past developments and their timing
	Uncover indirect influences and events within an era	A large-scale pattern map of past major decisions affecting current planning

Phase II: Opportunity

By understanding future customer changes, methods in the Opportunity phase help you develop an ability to see growth opportunities that exist today and extend into the future.

METHOD	GOAL	OUTCOME
	Identify relevant population group and shared values	A diagram of the target user population(s) with size and attributes
	Describe future user needs without extrapolating biases from today’s users	A comparison of two customer/user profiles, including anticipated needs
	Convey nonverbal and contextual details about a future use case	A short performance of user needs, either captured as a live skit or via video

METHOD

GOAL

OUTCOME

Identify relevant population group and shared values

A diagram of the target user population(s) with size and attributes

Describe future user needs without extrapolating biases from today’s users

A comparison of two customer/user profiles, including anticipated needs

Convey nonverbal and contextual details about a future use case

A short performance of user needs, either captured as a live skit or via video

Phase III: Solution

Methods in the Solution phase seek to define the questions that exist along different paths to innovation, which are specific to your industry, customers, organization, and team skills.

METHOD	GOAL	OUTCOME
	Determine future focus of opportunity through iterative filters	A visual map of the competitive landscape and emerging market areas
	Produce system models that show interactions and related components	A 3D prototype of a potential innovation solution
	Prioritize top decisions based on direct path to desired future	A visual high-level roadmap for future action

METHOD

GOAL

OUTCOME

Determine future focus of opportunity through iterative filters

A visual map of the competitive landscape and emerging market areas

Produce system models that show interactions and related components

A 3D prototype of a potential innovation solution

Prioritize top decisions based on direct path to desired future

A visual high-level roadmap for future action

Phase IV: Team

Methods in the Team phase focus on finding the talent and leadership your team needs to take an idea forward as a new opportunity or innovation.

METHOD	GOAL	OUTCOME
	Let you quickly filter promising innovation partners and teammates	Team rehearsal for communicating and receiving new ideas for target reactions
	Identify your team’s aptitude for radical innovation	A team score on five dimensions of innovation culture with a related set of supporting activities
	Map your personal or team's innovation network	A stakeholder map of the innovation players to bring an idea to life

METHOD

GOAL

OUTCOME

Let you quickly filter promising innovation partners and teammates

Team rehearsal for communicating and receiving new ideas for target reactions

Identify your team’s aptitude for radical innovation

A team score on five dimensions of innovation culture with a related set of supporting activities

Map your personal or team's innovation network

A stakeholder map of the innovation players to bring an idea to life

Phase V: Vision

Methods in the Vision phase sharpen your team’s vision so that it may take on a life of its own and guide everyone’s actions forward.

METHOD	GOAL	OUTCOME
	Provide a simple formula to tell a future vision	A short inspirational description about an idea’s future value
	Evaluate future vision in terms of its breakthrough potential	A quick scoring about an idea’s visionary potential
	Chart the most efficient success path for an innovation idea through an organization	A visual planning map revealing what to do (or not do) for optimal internal alignment and success

General Non-Commercial Use

Under the creative commons license ( CC BY-NC-SA 3.0 ), the Playbook for Strategic Foresight and Innovation is available for free download to individuals, companies, and organizations for non-commercial purposes only.
Parties interested in applying the foresight methods from the Foresight Framework for internal development, university teaching or educational reasons, or other purposes may do so with attribution and with no intention to profit.
Other third party trademarks referenced on the website and in the Playbook for Strategic Foresight and Innovation are the property of their respective owners.

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Commercial usage of the Foresight Framework and all related methods are restricted and full copyright are retained by the book's authors. You may not use trademarks, methods, or other intellectual property assets in connection with web sites, products, packaging, manuals, promotional/advertising materials, or for any other purpose except pursuant to an express written licensing agreement from the publisher. Contact the Innovation Leadership Group LLC's licensing team [email protected] for more information.

McKinsey Problem Solving: Six steps to solve any problem and tell a persuasive story

The McKinsey problem solving process is a series of mindset shifts and structured approaches to thinking about and solving challenging problems. It is a useful approach for anyone working in the knowledge and information economy and needs to communicate ideas to other people.

Over the past several years of creating StrategyU, advising an undergraduates consulting group and running workshops for clients, I have found over and over again that the principles taught on this site and in this guide are a powerful way to improve the type of work and communication you do in a business setting.

When I first set out to teach these skills to the undergraduate consulting group at my alma mater, I was still working at BCG. I was spending my day building compelling presentations, yet was at a loss for how to teach these principles to the students I would talk with at night.

Through many rounds of iteration, I was able to land on a structured process and way of framing some of these principles such that people could immediately apply them to their work.

While the “official” McKinsey problem solving process is seven steps, I have outline my own spin on things – from experience at McKinsey and Boston Consulting Group. Here are six steps that will help you solve problems like a McKinsey Consultant:

Step #1: School is over, stop worrying about “what” to make and worry about the process, or the “how”

When I reflect back on my first role at McKinsey, I realize that my biggest challenge was unlearning everything I had learned over the previous 23 years. Throughout school you are asked to do specific things. For example, you are asked to write a 5 page paper on Benjamin Franklin — double spaced, 12 font and answering two or three specific questions.

In school, to be successful you follow these rules as close as you can. However, in consulting there are no rules on the “what.” Typically the problem you are asked to solve is ambiguous and complex — exactly why they hire you. In consulting, you are taught the rules around the “how” and have to then fill in the what.

The “how” can be taught and this entire site is founded on that belief. Here are some principles to get started:

Step #2: Thinking like a consultant requires a mindset shift

There are two pre-requisites to thinking like a consultant. Without these two traits you will struggle:

A healthy obsession looking for a “better way” to do things
Being open minded to shifting ideas and other approaches

In business school, I was sitting in one class when I noticed that all my classmates were doing the same thing — everyone was coming up with reasons why something should should not be done.

As I’ve spent more time working, I’ve realized this is a common phenomenon. The more you learn, the easier it becomes to come up with reasons to support the current state of affairs — likely driven by the status quo bias — an emotional state that favors not changing things. Even the best consultants will experience this emotion, but they are good at identifying it and pushing forward.

Key point : Creating an effective and persuasive consulting like presentation requires a comfort with uncertainty combined with a slightly delusional belief that you can figure anything out.

Step #3: Define the problem and make sure you are not solving a symptom

Before doing the work, time should be spent on defining the actual problem. Too often, people are solutions focused when they think about fixing something. Let’s say a company is struggling with profitability. Someone might define the problem as “we do not have enough growth.” This is jumping ahead to solutions — the goal may be to drive more growth, but this is not the actual issue. It is a symptom of a deeper problem.

Consider the following information:

Costs have remained relatively constant and are actually below industry average so revenue must be the issue
Revenue has been increasing, but at a slowing rate
This company sells widgets and have had no slowdown on the number of units it has sold over the last five years
However, the price per widget is actually below where it was five years ago
There have been new entrants in the market in the last three years that have been backed by Venture Capital money and are aggressively pricing their products below costs

In a real-life project there will definitely be much more information and a team may take a full week coming up with a problem statement . Given the information above, we may come up with the following problem statement:

Problem Statement : The company is struggling to increase profitability due to decreasing prices driven by new entrants in the market. The company does not have a clear strategy to respond to the price pressure from competitors and lacks an overall product strategy to compete in this market.

Step 4: Dive in, make hypotheses and try to figure out how to “solve” the problem

Now the fun starts!

There are generally two approaches to thinking about information in a structured way and going back and forth between the two modes is what the consulting process is founded on.

First is top-down . This is what you should start with, especially for a newer “consultant.” This involves taking the problem statement and structuring an approach. This means developing multiple hypotheses — key questions you can either prove or disprove.

Given our problem statement, you may develop the following three hypotheses:

Company X has room to improve its pricing strategy to increase profitability
Company X can explore new market opportunities unlocked by new entrants
Company X can explore new business models or operating models due to advances in technology

As you can see, these three statements identify different areas you can research and either prove or disprove. In a consulting team, you may have a “workstream leader” for each statement.

Once you establish the structure you you may shift to the second type of analysis: a bottom-up approach . This involves doing deep research around your problem statement, testing your hypotheses, running different analysis and continuing to ask more questions. As you do the analysis, you will begin to see different patterns that may unlock new questions, change your thinking or even confirm your existing hypotheses. You may need to tweak your hypotheses and structure as you learn new information.

A project vacillates many times between these two approaches. Here is a hypothetical timeline of a project:

Step 5: Make a slides like a consultant

The next step is taking the structure and research and turning it into a slide. When people see slides from McKinsey and BCG, they see something that is compelling and unique, but don’t really understand all the work that goes into those slides. Both companies have a healthy obsession (maybe not to some people!) with how things look, how things are structured and how they are presented.

They also don’t understand how much work is spent on telling a compelling “story.” The biggest mistake people make in the business world is mistaking showing a lot of information versus telling a compelling story. This is an easy mistake to make — especially if you are the one that did hours of analysis. It may seem important, but when it comes down to making a slide and a presentation, you end up deleting more information rather than adding. You really need to remember the following:

Data matters, but stories change hearts and minds

Here are four quick ways to improve your presentations:

Tip #1 — Format, format, format

Both McKinsey and BCG had style templates that were obsessively followed. Some key rules I like to follow:

Make sure all text within your slide body is the same font size (harder than you would think)
Do not go outside of the margins into the white space on the side
All titles throughout the presentation should be 2 lines or less and stay the same font size
Each slide should typically only make one strong point

Tip #2 — Titles are the takeaway

The title of the slide should be the key insight or takeaway and the slide area should prove the point. The below slide is an oversimplification of this:

Even in consulting, I found that people struggled with simplifying a message to one key theme per slide. If something is going to be presented live, the simpler the better. In reality, you are often giving someone presentations that they will read in depth and more information may make sense.

To go deeper, check out these 20 presentation and powerpoint tips .

Tip #3 — Have “MECE” Ideas for max persuasion

“MECE” means mutually exclusive, collectively exhaustive — meaning all points listed cover the entire range of ideas while also being unique and differentiated from each other.

An extreme example would be this:

Slide title: There are seven continents
Slide content: The seven continents are North America, South America, Europe, Africa Asia, Antarctica, Australia

The list of continents provides seven distinct points that when taken together are mutually exclusive and collectively exhaustive . The MECE principle is not perfect — it is more of an ideal to push your logic in the right direction. Use it to continually improve and refine your story.

Applying this to a profitability problem at the highest level would look like this:

Goal: Increase profitability

2nd level: We can increase revenue or decrease costs

3rd level: We can increase revenue by selling more or increasing prices

Each level is MECE. It is almost impossible to argue against any of this (unless you are willing to commit accounting fraud!).

Tip #4 — Leveraging the Pyramid Principle

The pyramid principle is an approach popularized by Barbara Minto and essential to the structured problem solving approach I learned at McKinsey. Learning this approach has changed the way I look at any presentation since.

Here is a rough outline of how you can think about the pyramid principle as a way to structure a presentation:

As you build a presentation, you may have three sections for each hypothesis. As you think about the overall story, the three hypothesis (and the supporting evidence) will build on each other as a “story” to answer the defined problem. There are two ways to think about doing this — using inductive or deductive reasoning:

deductive versus inductive reasoning in powerpoint arguments

If we go back to our profitability example from above, you would say that increasing profitability was the core issue we developed. Lets assume that through research we found that our three hypotheses were true. Given this, you may start to build a high level presentation around the following three points:

example of hypotheses confirmed as part of consulting problem solving

These three ideas not only are distinct but they also build on each other. Combined, they tell a story of what the company should do and how they should react. Each of these three “points” may be a separate section in the presentation followed by several pages of detailed analysis. There may also be a shorter executive summary version of 5–10 pages that gives the high level story without as much data and analysis.

Step 6: The only way to improve is to get feedback and continue to practice

Ultimately, this process is not something you will master overnight. I’ve been consulting, either working for a firm or on my own for more than 10 years and am still looking for ways to make better presentations, become more persuasive and get feedback on individual slides.

The process never ends.

The best way to improve fast is to be working on a great team . Look for people around you that do this well and ask them for feedback. The more feedback, the more iterations and more presentations you make, the better you will become. Good luck!

If you enjoyed this post, you’ll get a kick out of all the free lessons I’ve shared that go a bit deeper. Check them out here .

Do you have a toolkit for business problem solving? I created Think Like a Strategy Consultant as an online course to make the tools of strategy consultants accessible to driven professionals, executives, and consultants. This course teaches you how to synthesize information into compelling insights, structure your information in ways that help you solve problems, and develop presentations that resonate at the C-Level. Click here to learn more or if you are interested in getting started now, enroll in the self-paced version ($497) or hands-on coaching version ($997). Both versions include lifetime access and all future updates.

Problem-Solving Frameworks: Go Down to the Root

Problems of all shapes and sizes pop up on a daily basis. So the big question is: How to solve them? We bring you several frameworks that could help.

Do you consider yourself a problem-solver? Well, you certainly should. Because that's what you and your team do every day.

First and foremost, you solve the problems that your prospective customers have, for which they want to find a solution (i.e. your product).

Then, there are unexpected errors and usability issues that your existing users face while using your product, or the bugs that your engineers encounter.

On a higher level, you need to find the right solution for the new features you want to develop, discover new opportunities for growth, and so much more.

Now, the big question is: How to solve all those problems?

We bring you several problem-solving frameworks that could help.

In this chapter

Icons 300 The Phoenix Checklist
Icons 300 Root Cause Analysis
Icons 300 CIRCLES Method
Icons 300 The mathematician’s “universal” way

The Phoenix Checklist

Have you ever wondered how the CIA goes about solving problems ? Well, they’ve developed The Phoenix Checklist to “encourage agents to look at a challenge from many different angles”.

The Phoenix Checklist was popularized by Michael Michalko, a former CIA creative consultant, in his book Thinkertoys , as a blueprint for dissecting the problem into knowns and unknowns to find the best possible solution.

Some of the questions of The Phoenix Checklist are:

Why is it necessary to solve this particular problem?

What benefits will you receive by solving it?

What is the information you have?

Is the information sufficient?

What is the unknown?

What isn't a problem?

Should you draw a diagram of the problem? A figure?

Where are the boundaries of the problem?

What are the constants of the problem?

Have you seen this problem before?

If you find a similar problem that has already been solved, can you use its method?

Can you restate the problem? How many different ways can you restate it?

What are the best, worst, and most probable solutions you can imagine?

There’s no doubt that The Phoenix Checklist can be a complementary problem-solving technique for your product team, even though it wasn’t developed with product managers in mind. Use it to frame, deconstruct, and reframe the problems you encounter.

Root Cause Analysis

Root Cause Analysis (RCA) is a problem-solving method that aims at identifying the root cause of a problem by moving back to its origin, as opposed to techniques that only address and treat the symptoms.

The RCA is corrective in its nature with a final goal to prevent the same problem from happening again in the future. But that doesn’t mean that root cause investigation is simple or that it only needs to be done once.

The starting questions are:

What is currently the problem?

Why does this problem occur?

But don’t stop at the first why. Keep asking why that happened , until you get to the bottom and the real cause.

When you first start using the RCA method, it will be a reactive approach to solving problems. It is typically in use when something goes wrong. But once you perfect this technique, you can use it as a proactive action towards identifying problems before they happen and preventing them from happening. The end goal of the Root Cause Analysis is continuous improvement.

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CIRCLES Method

The CIRCLES method is a problem-solving framework that helps product managers provide a meaningful response to any questions coming from design, marketing, customer success, or other teams.

The creator of the CIRCLES method is Lewis C. Lin, author of the book Decode and Conquer . The way he explains it , you should always start by clarifying the goal, identifying the constraints up front, and understanding the context of the situation.

The seven steps of the CIRCLES method are:

Comprehend the situation: Understand the context of the problem you’re solving

Identify the customer: Know who you’re building the product for

Report customer’s needs: Rely on the customer research to uncover pain points

Cut, through prioritization: Omit unnecessary ideas, tasks, and solutions

List solutions: Keep the focus on the most feasible solutions

Evaluate tradeoffs: Consider the impact, cost of delay, and other factors

Summarize your recommendation: Make a decision and explain your reasoning

The main goal of the CIRCLES method is to help you keep an open mind as you move through the steps, as well as to avoid jumping straight into the conclusions.

The mathematician’s “universal” way

Although there isn’t exactly a universal way to solve problems that would perfectly fit every situation and scenario, mathematician Claude Shannon developed a strong problem-solving system that has given results across disciplines.

The essential part of his framework involves creative thinking to get out of standard mental loops, critical thinking to question every answer and every possible solution, and the process of restructuring a problem , whether it’s by maximizing it, minimizing it, contrasting it, inverting it, or anything else.

As explained in the article from Quartz :

"Claude Shannon didn’t just formulate a question and then look for answers. He was methodological in developing a process to help him see beyond what was in sight."

Shannon’s problem-solving process includes:

Finding a problem

Understanding a problem

Going beyond obvious questions

Defining a shape and a form of a problem

Focusing on essential details, but always keeping a bigger picture in mind

Changing a reference point and reframing a point of view

Uncovering insights from the sea of information

That said, Claude Shannon certainly developed a methodology that is relevant for every problem-solving situation, not only math problems.

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36 Problem-solving techniques, methods and tools

When it comes to solving problems, getting ideas is the easy part.

But businesses often forget the other four stages of the problem-solving process that will allow them to find the best solution.

Instead of jumping straight to idea generation, your problem-solving framework should look like this:

Identify the problem
Reveal why it has occurred
Brainstorm ideas
Select the best solution

See how idea generation doesn’t appear until stage 3?!

In this extensive resource, we provide techniques, methodologies and tools to guide you through every stage of the problem-solving process.

Once you’ve finished reading, you’ll possess an extensive problem-solving arsenal that will enable you to overcome your biggest workplace challenges.

11 Problem-solving techniques for clarity and confidence

Before we dive into more comprehensive methodologies for solving problems, there are a few basic techniques you should know.

The following techniques will set you up for a successful problem-solving session with your team, allowing you to take on your biggest challenges with clarity and confidence. ‍

1. Take a moment, take a breath

When a problem or challenge arises, it’s normal to act too quickly or rely on solutions that have worked well in the past. This is known as entrenched thinking.

But acting impulsively, without prior consideration or planning, can cause you to misunderstand the issue and overlook possible solutions to the problem.

Therefore, the first thing you should always do when you encounter a problem is: breathe in and out.

Take a step back and make a clear plan of action before you act. This will help you to take rational steps towards solving a problem. ‍

2. Ask questions to understand the full extent of the issue

Another common mistake people make when attempting to solve a problem is taking action before fully understanding the problem.

Before committing to a theory, ask enough questions to unearth the true root of the issue.

Later in this article, we cover The 5 Why’s problem-solving methodology which you can use to easily identify the root of your problem. Give this a go at your next meeting and see how your initial understanding of a problem can often be wrong. ‍

3. Consider alternative perspectives

A common problem-solving issue is that of myopia—a narrow-minded view or perception of the problem. Myopia can occur when you’re too involved with the problem or your team isn’t diverse enough.

To give yourself the best chance of resolving a problem, gain insight from a wide range of sources. Collaborate with key stakeholders, customers and on-the-ground employees to learn how the problem affects them and whether they have found workarounds or solutions.

To paint the broadest picture, don’t limit your problem-solving team to a specific archetype. Try to include everyone, from the chief executive to the office janitor.

If you’re working with a small team, try the Flip It! problem-solving methodology to view the issue from a fresh angle. ‍

4. Make your office space conducive to problem-solving

The environment in which your host your brainstorming sessions should maximise creativity . When your team members trust each other and feel relaxed, they’re more likely to come up with innovative ideas and solutions to a problem.

Here are a few ways to get your employees’ creative juices flowing:

Play team-building games that maximise trust and build interpersonal relationships
Improve your team’s problem-solving skills with games that encourage critical thinking
Redesign the office with comfortable furniture and collaborative spaces
Boost job satisfaction by creating a positive work-life balance
Improve collaborative skills and learn to resolve conflicts

World Café is a problem-solving method that creates a casual environment conducive to creative thinking.

Keep reading to learn more about how World Café can help your team solve complex organisational problems. ‍

5. Use problem-solving methodologies to guide the process

Because problem-solving is a creative process, it can be hard to keep it on track. As more ideas get banded around, conflicts can arise that derail the session.

That’s why problem-solving methodologies are so helpful. They offer you proven problem-solving frameworks to guide your group sessions and keep them on track.

The Six Thinking Hats problem-solving method is a popular technique that guides the process and helps your team analyse a problem from all angles.

We’re going to take a look at our favourite problem-solving methodologies in the next section of this article, XY Tried and tested problem-solving methodologies. ‍

6. Use analogies to solve complex problems

Sometimes, solving a different problem can help you uncover solutions to another problem!

By stripping back a complex issue and framing it as a simplified analogy , you approach a problem from a different angle, enabling you to come up with alternative ideas.

After solving practice problems, your team might be more aptly equipped to solve real-world issues.

However, coming up with an analogy that reflects your issue can be difficult, so don’t worry if this technique doesn’t work for you.

The Speed Boat diagram is a visual tool that helps your employees view existing challenges as anchors holding back a boat which represents your end goals. By assigning a “weight” to each anchor, your team can prioritise which issues to tackle first. ‍

7. Establish clear constraints

Constraints make a big problem more approachable.

Before you tackle a problem, establish clear boundaries and codes of conduct for the session. This allows your team to focus on the current issue without becoming distracted or veering off on a tangent.

In an article published in the Harvard Business Review, authors Oguz A. Acar, Murat Tarakci, and Daan van Knippenberg wrote, “Constraints … provide focus and a creative challenge that motivates people to search for and connect information from different sources to generate novel ideas for new products, services, or business processes.” (Why Constraints Are Good for Innovation, 2019)

Lightning Decision Jam is a prime example of how constraints can assist the creative process. Here, your team are given strict time constraints and isn’t permitted to discuss ideas until the end. ‍

8. Dislodge preconceived ideas

Humans are creatures of habit.

We defer to strategies that have produced positive results in the past. This is typically beneficial because recalling our previous successes means we don’t need to constantly re-learn similar tasks.

But when it comes to problem-solving, this way of thinking can trip us up. We become fixated on a solution that worked in the past, but when this fails we’re dismayed and left wondering what to do next.

To resolve problems effectively, your employees need to escape the precincts of their imaginations. This helps to eliminate functional fixedness—the belief that an item serves only its predefined function.

Alternative Application is an icebreaker game that encourages employees to think outside the box by coming up with different uses for everyday objects. Try this at your next meeting or team-building event and watch your team tap into their creativity. ‍

9. Level the playing field

Having a diverse group of employees at your brainstorming sessions is a good idea, but there’s one problem: the extroverted members of your team will be more vocal than the introverts.

To ensure you’re gaining insight from every member of your team, you need to give your quieter employees equal opportunities to contribute by eliminating personality biases.

Read more: What icebreaker games and questions work best for introverts?

The obvious solution, then, is to “silence” the louder participants (it’s not as sinister as it sounds, promise)—all you have to do is ban your team from debating suggestions during the ideation process.

The Lightning Decision Jam methodology gives your employees equal opportunities to contribute because much of the problem-solving process is carried out in silence. ‍

10. Take a break from the problem

Have you ever noticed how the best ideas seem to come when you’re not actively working on a problem? You may have spent hours slumped over your desk hashing out a solution, only for the “eureka!” moment to come when you’re walking your dog or taking a shower.

In James Webb Young’s book, A Technique for Producing Ideas , phase three of the process is “stepping away from the problem.” Young proclaims that after putting in the hard work, the information needs to ferment in the mind before any plausible ideas come to you.

So next time you’re in a meeting with your team trying to solve a problem, don’t panic if you don’t uncover groundbreaking ideas there and then. Allow everybody to mull over what they’ve learned, then reconvene at a later date.

The Creativity Dice methodology is a quick-fire brainstorming game that allows your team to incubate ideas while concentrating on another. ‍

11. Limit feedback sessions

The way your team delivers feedback at the end of a successful brainstorming session is critical. Left unsupervised, excessive feedback can undo all of your hard work.

Therefore, it’s wise to put a cap on the amount of feedback your team can provide. One great way of doing this is by using the One Breath Feedback technique.

By limiting your employees to one breath, they’re taught to be concise with their final comments.

16 Tried and tested problem-solving methodologies

Problem-solving methodologies keep your brainstorming session on track and encourage your team to consider all angles of the issue.

Countless methods have wiggled their way into the world of business, each one with a unique strategy and end goal.

Here are 12 of our favourite problem-solving methodologies that will help you find the best-fit solution to your troubles. ‍

12. Six Thinking Hats

Six Thinking Hats is a methodical problem-solving framework that helps your group consider all possible problems, causes, solutions and repercussions by assigning a different coloured hat to each stage of the problem-solving process.

The roles of each hat are as follows:

Blue Hat (Control): This hat controls the session and dictates the order in which the hats will be worn. When wearing the Blue Hat, your group will observe possible solutions, draw conclusions and define a plan of action.
Green Hat (Idea Generation): The Green Hat signifies creativity. At this stage of the methodology, your team will focus their efforts on generating ideas, imagining solutions and considering alternatives.
Red Hat (Intuition and Feelings): It’s time for your employees to communicate their feelings. Here, your team listen to their guts and convey their emotional impulses without justification.
Yellow Hat (Benefits and Values): What are the merits of each idea that has been put forward thus far? What positive impacts could they have?
Black or Grey Hat (Caution): What are the potential risks or shortcomings of each idea? What negative impacts could result from implicating each idea?
White Hat (Information and Data): While wearing The White Hat, your team must determine what information is needed and from where it can be obtained.

For Six Thinking Hats to work effectively, ensure your team acts within the confines of each role.

While wearing The Yellow Hat, for example, your team should only discuss the positives . Any negative implications should be left for the Black or Grey hat.

Note: Feel free to alter the hat colours to align with your cultural context. ‍

13. Lightning Decision Jam (LDJ)

Lightning Decision Jam is a nine-stage problem-solving process designed to uncover a variety of perspectives while keeping the session on track.

The process starts by defining a general topic like the internal design process, interdepartmental communication, the sales funnel, etc.

Then, armed with pens and post-it notes, your team will work through the nine stages in the following order:

Write problems (7 minutes)
Present problems (4 minutes/person)
Select problems (6 minutes)
Reframe the problems (6 minutes)
Offer solutions (7 minutes)
Vote on solutions (10 minutes)
Prioritise solutions (30 seconds)
Decide what to execute (10 minutes)
Create task lists (5 minutes)

The philosophy behind LDJ is that of constraint. By limiting discussion, employees can focus on compiling ideas and coming to democratic decisions that benefit the company without being distracted or going off on a tangent. ‍

14. The 5 Why’s

Root Cause Analysis (RCA) is the process of unearthing a problem and finding the underlying cause. To help you through this process, you can use The 5 Why’s methodology.

The idea is to ask why you’re experiencing a problem, reframe the problem based on the answer, and then ask “ why?” again. If you do this five times , you should come pretty close to the root of your original challenge.

While this might not be a comprehensive end-to-end methodology, it certainly helps you to pin down your core challenges. ‍

15. World Café

If you’ve had enough of uninspiring corporate boardrooms, World Café is the solution.

This problem-solving strategy facilitates casual conversations around given topics, enabling players to speak more openly about their grievances without the pressure of a large group.

Here’s how to do it:

Create a cosy cafe-style setting (try to have at least five or six chairs per table).
As a group, decide on a core problem and mark this as the session topic.
Divide your group into smaller teams by arranging five or six players at a table.
Assign each group a question that pertains to the session topic, or decide on one question for all groups to discuss at once.
Give the groups about 20 minutes to casually talk over each question.
Repeat this with about three or four different questions, making sure to write down key insights from each group.
Share the insights with the whole group.

World Café is a useful way of uncovering hidden causes and pitfalls by having multiple simultaneous conversations about a given topic. ‍

16. Discovery and Action Dialogue (DAD)

Discovery and Actions Dialogues are a collaborative method for employees to share and adopt personal behaviours in response to a problem.

This crowdsourcing approach provides insight into how a problem affects individuals throughout your company and whether some are better equipped than others.

A DAD session is guided by a facilitator who asks seven open-ended questions in succession. Each person is given equal time to participate while a recorder takes down notes and valuable insights.

This is a particularly effective method for uncovering preexisting ideas, behaviours and solutions from the people who face problems daily. ‍

17. Design Sprint 2.0

The Design Sprint 2.0 model by Jake Knapp helps your team to focus on finding, developing measuring a solution within four days . Because theorising is all well and good, but sometimes you can learn more by getting an idea off the ground and observing how it plays out in the real world.

Here’s the basic problem-solving framework:

Day 1: Map out or sketch possible solutions
Day 2: Choose the best solutions and storyboard your strategy going forward
Day 3: Create a living, breathing prototype
Day 4: Test and record how it performs in the real world

This technique is great for testing the viability of new products or expanding and fixing the features of an existing product. ‍

18. Open Space Technology

Open Space Technology is a method for large groups to create a problem-solving agenda around a central theme. It works best when your group is comprised of subject-matter experts and experienced individuals with a sufficient stake in the problem.

Open Space Technology works like this:

Establish a core theme for your team to centralise their efforts.
Ask the participants to consider their approach and write it on a post-it note.
Everybody writes a time and place for discussion on their note and sticks it to the wall.
The group is then invited to join the sessions that most interest them.
Everybody joins and contributes to their chosen sessions
Any significant insights and outcomes are recorded and presented to the group.

This methodology grants autonomy to your team and encourages them to take ownership of the problem-solving process. ‍

19. Round-Robin Brainstorming Technique

While not an end-to-end problem-solving methodology, the Round-Robin Brainstorming Technique is an effective way of squeezing every last ounce of creativity from your ideation sessions.

Here’s how it works:

Decide on a problem that needs to be solved
Sitting in a circle, give each employee a chance to offer an idea
Have somebody write down each idea as they come up
Participants can pass if they don’t have anything to contribute
The brainstorming session ends once everybody has passed

Once you’ve compiled a long list of ideas, it’s up to you how you move forward. You could, for example, borrow techniques from other methodologies, such as the “vote on solutions” phase of the Lightning Decision Jam. ‍

20. Failure Modes and Effects Analysis (FMEA)

Failure Modes and Effects Analysis is a method for preventing and mitigating problems within your business processes.

This technique starts by examining the process in question and asking, “What could go wrong?” From here, your team starts to brainstorm a list of potential failures.

Then, going through the list one by one, ask your participants, “Why would this failure happen?”

Once you’ve answered this question for each list item, ask yourselves, “What would the consequences be of this failure?”

This proactive method focuses on prevention rather than treatment. Instead of waiting for a problem to occur and reacting, you’re actively searching for future shortcomings. ‍

21. Flip It!

The Flip It! Methodology teaches your team to view their concerns in a different light and frame them instead as catalysts for positive change.

The game works like this:

Select a topic your employees are likely to be concerned about, like market demand for your product or friction between departments.
Give each participant a pile of sticky notes and ask them to write down all their fears about the topic.
Take the fears and stick them to an area of the wall marked “fears.”
Then, encourage your team to look at these fears and ask them to reframe them as “hope” by writing new statements on different sticky notes.
Take these “hope” statements and stick them to an area of the wall marked “hope.”
Discuss the statements, then ask them to vote on the areas they feel they can start to take action on. They can do this by drawing a dot on the corner of the sticky note.
Move the notes with the most votes to a new area of the wall marked “traction.”
Discuss the most popular statements as a group and brainstorm actionable items related to each.
Write down the actions that need to be made and discuss them again as a group.

This brainstorming approach teaches your employees the danger of engrained thinking and helps them to reframe their fears as opportunities. ‍

22. The Creativity Dice

The Creativity Dice teaches your team to incubate ideas as they focus on different aspects of a problem. As we mentioned earlier in the article, giving ideas time to mature can be a highly effective problem-solving strategy. Here’s how the game works:

Choose a topic to focus on, It can be as specific or open-ended as you like. Write this down as a word or sentence. Roll the die, start a timer of three minutes and start writing down ideas within the confines of what that number resembles. The roles of each number are as follows:

Specification: Write down goals you want to achieve.
Investigation: Write down existing factual information you know about the topic.
Ideation: Write down creative or practical ideas related to the topic.
Incubation: Do something else unrelated to the problem.
Iteration: Look at what you’ve already written and come up with related ideas (roll again if you didn’t write anything yet). ‍
Integration: Look at everything you have written and try to create something cohesive from your ideas like a potential new product or actionable next step.

Once you’ve finished the activity, review your findings and decide what you want to take with you. ‍

23. SWOT Analysis

The SWOT Analysis is a long-standing method for analysing the current state of your business and considering how this affects the desired end state.

The basic idea is this:

Before the meeting, come up with a “Desired end state” and draw a picture that represents this on a flipchart or whiteboard.
Divide a large piece of paper into quadrants marked “Strengths”, “Weaknesses”, “Opportunities” and “Threats.”
Starting with “Strengths”, work through the quadrants, coming up with ideas that relate to the desired end state.
Ask your team to vote for the statements or ideas of each category that they feel are most relevant to the desired end state.
As a group, discuss the implications that these statements have on the desired end state. Spark debate by asking thought-provoking and open-ended questions.

The SWOT Analysis is an intuitive method for understanding which parts of your business could be affecting your long-term goals. ‍

24. The Journalistic Six

When learning to cover every aspect of a story, journalists are taught to ask themselves six essential questions:

Now, this approach has been adopted by organisations to help understand every angle of a problem. All you need is a clear focus question, then you can start working through the six questions with your team until you have a 360-degree view of what has, can and needs to be done. ‍

25. Gamestorming

Gamestorming is a one-stop creative-thinking framework that uses various games to help your team come up with innovative ideas.

Originally published as a book 10 years ago, Gamestorming contained a selection of creative games used by Silicon Valley’s top-performing businesses to develop groundbreaking products and services.

This collection of resources, plucked from the minds of founders and CEOs like Jeff Bezos and Steve Jobs, allows you to tap into the potentially genius ideas lying dormant in the minds of your employees. ‍

26. Four-Step Sketch

The Four-Step Sketch is a visual brainstorming that provides an alternative to traditional discussion-based ideation techniques .

This methodology requires prior discussion to clarify the purpose of the activity. Imagine you’re on a startup retreat , for example, and your team is taking part in a design sprint or hackathon.

Once you’ve brainstormed a list of ideas with your team, participants can look at the suggestions and take down any relevant notes. They then take these notes and turn them into rough sketches that resemble the idea.

Then, as a warm-up, give each participant eight minutes to produce eight alternative sketches (eight minutes per sketch) of the idea. These ideas are not to be shared with the group.

Finally, participants create new sketches based on their favourite ideas and share them with the group. The group can then vote on the ideas they think offer the best solution. ‍

27. 15% Solutions

15% Solutions is a problem-solving strategy for motivating and inspiring your employees. By encouraging your team to gain small victories, you pave the way for bigger changes.

First, ask your participants to think about things they can personally do within the confines of their role.

Then, arrange your team into small groups of three to four and give them time to share their ideas and consult with each other.

This simple problem-solving process removes negativity and powerlessness and teaches your team to take responsibility for change.

9 Problem-solving tools for gathering and selecting ideas

Problem-solving tools support your meeting with easy-to-use graphs, visualisations and techniques.

By implementing a problem-solving tool, you break the cycle of mundane verbal discussion, enabling you to maintain engagement throughout the session. ‍

28. Fishbone Diagram

The Fishbone Diagram (otherwise known as the Ishikawa Diagram or Cause and Effect Diagram), is a tool for identifying the leading causes of a problem. You can then consolidate these causes into a comprehensive “Problem Statement.”

The term “Fishbone Diagram” is derived from the diagram’s structure. The problem itself forms the tail, possible causes radiate from the sides to form the fish skeleton while the final “Problem Statement” appears as the “head” of the fish.

Example: A fast-food chain is investigating the declining quality of their food. As the team brainstorms potential causes, they come up with reasons like “poorly trained personnel”, “lack of quality control”, and “incorrect quantity of spices.” Together with other causes, the group summarises that these problems lead to “bad burgers.” They write this as the Problem Statement and set about eliminating the main contributing factors. ‍

29. The Problem Tree

A Problem Tree is a useful tool for assessing the importance or relevance of challenges concerning the core topic. If you’re launching a new product, for example, gather your team and brainstorm the current issues, roadblocks and bottlenecks that are hindering the process.

Then, work together to decide which of these are most pressing. Place the most relevant issues closer to the core topic and less relevant issues farther away. ‍

30. SQUID Diagram

The Squid Diagram is an easy-to-use tool that charts the progress of ideas and business developments as they unfold. Your SQUID Diagram can remain on a wall for your team to add to over time.

Write down a core theme on a sticky note such as “customer service” or “Innovation”—this will be the “head” of your SQUID.
Hand two sets of different coloured sticky notes to your participants and choose one colour to represent “questions” and the other to represent “answers.”
Ask your team to write down questions pertaining to the success of the main topic. In the case of “Innovation,” your team might write things like “How can we improve collaboration between key stakeholders?”
Then, using the other coloured sticky notes, ask your team to write down possible answers to these questions. In the example above, this might be “Invest in open innovation software.”
Over time, you’ll develop a spawling SQUID Diagram that reflects the creative problem-solving process. ‍

31. The Speed Boat

The Speed Boat Diagram is a visual metaphor used to help your team identify and solve problems in the way of your goals.

Here’s how it works:

Draw a picture of a boat and name it after the core objective.
With your team, brainstorm things that are slowing progress and draw each one as an anchor beneath the boat.
Discuss possible solutions to each problem on the diagram.

This is an easy-to-use tool that sparks creative solutions. If you like, your team can assign a “weight” to each anchor which determines the impact each problem has on the end goal. ‍

32. The LEGO Challenge

LEGO is an excellent creative-thinking and problem-solving tool used regularly by event facilitators to help teams overcome challenges.

In our article 5 and 10-minute Team-Building Activities , we introduce Sneak a Peek —a collaborative team-building game that develops communication and leadership skills. ‍

33. The Three W’s: What? So What? Now What?

Teams aren’t always aligned when it comes to their understanding of a problem. While the problem remains the same for everyone, they might have differing opinions as to how it occurred at the implications it had.

Asking “ What? So What? Now What?” Helps you to understand different perspectives around a problem.

It goes like this:

Alone or in small groups, ask your employees to consider and write What happened. This should take between five and 10 minutes.
Then ask So What? What occurred because of this? Why was what happened important? What might happen if this issue is left unresolved?
Finally, ask your team Now What? What might be a solution to the problem? What actions do you need to take to avoid this happening again?

This approach helps your team understand how problems affect individuals in different ways and uncovers a variety of ways to overcome them. ‍

34. Now-How-Wow Matrix

Gathering ideas is easy—but selecting the best ones? That’s a different story.

If you’ve got a bunch of ideas, try the Now-How-Wow Matrix to help you identify which ones you should implement now and which ones should wait until later.

Simply draw a two-axis graph with “implementation difficulty” on the Y axis and “idea originality” on the X axis. Divide this graph into quadrants and write “Now!” in the bottom left panel, “Wow!” in the bottom right panel, and “How?” in the top right panel. You can leave the top left panel blank.

Then, take your ideas and plot them on the graph depending on their implementation difficulty and level of originality.

By the end, you’ll have a clearer picture of which ideas to ignore, which ones to implement now, and which ones to add to the pipeline for the future. ‍

35. Impact-Effort Matrix

The Impact-Effort Matrix is a variation of the Now-How-Wow Matrix where the Y axis is marked “Impact” and the X axis is marked “Effort.”

Then, divide the graph into quadrants and plot your ideas.

Top left section = Excellent, implement immediately
Top right section = Risky, but worth a try
Bottom left section = Low risk, but potentially ineffective
Bottom right section = Bad idea, ignore

The Impact-Effort Matrix is a simple way for your team to weigh the benefits of an idea against the amount of investment required. ‍

36. Dot Voting

Once you’ve gathered a substantial list of ideas from your employees, you need to sort the good from the bad.

Dot voting is a simple tool used by problem-solving facilitators as a fast and effective way for large groups to vote on their favourite ideas . You’ll have seen this method used in problem-solving methods like Flip It! and Lightning Decision Jam .

Participants write their ideas on sticky notes and stick them to the wall or a flipchart.
When asked, participants draw a small dot on the corner of the idea they like the most.
Participants can be given as many votes as necessary.
When voting ends, arrange the notes from “most popular” to “least popular.”

This provides an easy-to-use visual representation of the best and worst ideas put forward by your team.

Give your problems the attention they deserve at an offsite retreat

While working from home or at the office, your team is often too caught up in daily tasks to take on complex problems.

By escaping the office and uniting at an offsite location, you can craft a purposeful agenda of team-building activities and problem-solving sessions. This special time away from the office can prove invaluable when it comes to keeping your business on track.

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A guide to problem framing: best practices & templates

Two people looking at a laptop and having a conversation

When creating solutions and products, it’s critical to correctly frame the problem you’re attempting to solve.

Remember the Google Glass? What about the Segway? Taken on their own account, these were groundbreaking products with cutting-edge technology. No one had seen anything like them before. Yet they failed for a simple reason: They were solutions in search of a problem.

Now imagine if their creators had spent more time trying to understand the problem their customers faced. Imagine they had actually tried to identify a real challenge and properly define how it could be addressed. The result would have likely been closer to a Tesla or even an iPhone — at the very least, we wouldn’t be talking about them in nearly the same way.

This shows just how important it is to frame a problem before trying to solve it. Let’s go over in detail how you can apply problem framing to your next project.

What is problem framing?

Problem framing is a process for analyzing, understanding, and ultimately defining a problem or challenge in order to develop an effective solution. While it can be done on an individual level, it is typically practiced across teams so that you can achieve alignment and work more cohesively toward an agreed-upon outcome.

In short, problem framing is an opportunity to take a step back, assess the landscape of your problem and break down its root causes, then focus on a solution that is most likely to lead to the outcome you want.

Why problem framing is critical for better outcomes

Framing the problem is important because it sets the direction and scope of the solution design process, ensuring that efforts are focused on addressing the core issues. It helps avoid wasted time and resources on irrelevant or superficial solutions.

Good design and effective iteration can help improve a product, but they won’t tell you if you’re addressing the right problem — only problem framing can do that. Here are some ways this process can ensure your solution achieves better results:

It provides clarity. Whether your team isn’t sure what problem they’re facing or can’t reach an agreement, taking the time to break the problem apart can ensure everyone understands it. And that is crucial to developing a solution that actually works.
It narrows the scope. With a better understanding of the problem, you can eliminate everything but the most essential aspects that need to be addressed. That means only addressing underlying issues instead of just their symptoms.
It achieves alignment. By having a clear definition in hand, you can ensure that all team members and stakeholders share a common understanding of the problem and how to address it. This will help reduce misunderstandings and conflict.
It increases efficiency. While some may think problem framing is an extra step, it can actually help keep you from wasting resources and time by preventing you from focusing on irrelevant or ineffective solutions.

How to frame a problem

Whether you think you have a good idea of your problem or have no clue where to begin, learning how to properly frame it can give you new insights into how to solve it. Here’s a process for doing just that.

Create a problem statement

A good first step is to make sure that everyone can agree on what exactly the problem is. This is a great opportunity to write out a problem statement, or a clear and concise explanation of the problem or challenge you intend to solve.

The goal behind writing a problem statement is to describe the problem as comprehensively as possible, while also spurring your team into action. If your team can’t even reach an agreement on what the problem is, then try to discuss the problem from multiple angles to ensure you’re incorporating multiple perspectives. This will help you achieve alignment.

Even when everyone already has a good idea of the problem, this step can still help ensure complete clarity by taking the simple but effective step of making your team write it down. Learn more about what goes into creating a good problem statement in our full guide .

Identify and understand the problem's root cause

Although identifying your problem’s root cause or causes should be a part of writing out your problem statement , it’s important enough to deserve a discussion on its own. After all, if you are just focusing on the symptoms of your problem, then any solution you develop will ultimately fail.

The key to uncovering a problem’s root cause is to ask why it is happening, rather than what. Typically, there will be multiple answers to this. One way to start organizing and categorizing these different causes and their various effects is by using a fishbone diagram . Start out by writing down your problem, then come up with different categories that could be contributing to it. From there, start brainstorming different causes.

Once you have everything laid out cleanly, you can vote on what you think are the most significant contributors — or, if necessary, even rethink the problem itself.

Empathize with the end-users of the problem

Once you have a good idea of your problem and can articulate it, you also need to ensure that this is a problem your stakeholders face. That means being able to properly understand and empathize with their needs.

To accomplish this, consider organizing an empathy mapping session . Start out by gathering a diverse range of stakeholders in order to reduce biases and leverage different perspectives. Ask them to share their opinion regarding the product, service, or situation, encouraging open-ended responses. As you gather this feedback, divide it into four different categories: thoughts, feelings, actions, and observations —then start looking for areas of improvement. This is where your highest priority problems will be.

The act of interviewing your stakeholders, writing down their responses, and organizing them across different categories should give you a much deeper understanding of the user’s point of view and their needs.

Frame the problem to brainstorm solutions

With your user research in hand and your problem statement honed, it’s time to start framing the problem in order to come up with effective solutions.

During this process, your goal should be to get your team to rethink the problem in creative ways to help you find new ways to solve it. While there are many ways to do this, the Mural problem framing template provides a simple three-step procedure that can help you explore your challenge in new ways to get the right answer. Each person must transform the problem into four different questions that invite deeper, more nuanced thinking. These questions are then discussed, voted on, and narrowed down to the most promising, providing you with a clear frame for future work.

Tips to effectively frame the problem

Thinking through problems in new ways and effectively framing them involves outside-the-box creativity , a healthy dose of empathy, and a willingness to take risks. This can be intimidating for some people. So here are some quick tips to help make this process more effective.

Start with asynchronous collaboration

Focused sessions are the most effective sessions — and what you probably want to focus on the most while problem framing is coming up with possible solutions. That’s why encouraging stakeholders, end-users, and other participants to start collaborating asynchronously on ways to reframe and rethink your problem can be so beneficial.

Plus, getting participants to work on their own can help avoid groupthink, or the tendency to come up with ideas people will agree with rather than ideas that are actually useful. This will ultimately lead to better decisions and more effective solutions.

In-person sessions aren’t the only way to collaborate! Learn how async collaboration can solve your meeting problem .

Map out the context of the problem

Helping your team understand the drivers and impacts of the issue you are trying to solve will help them gain a more nuanced view on why this issue exists, as well as how best to solve it. This is why bringing in end users and empathizing with their needs is so important — but there’s no reason you have to stop there. By creating a customer journey map , you can identify vital pain points in the customer experience, locate areas for improvement, and create solutions that are personalized to the customer.

Mural offers several customer journey templates to get you started. For instance, our map template lets you break down the journey across five separate components for a more granular view, while our experience diagramming template is great for examining individual customer’s experiences.

Don't be afraid to dig deeper with stakeholders and the end-users

Fully understanding an issue and how it affects your stakeholders can take time. For some, this can be frustrating. After all, your objective is to come up with a solution, which will likely require a fair amount of design and iteration itself.

Try to resist the urge to jump ahead. Instead, embrace the problem-framing process as much as possible by digging in deep with your stakeholders and end users. Really try to explore and understand why their problem exists in the first place so you can find a better potential solution.

Even if all this takes extra time, just remember that it’s better to properly identify and understand the problem you aim to solve rather than solving the wrong problem.

Hold a vote to prioritize solutions

If you’re fortunate, you’ll come to the end of your problem framing session with a wealth of possible solutions to choose from. But this can also be overwhelming. Which is the best course of action? How should you decide?

When faced with these questions, you could try creating a prioritization matrix . This simple tool allows you to quickly identify and weigh the most important factors when making a decision. These could include factors like risk, costs, benefits, and stakeholder interests. You can then place them on a matrix according to the criteria of your choosing, such as potential difficulty and potential impact.

Once you’ve narrowed down your solutions, you could hold a vote to further prioritize what you’ll work on next. Lucky for you, Mural comes with a built-in voting feature that makes this easy.

Hold better problem-framing sessions

Often used in the design thinking process , problem framing is an essential step for understanding the issues you need to solve and uncovering creative new solutions for addressing them. And it doesn’t have to be limited to the beginning of projects. As your projects change and evolve, problem framing can be a useful process for realigning your team and making sure they are staying focused on what matters most.

But you’re not doing it on your own. With its array of tools, templates, and features, the Mural platform is designed to help you at every step of the process: from the first sticky note, to the project’s last step in execution.

Start designing with digital whiteboard platform or go ahead and dive into our library of templates . And don’t forget to let us know what you come up with!

Looking to level-up client engagements? Learn how to make client collaboration more engaging and personalized with this cheat-sheet.

Frequently asked questions on problem framing

What is the main focus of problem framing.

The main focus of problem framing is to define the problem accurately, understand its underlying causes, and identify its broader implications. It aims to provide a clear and comprehensive view of the problem, enabling teams to develop targeted and effective solutions.

What is the difference between problem statements and problem framing?

Problem statements simply state the issue at hand, while problem framing goes a step further by providing context, boundaries, and a deeper understanding of the problem's root causes and impact.

What are the main benefits of problem framing?

The benefits of problem framing include clear direction for the project, targeted and impactful solutions, user-centric design, fostering innovation and creativity, and improved problem-solving and decision-making. It ensures that organizations solve the right problems and achieve more successful outcomes.

About the authors

David Young

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PDCA and OODA: Which is the Better Problem-Solving Method?

Author: Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

Choosing the right problem-solving framework is a pivotal decision that can significantly influence the efficiency and effectiveness of any organization. With a multitude of methodologies out there, PDCA (Plan-Do-Check-Act) and OODA (Observe-Orient-Decide-Act) stand out as tried-and-true approaches to tackling complex challenges.

While PDCA has its roots in quality control and continuous improvement, OODA originated in military strategy and has been adapted for rapid decision-making across various fields. This article aims to dissect both frameworks to help you discern which is better suited for your problem-solving needs. We’ll delve into the origins, key steps, and practical applications of each method, analyze their strengths and weaknesses, and even look at real-world case studies. By the end, you’ll be equipped to make an informed choice between PDCA and OODA.

Understanding PDCA

Origin of pdca.

The PDCA cycle, often referred to as the Deming Wheel or Shewhart Cycle, is a four-step model for continuous improvement and problem-solving. Conceived by Walter Shewhart, an American statistician, and later popularized by W. Edwards Deming, the cycle has its roots in quality control during the manufacturing processes of the mid-20th century. The framework has since transcended its initial context, becoming a universal model applied in various industries and sectors for quality management and improvement.

Four Steps Explained

Plan : The first step involves identifying a problem or a potential improvement area and then planning a change. This phase typically encompasses setting objectives, determining the resources required, and devising the metrics that will gauge success or failure.
Do : This step entails implementing the planned change on a small scale as a pilot test. It’s crucial to document all changes and data collected so that the information can be analyzed later.
Check : Here, the data collected during the ‘Do’ phase is analyzed. The purpose is to evaluate whether the change led to improvement and met the objectives set during the ‘Plan’ phase.
Act : In the final step, if the change is deemed successful, it is implemented on a broader scale. If not, the cycle begins anew, aiming to refine the plan with the insights gained.

Industries Where PDCA is Commonly Used

Given its origins in manufacturing, PDCA is most commonly used in this sector for quality control and process improvement. However, the versatility of the PDCA cycle has made it applicable in several other industries as well, including:

Software Development
Public Sector
FMCG (Fast-Moving Consumer Goods)
Logistics and Warehousing

Strengths and Weaknesses

Simplicity : The PDCA cycle is straightforward, easy to understand, and implement.
Flexibility : It can be applied to a wide array of problems and industries.
Data-Driven : The methodology encourages data collection for informed decision-making.
Continuous Improvement : Being cyclical, it fosters a culture of ongoing improvement.
Limited Scope : PDCA may not be ideal for solving complex, multifaceted problems.
Resource Intensive : It often requires thorough planning and data collection, demanding more resources than some other rapid models.
Repetitiveness : If not done carefully, the cycle can become an endless loop without resolution.

By understanding PDCA in depth, you can better evaluate its utility for your specific needs, especially when comparing it to other methodologies like OODA. This framework has its merits and limitations, making it crucial to understand when and where it can best be applied.

Understanding OODA

Origin of ooda.

The OODA Loop, which stands for Observe, Orient, Decide, and Act, was developed by U.S. Air Force Colonel John Boyd. Originally, the framework was used for combat operations processes to make faster and more effective decisions in fluid, high-stakes environments. Boyd’s concept has transcended its military roots and is now utilized in various settings, including business and crisis management, to aid in rapid decision-making and adaptive strategies.

Observe : This is the initial phase where you collect raw data from your environment. It involves actively scanning for information that could impact your decisions. This could be market trends, customer feedback, or any other form of actionable data.
Orient : In this phase, you process the information gathered. You use your existing knowledge, cultural background, and prior experiences to interpret the raw data. This is the stage where contextual analysis occurs.
Decide : Based on the orientation phase, you formulate a set of possible actions or decisions. You weigh the pros and cons and select the best course of action for your specific situation.
Act : Finally, you implement the decision made. Unlike PDCA, where the ‘Do’ phase often involves a small-scale test, OODA’s ‘Act’ is usually swift and large-scale, aiming for immediate results.

Industries Where OODA is Commonly Applied

While OODA originated in the military, its principles of rapid, adaptive decision-making have been adopted in several other sectors, such as:

Emergency Services and Crisis Management
Financial Trading
Cybersecurity
Competitive Sports
Strategic Business Management
Speed : OODA is designed for rapid decision-making, making it suitable for volatile environments.
Adaptability : The framework is inherently adaptable, allowing for quick adjustments in strategy.
Situation Awareness : The ‘Observe’ and ‘Orient’ phases ensure a strong awareness of environmental variables.
Immediate Action : Allows for direct, often large-scale, action based on situational awareness.
Risk of Hasty Decisions : The speed of the cycle can sometimes lead to hastily made, less-than-optimal decisions.
Context-Specific : OODA may not be as effective for problems that require a detailed, long-term planning approach.
Resource Intensive : Despite its speed, effective observation and orientation can be resource-intensive.
May Lack Depth : Due to its emphasis on speed, there may be insufficient time for in-depth analysis or testing.

Understanding the intricacies of the OODA Loop will empower you to decide when it is the most appropriate methodology to employ. Like PDCA, OODA has its own set of pros and cons that make it suitable for certain scenarios and not for others.

Key Differences Between PDCA and OODA

Understanding the distinctions between PDCA and OODA is essential for choosing the right framework for your needs. Both methodologies have their unique strengths and weaknesses, but they differ in several key aspects, from speed to suitability for various industries. Let’s dive into these differences.

Speed of Implementation

PDCA : Generally, PDCA is more deliberate and takes a longer time for implementation. This is mainly because of its emphasis on planning and checking, which includes data collection, analysis, and pilot testing.
OODA : Designed for rapid decision-making, the OODA Loop focuses on quick, large-scale implementation, often bypassing smaller tests or in-depth analysis for immediate action.

Flexibility and Adaptability

PDCA : While PDCA is flexible and can be applied to a wide range of industries, its structured approach means that changes during implementation are more difficult and time-consuming.
OODA : The OODA Loop is inherently adaptive, allowing for quick pivots and strategy shifts. It’s designed to deal with rapidly changing, fluid environments.

Complexity of Problems Addressed

PDCA : This methodology is generally better suited for problems that can be defined clearly and that require a structured approach to solution-building. However, it may struggle with extremely complex, adaptive challenges.
OODA : OODA excels in high-stakes, complex situations where decisions need to be made quickly and adaptively. It’s particularly effective when the problem parameters are constantly changing.

Required Resources

PDCA : PDCA often requires more resources for planning, data collection, and analysis. The iterative nature of the cycle also implies that multiple rounds may be needed, each consuming additional resources.
OODA : Although speedy, OODA still requires significant resources for the observation and orientation phases to be effective. It may require specialized knowledge or technologies to gather and process real-time data.

Suitability for Various Industries

PDCA : Originating from manufacturing and quality control, PDCA is commonly used in sectors that value process optimization and continuous improvement, such as healthcare, education, and logistics.
OODA : Initially designed for military applications, OODA has been adapted for use in industries that require rapid response and adaptability, such as emergency services, financial trading, and cybersecurity.

In sum, PDCA and OODA offer contrasting approaches to problem-solving and decision-making. PDCA is a methodical, data-driven framework suitable for well-defined problems requiring detailed analysis. In contrast, OODA is tailored for complex, rapidly changing environments where quick, adaptive decisions are crucial.

Case Studies

To truly appreciate the applicability and effectiveness of PDCA and OODA, it’s essential to examine real-world cases where these methodologies have been successfully employed. These examples not only provide a tangible context but also highlight the unique benefits and limitations of each framework.

A Real-World Example of PDCA in Action

Toyota production system.

Toyota, a giant in the automotive industry, employs PDCA through its Toyota Production System. The method is applied to optimize various processes, from supply chain management to quality control.

Plan : Toyota identifies a problem area, such as a bottleneck in the assembly line, and develops a plan to eliminate it.
Do : The plan is then implemented on a small scale, perhaps in one section of the assembly line, and data is collected for analysis.
Check : Toyota rigorously checks whether the changes yield the desired improvements in efficiency.
Act : If successful, the change is then rolled out across other assembly lines; otherwise, the cycle restarts.

A Real-World Example of OODA in Action

Emergency response during natural disasters.

The OODA loop has been used effectively in emergency management, specifically during natural disasters like hurricanes and wildfires.

Observe : Real-time data on weather conditions, affected populations, and resource availability is collected.
Orient : The data is then processed to understand the gravity and extent of the disaster.
Decide : Decision-makers identify key actions, such as evacuations or resource deployment, based on the available information.
Act : Emergency services act swiftly, often within hours, to mitigate the disaster’s impact.

Comparative Analysis

Speed of Decision-making : The emergency response case showcases how OODA is built for rapid, real-time decisions, whereas Toyota’s application of PDCA demonstrates a slower, more meticulous approach.
Complexity : While both cases involved complex problems, the PDCA method was employed for a well-defined issue (assembly line efficiency), whereas OODA was used for a more chaotic, rapidly evolving situation (natural disaster).
Resource Requirements : Both methodologies require substantial resources, but PDCA usually involves a longer period of planning and data collection. OODA, although quick, requires real-time data gathering and processing capabilities.
Adaptability : OODA’s real-world application shows a higher level of adaptability to rapidly changing situations. In contrast, PDCA, as applied by Toyota, indicates a more rigid, iterative process aimed at continuous improvement.

Depending on your specific problem and industry context, one of these frameworks may offer a more effective approach.

When to Use Which

After delving into the principles, key differences, and real-world applications of PDCA and OODA, the natural question that arises is, “When should I use which framework?” This section aims to provide clear guidelines to help you make that decision based on various scenarios and criteria.

Scenarios Where PDCA is More Appropriate

Process Optimization : When the goal is to improve an existing process, particularly one that is well-defined and stable, PDCA offers a more structured approach.
Quality Control : If you are aiming for incremental improvements in quality, such as reducing defect rates in manufacturing or improving customer satisfaction metrics, PDCA is highly suitable.
Data-Driven Environments : In scenarios that require in-depth data analysis, like optimizing marketing strategies or enhancing healthcare protocols, PDCA’s methodical nature is beneficial.
Long-Term Planning : For projects that don’t demand immediate action and allow time for planning, testing, and evaluation, PDCA is more fitting.

Scenarios Where OODA is More Fitting

High-Stakes, Rapidly Changing Environments : In settings like emergency response or financial trading, where decisions have to be made rapidly, OODA is preferable.
Ambiguous Situations : When you’re dealing with problems that lack clear definition and are constantly evolving, the flexibility of OODA is highly beneficial.
Competitive Scenarios : In fast-paced markets or sports where real-time adaptability gives you an edge over competitors, OODA is more suitable.
Resource Availability for Real-time Analysis : If your organization has the capability for real-time data collection and analysis, OODA can be very effective.

Criteria to Consider When Choosing a Framework

Speed Requirement : Do you need immediate results, or is your timeline more flexible?
Complexity : Is the problem well-defined, or is it volatile and ever-changing?
Resource Availability : Do you have the resources for in-depth planning and data analysis (PDCA), or for real-time data collection and rapid action (OODA)?
Industry Norms : What frameworks are commonly used in your industry? Each methodology has sectors where it excels.
End Goal : Are you looking for continuous, incremental improvements (PDCA) or quick, adaptive problem-solving (OODA)?

In conclusion, both PDCA and OODA offer valuable frameworks for problem-solving and decision-making but in different contexts and scenarios. The choice between them should be made after carefully considering the specific requirements of your situation and the resources you have at your disposal.

Combining PDCA and OODA — A Synergistic Approach

While PDCA and OODA each have their unique advantages and ideal use-cases, there are scenarios where integrating the two can yield superior outcomes. This isn’t a matter of choosing one over the other but harnessing the strengths of both in a synergistic approach.

How the Two Can Complement Each Other

Initial Planning with PDCA, Rapid Adaptation with OODA : Use PDCA for the initial planning stages to ensure that the problem is well-understood and that resources are allocated efficiently. Then, switch to OODA for real-time decision-making and adaptation.
Data-Driven Flexibility : PDCA’s strength in data collection and analysis can feed into OODA’s orientation phase, providing a solid empirical foundation for quicker, more accurate decisions.
Iterative Improvement : Use OODA for rapid cycles of action but periodically engage in PDCA cycles to review performance, analyze results, and set new objectives. This way, you maintain adaptability while fostering continuous improvement.
Problem Complexity : For problems that have both well-defined and ambiguous elements, PDCA can tackle the former while OODA can be deployed for the latter.

Examples of Integrated Approaches

Healthcare Emergency Rooms : Initial procedures and protocols can be designed using PDCA to ensure they are as effective as possible. When unpredictable emergency cases come in, medical teams could employ OODA loops to make rapid decisions based on real-time patient data.
Supply Chain Management in FMCG : PDCA can be used to optimize the supply chain logistics and inventory levels. During sudden market changes like a spike in demand or supply interruptions, OODA can provide the adaptability needed to make quick adjustments.
Cybersecurity : PDCA could be employed for regular security audits, vulnerability assessments, and planning system upgrades. In the event of a real-time security breach, OODA is ideal for quick identification of the threat and immediate action.
Consulting for Business Transformation : Consultants can use PDCA to create an initial strategy for business transformation. As they start implementing changes and confront real-world challenges and feedback, OODA can guide adaptive modifications to the strategy.

By integrating PDCA and OODA, organizations can tap into both detailed, analytical planning and rapid, adaptive action. This hybrid approach offers a dynamic, responsive way to tackle complex challenges that neither method could fully address on its own.

In our comprehensive exploration of PDCA and OODA, two highly influential problem-solving frameworks, we’ve navigated through their origins, key steps, application across industries, and inherent strengths and weaknesses. We’ve also delved into real-world case studies to grasp their practical implications and examined various scenarios to discern when each approach is most effective. Importantly, we’ve explored how these seemingly disparate frameworks can synergistically complement each other, enriching our toolkit for tackling an array of challenges.

Final Recommendations : If you’re in an environment that values incremental improvement, relies on deep data analysis, and has the luxury of time for planning, PDCA is your go-to framework. For those in fast-paced, ever-changing scenarios requiring rapid decision-making, OODA is a better fit. However, don’t hesitate to integrate both methodologies to capture the best of structured planning and agile action. The most effective problem-solving often lies in the nuanced blend of multiple approaches.

Isniah, S., Purba, H.H. and Debora, F., 2020. Plan do check action (PDCA) method : literature review and research issues. Jurnal Sistem dan Manajemen Industri , 4 (1), pp.72-81.
Johnson, C.N., 2002. The benefits fo PDCA . Quality Progress , 35 (5), p.120.
Richards, C., 2020. Boyd’s OODA loop .
Enck, R.E., 2012. The OODA loop. Home Health Care Management & Practice , 24 (3), pp.123-124.

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Daniel Croft

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website www.learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

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The Problem Solving Framework

Define your problem before jumping into immediate solutions.

Effective problem-solving isn't about jumping quickly into solutions; it's about solving the right problems in the right way.

Personally, I don’t like never-ending discussions, finding another blocker, or asking for one more requirement in your ticket. I prefer to move fast with limited information and some degree of uncertainty. I strongly believe in an iterative approach, where relevant data and good decisions emerge during the journey.

Yet, such an iterative approach only makes sense if we work on problems worth solving with the most optimal solutions to them.

Here, you can find a PDF cheat sheet that sums up this article.

How to Solve Problems?

For inspiration on building a problem-solving framework, I recommend the short, humorous, yet insightful book " Are Your Lights On " by Don Gause and Gerald Weinberg. This book emphasizes the importance of carefully defining the problem before rushing into solutions. It challenges readers to think critically, question assumptions, and consider multiple perspectives.

In organizations where the engineering team is viewed as a "feature factory", the discovery process can be perceived as wasteful. As long as software engineers don't produce something tangible (like pull requests or features), their work is undervalued. The trap here is the assumption that Product Managers, senior management, or the CEO have all the answers.

Side note : I have covered the true role of software engineers in empowered organizations in a few of my past articles:

Building a Team of Missionaries, Not Mercenaries

Focusing on Solutions, Not Problems

In such environments, engineering teams come up with solutions too quickly. This isn’t surprising in the end, as they are inventors and creators with strong technical skills, often the only ones in the company who can build things. They are frequently assessed by what they produce, not by what they think through.

But here's the trap: in order to solve a problem, it must first be defined. If engineers jump immediately into the solution, it doesn't mean the problem is undefined. It means it's defined with some (hidden) assumptions, biases, and personal interests.

There is also another challenge with software engineers. If not jumping into solutions too quickly, they also tend to overthink their problems indefinitely, multiplying missing requirements, finding edge cases, and overall getting stuck in a quest for perfection.

What's the Problem?

In the complex world we live in, the initial solution is rarely the optimal one. Complex problems may have multiple definitions, none of which is ultimately the right one. A problem may have multiple stakeholders, each with their own solution, and these stakeholders may have different power to articulate their preferences (the loudest one in the room, the most senior on the org chart, or those who prefer to remain silent).

The book describes problems from a few different angles, For example:

A PROBLEM IS A DIFFERENCE BETWEEN THINGS AS DESIRED AND THINGS AS PERCEIVED . —"Are Your Lights On"

This means that to solve a problem, you can either focus on achieving the desired state or change your perception of the problem. You can check the book for more ideas or continue reading for a systematic framework I came up with based on the lecture and my personal experiences.

The Problem-Solving Framework

Here’s a framework that will help both groups:

For teams that tend to jump into instant solutions, this framework provides perspective and support in problem framing.

For teams that overthink their problems, it helps narrow the focus to "just enough" information to start iterations.

Inspired by "Are Your Lights On", here is an 8-step framework to help find optimal solutions for problems faced by software engineering (or, more generally, product engineering) teams.

The 8 Steps of Problem Solving

Recognizing the problem (What’s a problem?)

Defining the problem (What are the facts behind the problem?)

Exploring the problem's depths (What are root causes of the problem?)

Identifying stakeholders (Who have the problem?)

Assessing the willingness to solve (Is it worth solving the problem? Is it aligned with broader goals and strategy?)

Developing solution strategies (What are options for solving problems? Which are the optimal ones?)

Implementing the solution

Monitoring and reviewing (Are success metrics defined and achieved through the solution?)

The 8 Steps of Problem Solving - Explained

Here are detailed descriptions for each step:

Recognizing the Problem : Acknowledge that a problem exists. This step doesn't necessarily require a deep understanding of the problem but recognizes that something needs attention.

Defining the Problem : Clearly articulate and define what the problem actually is. Gather and analyze data, synthesizing inputs to state the problem clearly and concisely.

Exploring the Problem's Depths : Look beyond the surface to understand the complexity of the problem. Conduct root cause analysis or interviews with users and team members, considering external factors.

Identifying Stakeholders : Identify all parties impacted by the problem, as well as those who will be involved in implementing solutions. Understand different perspectives and interests of these stakeholders.

Assessing the Willingness to Solve : Consider the pros and cons from different stakeholders' viewpoints. Decide if the problem is worth solving, considering factors like impact, business goals, and priorities.

Developing Solution Strategies : Brainstorm potential solutions and evaluate their feasibility. Encourage creative thinking and consider multiple approaches. Evaluate each proposed solution in terms of effectiveness, cost, and impact on stakeholders.

Implementing the Solution : Plan and execute the implementation process in detail, keeping all stakeholders informed.

Monitoring and Reviewing : Establish clear metrics for success and regularly review them. Gather feedback from all relevant stakeholders and be prepared to make adjustments if necessary.

I recommend going through the framework's steps with each significant problem you are facing:

Technical debt challenges, e.g., monolith breakdown, framework migration, dependencies update (and anything else you can classify with Ten Types of Technical Debt ).

Product development, like creating new features or delivering new value to customers (stating your work as a problem to solve, not a task to deliver is a big shift on its own).

Challenges related to SDLC process, like delivery frequency, testing automation, CI/CD processes.

Team-related challenges, like team empowerment, expectations, and performance management, team empowerment and productivity (you can check Top Ten Factors of Developers' Productivity ).

More Materials

I've prepared additional materials for paid subscribers who support Practical Engineering Management, including a FigJam Template, Markdown template and example problems from my professional career.

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The 4S problem-solving method

David Ahmed Walby

Here I’ll break down the 4S method — an integrated, four-stage problem solving approach that combines the tools of strategy consulting with insights from cognitive science and design thinking. Originally intended for MBA students heading to strategy consulting firms, the method can work for anyone.

State: First, you have to state the problem properly, identifying the core question at hand. Preparation has great value to problem solving

“If I had an hour to solve a problem I’d spend 55 minutes thinking about the problem and five minutes thinking about solutions.” — Einstein

2. Structure: Second, you need to structure the problem around candidate solutions that you’ll then test and investigate systematically.

3. Solve: Third, you’ll solve the problem by following one of three distinct paths: hypothesis-driven problem solving, issue-driven problem solving, or the creative path of design thinking.

4. Sell: Finally, you have to sell your solution to the problem owner.

Project-managing is the ability to state a problem, break it down into addressable pieces and collaboratively drive the solution definition and execution process. It goes far beyond the spreadsheet filling and task-chasing approach that less experienced problem-solvers often fall into.

The 4S method/framework is a map to navigate the uncertain path of business problems. Having a high-level, birds-eye view of the problem-solving process helps to keep a structured approach to solving complex business problems. Let’s break the 4S’ down in a bit more detail…

The “Problem Statement” stage is a collaborative effort to define the scope of the problem. It is an opportunity to engage with stakeholders through interviews and workshops with the goal of integrating the different perspectives. The TOSCA framework is used for structuring the problem definition (Trouble, Owner, Success Criteria, Constraints and Actors). You can allocate each of these elements to different team members to analyse, craft the statement and present to others. This increases speed whilst integrating different perspectives. Regularly reference the Statement in a slide & open every project progress presentation. This helps us stay focused on the problem statement throughout the process & make adjustments accordingly.

The “Problem Structure”. The benefit of the 4S method is that it provides additional insights into how to decompose the work. The idea is to use industry, functional and logical frameworks to decompose the problem into an issue tree. Here is where the project management & strategy interlinks become most clear: project managers can use strategy frameworks to structure the problem (for example, the Ansoff matrix, BCG growth-share matrix, PESTEL, Porter’s five forces).

But strategy is not the only “sister-field” that PMs can use as input. Operations, Marketing and Finance frameworks are also useful when handling business change projects. For example, market size, revenue breakdown, market share, McKinsey 7S, cost breakdown, etc. Where you cannot apply industry or functional frameworks, good old-fashioned logical frameworks can support you, e.g, high-low matrixes.

Accumulating a library of such frameworks throughout our careers comes in handy. These frameworks are the structure of the issue tree that represents the problem decomposition. Many trees will fit your problem, depending on your project/organisation. Start with the one that best fits your problem and provides a map for the problem-solving. It does not need to be perfect, but it has to enable progress . The issue tree will be iterative & help you allocate the work for the next stage.

The “Solve” stage entails unpacking each branch of the issue tree into granular questions. These questions pave the way to the data gathering and analysis. Greater cross-functional collaboration comes into play here.

The goal is to design solutions that follow logically from the analysis and address the problem statement. Here, the project can grow in different directions as the different teams conduct their data gathering efforts. Project managers thus need to to tightly coordinate this process and bring the insights together against the issue tree. Beware incoherent and controversial data. Some issue branches might morph into something big & spin off as mini-projects in themselves, which may add time to execution. Having steps one & two, a well-defined Problem-Statement, helps identify the most meaningful findings to progress.

The “Sell” stage is about selling the solution to the stakeholder(s). The 4S method entails using the “Pyramid Principle” for this. As Project Managers, we need to keep our stakeholders engaged. They care about the end result, not about the process. The Pyramid Principle tells us to front-load the solutions, and justify them with the most meaningful data points.

An example sentence is: “We should X because of A, B and C insights”. Start with the best & most engaging piece of information .

There we have it! The summary of the 4S problem-solving method. Now go forth & conquer

*If you found this helpful, please clap and/or share :)

Written by David Ahmed Walby

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Review Article
Open access
Published: 09 July 2024

Non-convex optimization for inverse problem solving in computer-generated holography

Xiaomeng Sui 1 , 2 ,
Zehao He 1 ,
Daping Chu ORCID: orcid.org/0000-0001-9989-6238 2 , 3 &
Liangcai Cao ORCID: orcid.org/0000-0002-8099-2948 1

Light: Science & Applications volume 13 , Article number: 158 ( 2024 ) Cite this article

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Imaging and sensing

Computer-generated holography is a promising technique that modulates user-defined wavefronts with digital holograms. Computing appropriate holograms with faithful reconstructions is not only a problem closely related to the fundamental basis of holography but also a long-standing challenge for researchers in general fields of optics. Finding the exact solution of a desired hologram to reconstruct an accurate target object constitutes an ill-posed inverse problem. The general practice of single-diffraction computation for synthesizing holograms can only provide an approximate answer, which is subject to limitations in numerical implementation. Various non-convex optimization algorithms are thus designed to seek an optimal solution by introducing different constraints, frameworks, and initializations. Herein, we overview the optimization algorithms applied to computer-generated holography, incorporating principles of hologram synthesis based on alternative projections and gradient descent methods. This is aimed to provide an underlying basis for optimized hologram generation, as well as insights into the cutting-edge developments of this rapidly evolving field for potential applications in virtual reality, augmented reality, head-up display, data encryption, laser fabrication, and metasurface design.

Perceptually motivated loss functions for computer generated holographic displays

Adaptive constraints by morphological operations for single-shot digital holography

Diffraction-engineered holography: Beyond the depth representation limit of holographic displays

Introduction.

Holography is a long-existing concept first raised by Dennis Gabor in the late 1940s, which aimed at improving resolution in electron microscopy 1 . In the 1960s, the development of laser technology enabled practical optical holography 2 , 3 . Early demonstration of optical holography can be described with two steps: interferential recording of an object wavefront and diffractive reconstruction from a hologram. Recent advancements in digital devices have enabled both the recording and the reconstruction processes to be performed computationally. One branch of holography involves optically recording an object wavefront and computationally reconstructing it from a digital hologram 4 , 5 , commonly referred to as digital holography 6 . This approach enables promising applications such as imaging, measurement, and detection. Another branch of holography involves computationally generating a hologram and optically reconstructing an object’s wavefront, commonly referred to as computer-generated holography (CGH), which provides an approach to digitally modulate a volumetric wavefront 7 . This technology, half inherited from optical holography and half advanced by computer science, has become an emerging focus of academia and industry 8 , 9 , 10 .

Computer-generated holograms, encoded on various types of holographic media, enable a wide range of applications. Holograms fabricated as diffractive optical elements (DOEs) 11 or metasurfaces 12 , 13 , 14 can reproduce specific spatial light fields, achieving structured light projection 15 , 16 , 17 , data storage 18 , 19 , and optical encryption 20 , 21 , 22 , 23 , 24 . With refreshable devices like spatial light modulators (SLMs) 25 , 26 , 27 , as is shown in Fig. 1 , CGH is able to assist many fields of investigations, including three-dimensional display, holographic lithography 28 , optical trapping 29 , and optogenetics 30 , 31 , 32 . In recent years, CGH also boosts the birth and growth of potential markets of virtual reality (VR) 33 , 34 , 35 , 36 , 37 , 38 , augmented reality (AR) 39 , 40 , 41 , 42 , head-up display 43 , 44 , 45 , holographic printing 46 , optical communication 47 , and optical computing 48 . Although these applications and fields of investigation involve the encoding of holograms with various elements 49 , 50 and devices 51 , 52 , the algorithms for hologram synthesis are similar and can be universally applied 53 . Therefore, computing a hologram for faithful reconstructions is an issue closely linked to fundamental physics and is widely investigated in general fields of optics. The computation of holograms is a strict adherence to the physics basis of holography while being a compromise to the existing hardware 54 , which requires holograms to be phase-only, amplitude-only, or rarely complex-amplitude. The object wave used for CGH can be reconstructed from either an interference pattern with a reference beam 55 , 56 or a diffraction pattern of the object 57 . In early investigations 58 , holograms computed from diffractive wave propagations were found to be more energy-efficient compared to those computed from interferences. These wave-propagation methods yielded complex holograms (CHs) using computer-guided plotters employing the detour phase principle 59 . Subsequently, phase-only holograms (POHs) were proposed 60 , generated on the assumption that a scattered wavefront can be reconstructed with only the phase term. Proper computation of a diffraction-based hologram is essential for the optical reconstruction of CHs and POHs, and it gradually becomes vital for generating amplitude-only holograms 61 .

References 17 , 18 , 20 , 27 , 49 , 208 are reprinted with permission from Springer Nature. References 39 , 50 , 68 , 141 are reprinted with permission from © Optical Society of America. References 33 , 40 , 132 , 133 are reprinted with permission from © ACM. Reference 215 is reprinted with permission from © AAAS. References 25 , 26 , 41 , 51 , 52 , 61 , 66 , 69 , 213 are reprinted under a Creative Commons Attribution 4.0 International License

The fundamental concern of the diffraction-based hologram computation can be neatly described as solving a hologram from a given intensity distribution of the object 62 , as is shown in Fig. 2a , which is an inverse problem with constraints imposed by physical basis and hardware implementation. This inverse problem is relatively different from the phase retrieval problems in imaging because a hologram satisfying all the constraints and reconstructing an artificial intensity distribution is not ensured to exist 63 . Nevertheless, the relation between the reconstructed wavefront and its intensity is ill-conditioned 64 . Multiple candidate holograms that approximately satisfy the constraints can be solved through the non-convex optimization 65 . Various optimization algorithms are thus introduced in hologram synthesis and rapidly bring about breakthroughs for CGH in noise reduction 66 , contrast enhancement 67 , crosstalk suppression 68 , and computing acceleration 69 . With the significant enhancement of CGH capabilities through optimization algorithms, achieving appropriate hologram optimization tailored to the physics process emerges as a central target, which ensures desired optical reconstructions. The motivation of computing all kinds of holograms with faithful reconstructions has pushed forward the advancement of optimization algorithms for CGH.

a The synthesis of computer-generated holograms can be described as an inverse problem. b Constraints, frameworks, and the initialization condition need to be considered in hologram optimization. c Constraints are imposed by physics and hardware in hologram optimization. Some optimization frameworks are widely used in hologram optimization: d alternating projections, where elementary projections occur to approach the intersection points of two or more enclosed feasible sets; e first-order gradient descent methods, where a local optimal solution is searched along the gradient descent direction; f second-order gradient descent methods, where the “steepest” gradient descent direction is further found with the assistance of second-order gradient

This review article focuses on optimization algorithms for hologram generation in CGH, which have become essential tools in hologram synthesis over the past decades. Concluded from existing optimization algorithms appropriately adapted to CGH inverse problem solving, as is shown in Fig. 2b , some crucial factors need to be considered, including constraints, framework, and initialization. Constraints refer to the conditions that a candidate solution should satisfy, usually modeled with the physical basis and the hardware implementation of CGH. Restricted by the constraints, possible solutions of the inverse problem constitute an enclosed feasible set γ , within which the optimization algorithms search for a solution locally or globally. The optimization framework chosen determines the path of searching within the feasible set, leading to variations in computing time, storage, and sometimes even convergence points. Initialization, especially the choice of the initialization condition, has a significant impact on the final convergence point. With a comprehensive overview of the original and recent designs of optimization algorithms, suitable handling of core issues concerning feasible hologram optimization is illustrated, offering a basis for applying optimized holograms to various fields of investigation.

Constraints

Optimization algorithms are designed to retrieve a computer-generated hologram $H({\bf{u}})=A({\bf{u}}){e}^{i\phi ({\bf{u}})}$ from a specific object wave $h({\bf{r}})=a({\bf{r}}){e}^{i\varphi ({\bf{r}})}$ in an inverse problem solving situation of CGH, where a ( r ) is the amplitude, φ ( r ) is the phase, ${\bf{r}}=(x,y)$ and ${\bf{u}}=(u,v)$ are the position vectors on the object plane and the hologram plane, respectively. As shown in Fig. 2c , such an optimization is restricted by several constraints 64 , 65 :

Object intensity ${a}^{2}({\bf{r}})={I}_{{\rm{obj}}}({\bf{r}})$ ;

Finite bandwidth ${\Delta }_{H} \,<\, \infty$ and ${\Delta }_{h} \,<\, \infty$ ;

Finite spatial scale ${L}_{u} \,<\, \infty$ and ${L}_{v} \,<\, \infty$ ;

Hologram intensity for POHs ${A}^{2}({\bf{u}})={E}_{{\rm{uni}}}$ .

Constraint ① describes the pre-defined object intensity, which is fed as a constraint in optimization to ensure a faithful reconstruction. Constraint ② describes a finite bandwidth throughout the process of propagation, where Δ H and Δ h represent the hologram and object wave bandwidths, respectively. Constraint ③ describes the finite spatial scale of the hologram, which is usually conducted by zero padding in practical computation. L u and L v represent the length and the width of the hologram to be optimized respectively. Constraint ④ is optional and specially imposed due to a constant hologram intensity of POHs, where ${E}_{{\rm{uni}}}$ is the hologram intensity.

These constraints ensure a correct optimization adapting to the physical model of holography and enable a faithful reveal of the reconstruction performance in numerical simulations. Errors and omissions of the constraints imposed on optimization can lead to a mismatch between the numerical and optical reconstructions 70 , usually shown as obviously excessive speckle noise and artifacts appearing in the optical reconstructions compared to the numerical ones 71 . Given all these constraints imposed, we can deduce that the object phase φ ( r ) is the only unsettled input factor in optimization, which provides a degree of freedom to design the hologram 72 . With different initializations of φ ( r ), the path and the outcome of optimization can differ greatly, leading to various performances of optical reconstructions.

The effectiveness of optimization is largely decided by whether the constraints are correctly imposed or not. The way the constraints are imposed is determined not only by the type of holograms but also by the diffractive calculation method utilized to implement computational free-space propagation. Existing diffractive calculation methods demonstrated for hologram optimization are mainly conducted by parallel computation based on the Fourier transform 73 . Among them, using a single fast Fourier Transform (FFT) to compute Fraunhofer diffraction at infinity is one of the mostly used propagation strategies 74 , which is easy and simple enough to implement in research. Fresnel diffraction is often chosen to generate far-field holograms 75 , with diffractive calculation methods including the single Fourier-transform Fresnel (SFT-FR) approach 76 , the Fresnel transfer function approach, and the Fresnel impulse response approach 77 . Besides, some methods derived directly from the first Rayleigh-Sommerfeld integral theory present high practicability in CGH 78 , covering both near-field and far-field propagations, among which the representative examples are the Rayleigh-Sommerfeld convolution method 79 and its corresponding Fourier form angular spectrum method (ASM) 80 .

Here, we uniformly utilize the single FFT method 81 , 82 to illustrate 2D hologram optimization algorithms and the band-limited ASM 83 for the 3D case. Given different diffractive calculation methods, the most controversial part of imposing constraints lies in defining a proper bandwidth restriction to describe constraint ② , which is discussed in the following sections.

The optimization algorithm searches for an optimal solution as the desired hologram within a closed set restricted by the constraints. Several effective optimization frameworks are widely used, including alternating projection methods, which are depicted in Fig. 2d , and gradient descent methods. More specifically, the gradient descent methods also incorporate the first-order gradient descent as depicted in Fig. 2e , and the second-order gradient descent as depicted in Fig. 2f , of which the representative examples are stochastic gradient descent (SGD) and the quasi-Newton method respectively. Some other optimization frameworks are also applied to CGH, like iterative shrinkage-thresholding algorithms 84 and simulated annealing 85 . Yet, these frameworks are less widely used in hologram synthesis.

Alternating projections

The alternating projections describe a category of optimization methods to approximate a point in the intersection of two or more enclosed feasible sets separately restricted by different constraints 86 . This is achieved by a pair of elementary projections repeatedly occurring in the optimization, which construct an iterative computation loop 87 . The Gerchberg-Saxton algorithm (G-S algorithm) 88 was published in 1972 as the first account of alternating projections solving a phase retrieval problem, in which a pair of projections were used to reconstruct phase from two intensity measurements. As is shown in Fig. 3a , the phase of a specific wavefront is retrieved with the amplitudes on both the object plane $a^{\prime} ({\bf{r}})$ and the Fourier plane $A^{\prime} ({\bf{u}})$ repeatly replaced by known distributions, which are discretized into a ${M}_{x}\times {N}_{y}$ matrix and a ${M}_{u}\times {N}_{v}$ matrix respectively. Later presented by Fienup, this alternating scheme was improved to solve the problem of finding a Fourier transform pair satisfying the constraints in both planes, which was known as the error reduction algorithm 89 . As is shown in Fig. 3b , the error reduction algorithm enhances the flexibility of the alternating projections and enables various non-negative constraints to be imposed on dual planes. After that, a series of input-output algorithms 90 were further developed to accelerate the convergence of the error reduction algorithm. Input-output algorithms differ from error reduction algorithms during the nonlinear operation on the object plane. In the basic input-output (IO) algorithm, the object constraints are imposed only on the points that violate the object constraints $h({\bf{r}})\notin {\gamma }_{o}$ . Such a change is based on the idea that the distribution of $h^{\prime} ({\bf{r}})$ for the next iteration does not have to satisfy the object constraints but is given to drive a desired and constrained output. Based on this thought, different nonlinear operations can be introduced on the object plane, as is shown in Fig. 3c , through which the output-output (OO) algorithm and the hybrid input-output (HIO) algorithm were developed. The HIO algorithm possesses an advantage in avoiding the stagnation problem, which occurs sometimes in the OO algorithm and prevents the optimization from getting close to the solution. In some situations, the unique characteristics of the HIO algorithm set it apart from the input-output algorithm series for its imaging applications 91 , 92 . All these alternating projection algorithms are now widely studied as early solutions to phase retrieval problems. They have been derived into different forms for specific applications 93 .

a Gerchberg-Saxton algorithm (G-S algorithm) 88 . b Error reduction algorithm 89 . c Input-output algorithm series, including the basic input-output algorithm (IO), the output-output algorithm (OO), and the hybrid input-output algorithm (HIO) 90 . d Iterative Fourier-transform algorithm (IFTA) 70 . e Signal window based soft-encoding IFTA 71 . f Phase mask based on IFTA 106

Concurrent with the advancement of algorithm flows, numerous efforts are made to adapt alternating projection algorithms into the physical model of CGH. Specially in hologram optimizations, alternating projections are applied to two enclosed sets associated with potential object solutions γ o and potential hologram solutions γ h , which are restricted by object constraints and hologram constraints respectively. The preliminary applications of alternating projections to solve the hologram synthesis problem in CGH appeared just before the first report of the G-S algorithm. Gabel and Liu proposed a flow chart with Fourier transform pairs to minimize binary hologram reconstruction errors in 1970 94 . Hirsch et al. 95 invented a technique for optimizing Kinoforms with a loop of forward and backward propagations in 1971. In the early studies on optimization algorithms for CGH 96 , Fourier transform pairs were widely used for diffractive calculation since they could easily simulate Fraunhofer diffractions at infinity. When this scheme became known as the error-reduction algorithm and was extended into an input-output algorithm series, Fienup clarified that such an iterative Fourier transform loop is the alternating projections to solve a hologram from specific constraints on the object plane and hologram plane, rather than simple exchanges of amplitude values on dual planes 62 , 97 .

With the extension of the categories of constraints, holograms can be computed well in line with the theoretical model of holography. In 1988, an iterative Fourier transform algorithm (IFTA) specially applied to CGH was proposed by Wyrowski and Bryngdahl 70 . As is shown in Fig. 3d , the IFTA scheme additionally includes the bandwidth constraint ② and the spatial scale constraint ③ in computation. A dense sampling on the object plane was proposed by applying the bandwidth constraint of ${\Delta }_{h}={\Delta }_{I}/2$ , where Δ I was the bandwidth of the object intensity field 79 . The theoretical basis of this operation is that the spectra of the object wave and the spectra of the object intensity are related by autocorrelation. Minor errors and noises were able to be revealed in the numerical reconstruction, as a joint result of physical constraints and dense sampling. The performance of an optimized hologram can be sufficiently improved in optical reconstruction, with a desired object intensity fed as a constraint on the object plane. In the subsequent studies on IFTA, signal windows, energy operators, and soft encoding are introduced into the algorithm. The signal window utilizes the redundancy of hologram design and distributes the noises outside the signal window 98 . Because the object and the hologram are both finite in spatial scale, the object wave is defined within a window W O in computation, and the corresponding hologram is restricted within a window W H , as shown in Fig. 3e . On the object plane, a weighting factor is usually introduced to adjust the energy distribution ratio in and out of the window W O 71 , so that the object intensity constraint is only imposed within the signal window. On the hologram plane, with W H introduced as the bandwidth and special scale constraint on the hologram. The definition of the signal window allows for the use of amplitude freedom other than phase freedom on the object plane while optimizing holograms 99 , 100 . Introducing the double freedoms loosens the object intensity constraint ① , which exchanges for higher reconstructing accuracy by allowing noises in less-concerned areas 101 , 102 . Coordinated with quadratic phase initializations, IFTA algorithms with double freedoms can achieve speckle-free reconstructions 103 , 104 . The introduction of signal windows makes use of the dark area outside the object window to accommodate minor errors produced in the optimization of a POH, which also accelerates the process of reaching to the convergence. To ensure an appropriate distribution of the signal and the noise, energy operators E and 1/ E are both used to normalize the intensities in the transformation between the object plane and the hologram plane. The soft encoding strategy was introduced to control the direction of optimization in IFTA. One way of achieving soft encoding is to apply a varying operation on the hologram plane 71 . This varying operation leads to minimal changes in the object phase and results in a smooth transition towards the desired optimizing direction. The signal window and the soft encoding, when combined, work for various types of initial object phases in IFTA, offering this algorithm a great deal of flexibility. Apart from the random phase, which was originally used as the object phase for Kinoform, some remarkable attempts at various phase initialization also include the quadratic phase 71 , the constant phase 105 , and the pre-optimized phase 64 . The utilization of constant phase and quadratic phase is driven by a demand for speckle suppression in CGH. The pre-optimized phase is utilized to develop a less iterative 106 , 107 or noniterative 108 , 109 , 110 approach to quickly generate holograms, which greatly accelerates the computation. As is shown in Fig. 3f , such algorithms can be divided into two steps: the first step optimizes a random phase mask within the signal window, which to the largest extent satisfies the constraints on the dual planes; the second step optimizes the hologram with the pre-optimized phase input as the initial object phase. The pre-optimized phase can be utilized to initialize object waves with different intensity patterns. And the computation can thus be simplified into a loop of optimizing holograms with only several iterations, or even without iterations.

Despite the introduction of alternating projection algorithms, the reconstruction of CGH can still be plagued by various unwanted effects, including speckle noise, artifacts, and stripes. These effects may trap the optimization into stagnation and remain in reconstruction even after convergence. Thus, some modifications applied to optimization algorithms are also studied. Since the complex distributions on both the object plane and the hologram plane are calculated in iterations, the framework of the alternating projections possesses the flexibility to include manipulations on the object phase 111 , Gaussian illumination 112 , weighting factors 113 , internal processing in the loop 114 , partitioned optimization 115 , 116 and multi-loop optimization 117 . With highly promoted reconstructing accuracy and computation stability enabled by accumulated improvements on alternating projection algorithms, alternating projection algorithms occupy an indispensable part in optimizations of CGH, especially for the synthesis of holograms encoded on static holographic media, like DOEs 118 , 119 and metasurfaces 120 , 121 , 122 .

The highly developed schemes enable alternating projection algorithms to be applied to hologram generation based on neural networks in the early stages 123 , which provide training datasets of ground-truth holograms. Despite the quick advancements of CGH combined with various neural networks in recent years 124 , 125 , a pre-optimization carried out by the alternating projections is still a widely adopted choice for supervised learning 126 , 127 , 128 , 129 .

Stochastic Gradient Descent (SGD)

Because of the existence of specific object intensity distributions, the inverse problem of hologram synthesis in CGH can also be cast as the optimization of a parameterized objective function requiring minimization with respect to its parameters. Since the choice of the objective function is often stochastic and differentiable with respect to its parameters, SGD is considered as an efficient and effective first-order gradient descent ( $\nabla {\mathcal{L}}$ ) framework for optimization. Although such a scheme searching for a local optimal solution along the gradient descent direction has been early applied to phase retrieval 130 , 131 , SGD was hardly applied to CGH till recent years. In 2019, Chakravarthula et al. chose such a framework to demonstrate the loss functions they introduced for Wirtinger holography 132 . In 2020, Peng et al. utilized SGD to carry out a camera-in-the-loop optimization 133 .

Feasible gradient descent requires the gradient of the object function to be comparable, or in other words, the gradient with respect to the variable is a real value. Yet, a scalar wavefront is complex, which creates a major difficulty in applying gradient descent strategies in hologram optimization. Since POHs only concern the phase component of the holographic wavefront on the hologram plane, the optimization of POHs becomes relatively easy for implementation. With this regard, a POH can be synthesized by constructing an objective function ${ {\mathcal{L}}}_{P}$ associated with a forward model and solving the minimization problem:

${ {\mathcal{L}}}_{P}$ is also referred as a loss function, which usually describes the difference between the reconstructed intensity I ( ϕ ) and the object intensity I obj . I ( ϕ ) represents the reconstructed intensity as a function with respect to the POH ϕ . Since the reconstructed intensity I ( ϕ ) and reconstructed wave h ( ϕ ) are linked by an ill-conditioned relation $I(\phi )={|h(\phi )|}^{2}$ , the optimization for this hologram synthesis problem is non-convex. In this case, SGD is a relatively efficient optimization method to solve this problem because only first-order partial derivatives concerning all the variables are computed, which have the same computational complexity as just evaluating the objective function. Adam algorithm 134 , shown in Fig. 4a , is one of the most widely implemented SGD-based algorithms for solving the hologram synthesis problem.

a SGD optimization of a phase-only hologram ( POH). The Adam algorithm updates the POH by calculating the 1st-moment vector b and the 2nd-moment vector p . b SGD optimization of a complex hologram (CH). The Adam algorithm updates the object phase of the CH. c Quasi-Newton optimization of a POH. The L-BFGS algorithm updates the POH by calculating the first-order gradient g and the inverse Hessian matrix $\bar{H}$ . d Quasi-Newton optimization of a CH. The L-BFGS algorithm updates the object phase of the CH

To minimize the expected value of ${ {\mathcal{L}}}_{P}$ , the Adam algorithm updates the exponential moving averages of the partial derivative ${\nabla }_{\phi }{ {\mathcal{L}}}_{P}$ and the elementwise square gradient ${({\nabla }_{\phi }{ {\mathcal{L}}}_{P})}^{2}$ , which are described as the 1st-moment vector b and the 2nd-moment vector p . The optimization only requires the first-order gradient of the objective function ${ {\mathcal{L}}}_{P}$ with respect to the POH ϕ , for which reason efficient computation can be achieved with small memory. In such a framework, the object constraint is imposed through the minimization problem itself, while the hologram constraints are applied using the partial derivative ${\nabla }_{\phi }{ {\mathcal{L}}}_{P}$ , which is calculated in each update of optimization. Although we write ${ {\mathcal{L}}}_{P}$ in a general form of stochastic scalar function with respect to the reconstructed intensity I ( ϕ ) and the object intensity I obj , the choice of ${ {\mathcal{L}}}_{P}$ is actually of great diversity for hologram synthesis 135 , 136 . In many CGH implementations, ${ {\mathcal{L}}}_{P}$ is composed of a sum of subfunctions evaluating reconstructing errors 137 , and a normalization term is occasionally added to balance other reconstruction parameters 132 , 138 . This flexibility allows SGD to achieve a number of functional holographic display demonstrations, as is shown in Fig. 5 .

a Energy envelope expansion 139 . b Speckle suppression and contrast enhancement 67 . c Improvement in accommodation response 138 . d Optimization of high diffraction orders 140 . e Uneven liquid crystal modulation 143 . f Étendue expansion 84 . References 140 , 143 are reprinted with permission from © Optical Society of America. Reference 138 is reprinted with permission from © ACM. References 67 , 84 , 139 are reprinted under a Creative Commons Attribution 4.0 International License

For the synthesis of CHs, some actions need to be taken to ensure the calculated gradient is a real value. Here we accordingly provide an extended scheme for the optimization of CHs using SGD. This is achieved simply by switching the output onto the object plane instead of the hologram plane, given that the object phase is the only floating parameter of the optimization model. The minimization problem is accordingly changed, which can be given as:

where ${ {\mathcal{L}}}_{C}$ is the loss function, and $I(\varphi ^{\prime} )$ is the reconstructed intensity function with respect to the object phase $\varphi ^{\prime}$ . Equation ( 2 ) determines that the output of this optimization is the object phase, as shown in Fig. 4b , which is again turned into an optimization on a phase distribution. The basis of this scheme is the fact that with a given propagation model and a given object intensity, the complex hologram is only decided by the object phase. Different from that of POHs, the optimization of CHs includes both forward and backward propagations, resulting in a different expression of the gradient ${\nabla }_{\varphi ^{\prime} }{ {\mathcal{L}}}_{C}$ . With the optimized object phase ${\varphi }_{{\rm{opt}}}$ and the known object intensity I obj , the desired CH can be further calculated through an additional diffractive propagation.

Through the combination of a well-performed physical model, a well-chosen initial object phase, and a well-defined loss function, SGD itself has been verified to achieve good reconstructions of POHs, which leads to impressive accomplishments in 3D display with less or without speckles 67 , 139 . And, because the early adoption of SGD in CGH was linked with camera-in-the-loop optimization 133 , hardware involution was developed in tandem with the promotion of SGD-based hologram synthesis, in which the pattern captured by the camera replaced the reconstructed intensity in optimizations. With camera-in-the-loop optimization, subsequent reconstructions of SGD were further improved significantly by suppressing noises in optical setups, including high diffraction orders 140 , DC term 141 , speckles 66 , 142 , phase uniformity 143 , and aberrations 144 .

Because gradient descent contributes one of the most common optimizers to unsupervised learning of neural networks, the introduction of SGD neatly builds up a connection between CGH and unsupervised learning 145 , 146 , 147 . As the investigations in Fig. 6 have presented, unsupervised neural networks based on SGD accelerate the high-accuracy generation of holograms to ~0.01 s when trained by comparing I and I obj through a defined loss function rather than large datasets 148 , 149 , 150 . As a step already taken further, unsupervised learning coordinated camera-in-the-loop training perfectly solves the problem of the long processing time that comes with camera-in-the-loop optimization 133 . This scheme pushes the boundaries of optimization-based hologram synthesis by demonstrating a trade-off between computation time, reconstruction quality, and system integration 151 , 152 , 153 , 154 .

a DeepCGH 149 . b Holo-encoder 148 . c Learned hardware-in-the-loop phase retrieval 151 . d Neural holography with camera-in-the-loop training 133 . e Neural 3D holography for AR/VR display 152 . f Time-multiplexed neural holography 153 . References 148 , 149 are reprinted with permission from © Optical Society of America. References 133 , 151 , 152 are reprinted with permission from © ACM. Reference 153 is reprinted with permission from the authors

It is worth noting that the proposal of hologram optimization based on the alternating direction method of multipliers (ADMM) is closely associated with SGD. The ADMM breaks the optimization problem into subproblems with respect to multiple variables, which is achieved by modifying the minimization formula into an augmented Lagrangian form 155 , 156 . The final hologram is acquired by solving subproblems alternatingly 157 , which requires an inner loop of optimization in the hologram synthesis. The existing scheme of this loop is achieved by the Adam algorithm 152 , which incorporates the diffractive propagation model implemented by matrix manipulation.

Quasi-Newton method

The quasi-Newton method has become a widely used optimization framework for hologram synthesis in recent years. The quasi-Newton method is a second-order gradient descent method, which minimizes the loss function by constructing and storing a series of matrices that approximate the Hessian or inverse Hessian matrix of the loss function 158 . This operation is associated with the calculation and storage of the second-order gradient ( ${\nabla }^{2} {\mathcal{L}}$ ) of the loss function, which requires a larger amount of computation and storage compared with SGD. However, the calculation of the second-order gradient allows for a further search on the optimal direction, providing a possible “steepest” path on gradient descent. The combination of CGH and the quasi-Newton method was introduced by Zhang et al. when they proposed the non-convex optimization for volumetric CGH (NOVO-CGH) 68 . Later in 2019, the quasi-Newton method was also used in Wirtinger holography 132 .

The limited memory BFGS (L-BFGS) algorithm occupies the mainstream in the existing implementation of the quasi-Newton method in hologram synthesis 159 , 160 , which is chosen for its relatively high efficiency using a limited amount of storage. As depicted in Fig. 4c , ${ {\mathcal{L}}}_{P}$ is the loss function to be minimized given in Eq. ( 1 ) for POH synthesis. Similar to SGD, constraint ① in the quasi-Newton method is also imposed through the minimization problem itself, while constraints ② , ③ , and ④ are imposed in the expression of the partial derivative ${\nabla }_{\phi }{ {\mathcal{L}}}_{P}$ . The POH is updated by calculating both the first-order gradient $g={\nabla }_{\phi }{ {\mathcal{L}}}_{P}$ and the inverse Hessian matrix $\bar{H}$ . The inverse Hessian is related to the second-order gradient ${g}_{i+1}-{g}_{i}$ , which is estimated by adding up a series of correction matrices of each update in computation 161 . The accumulation of correction matrices is the major reason why the second-order gradient descent requires a greater amount of computation and storage. As a practical approach to implementing the quasi-Newton method, the L-BFGS algorithm has an upper limit for the number of correction matrices that can be stored. Once the number of updates reaches the storage limit, the stored correction matrices are discarded, and the correction matrices are reaccumulated.

Similarly, the quasi-Newton method is able to synthesize CHs by switching the output to the object phase φ and calculating the corresponding hologram through diffractive propagation, as is illustrated in Fig. 4d . The minimization problem can also be described with the expression in Eq. ( 2 ).

Although the quasi-Newton method and SGD are the second-order gradient descent and first-order gradient descent methods, respectively, they share the same derivation for ${\nabla }_{\phi }{ {\mathcal{L}}}_{P}$ and ${\nabla }_{\varphi ^{\prime} }{ {\mathcal{L}}}_{C}$ . Since a second-order gradient is introduced, the quasi-Newton method usually presents higher reliability in searching for the direction of gradient descent, which enables generally higher reconstructing accuracy of holograms with diverse propagation models in practice 68 . However, as a consequence of the large amount of computation in optimization, the quasi-Newton method requires much longer computing time and larger memory compared with other optimization frameworks 149 , 162 .

Optimization pipelines for 3D holography

In this section, we describe the way how various optimization frameworks are applied to 3D holography. The flexibility of the optimization frameworks also brings with it a diversity of pipelines for the hologram synthesis of 3D objects. Many diffractive propagation models are applicable for volumetric optimization. Here, we unify them into the band-limited ASM 83 , for a better illustration of different optimization pipelines. Three major existing optimization pipelines for 3D holography are discussed in detail. These pipelines were proposed alongside the advancement of alternating projection algorithms and have been combined with other optimization frameworks.

Despite the existence of the point-cloud sampling strategy 163 and the polygon-based sampling strategy 164 , in the optimization pipelines for 3D holograms, the object wave is mainly partitioned by layers 165 , 166 , 167 . One ancient approach to optimization for 3D holography is oriented from wavefront superposition 58 , 105 , which is a very conventional principle of holography 168 . As is shown in Fig. 7a , the alternating projections occur in each single layer of the object wave ${h}_{l}({\bf{r}})$ with the object intensity constraint ① imposed on each ${h}_{l}({\bf{r}})$ . ${z}_{l}$ represents the propagation distance for the ${l}^{{\rm{th}}}$ layer. Each projection generates an optimized diffractive wavefront ${H}_{z}({\bf{u}})$ for every sampled depth z . The final hologram is synthesized by the superposition of all the wavefronts.

a superposition method. b global method. c sequential method

The superposition method has been applied to the optimization of holograms, which is especially preferred in the synthesis of CHs 169 and AOMs 170 . This is due to the fact that the superposition itself does not break any constraints on CHs, while the hologram intensity constraint ④ for POHs can be violated after superposition 171 , 172 , 173 . To enable a better generation of POHs with the superposition method, a middle complex-amplitude plane is usually added to receive the superposition of waves from multiple depths 136 , 174 , 175 . Superposition optimization enables the preservation of full-depth cues of the object wave and possesses a competitive edge in applications like 3D display 176 . However, it brings about a degradation in reconstructed accuracy for POHs. The optimization part of the superposition method is essentially about solving planer optimization problems, which can be implemented by alternating projections, SGD, and the quasi-Newton method.

After the wide utilization of superposition optimization, the idea of global optimization is developed 177 , which enables a broader range of applications of CGH, especially those based on POHs. As is shown in Fig. 7b , the projections occur between the object volumetric matrices h ( r , z ) and the hologram plane, with the object intensity constraint ① imposed on the 3D matrix of the object wave h ( r , z ). Because the hologram intensity constraint ④ restricts the hologram $H^{\prime} ({\bf{u}})$ throughout the optimization, the capability of such a global method in generating appropriate POHs is highlighted. A distinct characteristic of global optimization is that the dark voxels on the front layer are also involved in the optimization, blocking the desired intensity on the back layer. The crosstalk breaking performance becomes more remarkable when an object wave is scattered and reconstructed with speckles, but still requires slow phase changes between consecutive planes. This characteristic makes POHs generated by the global method more applicable in fields like optical encryption 178 , 3D beam shaping 179 , 180 , 181 , and data storage 176 , 182 . However, the global method is yet less suitable for 3D display 183 , in which the crosstalk breaking disturbs the visibility of distant scenes and results in an unreasonable energy distribution 100 . Intensive modifications have been made to improve the performance of the global methods 184 , 185 , 186 , and a corresponding pre-optimization scheme has also been proposed 187 . The 3D optimization of POHs with the global method can be carried out by alternating projections, SGD, and the quasi-Newton method 68 , 188 . However, due to the difficulty in selecting appropriate outputs for gradient-descent frameworks, the feasible global optimization of 3D CHs is currently more restricted within algorithms achieved by alternating projections 189 .

Sequential optimization is another viable scheme that can satisfy the hologram intensity constraint ④ for POHs. An earlier form of the sequential method was the optimization between object planes, called the ping-pong algorithm 190 . Then the hologram plane was also included in optimization 191 , 192 . As is shown in Fig. 7c , the sequential method is characterized by sequential propagations from distant object planes $h^{\prime} ({\bf{r}},{z}_{l+1})$ to less distant object planes $h^{\prime} ({\bf{r}},{z}_{l})$ , and from the nearest object plane $h^{\prime} ({\bf{r}},{z}_{1})$ to the hologram plane $H^{\prime} ({\bf{u}})$ . The hologram $H^{\prime} ({\bf{u}})$ is subject to the hologram intensity constraint ④ . In order to form the loop, the constrained hologram H ( u ) is then propagated sequentially through each object plane and to the most distant one, with the object intensity constraint ① imposed on every $h({\bf{r}},{z}_{l})$ . Because of the existence of the dark voxels, sequential optimization possesses a crosstalk-breaking characteristic like global optimization, which makes this method suitable for encryption and storage 193 . The specific problem of the sequential method is that its corresponding reconstructions have decreasing accuracy as the light propagates. And because sequential propagations are required, the implementation of the sequential method is mostly achieved by alternating projections.

Apart from the optimization pipelines, loss function formulation is another crucial factor affecting the performance of 3D holographic reconstruction. In 3D holographic applications, especially for holographic display, not only the accuracy of focus reconstruction is important, but the visual effect of defocus blur is also a great concern in evaluation. The defocused performance of 3D holographic reconstruction is related to the object phase distribution and the visible parallax within the maximum diffraction angle. On this basis, a well-defined loss function can model the spatial variation of diffractive patterns. Representative approaches to cast loss functions include the voxel distribution method, the focal stack method, and the light field method. As is shown in Fig. 8a , the voxel distribution method voxelizes and remaps the object into a 3D volume containing bright voxels and dark voxels 68 , 69 , 149 , which is further transferred into the object matrix associated with the loss function. The hologram pixels diffract light to focus on points in space to create bright voxels under illumination. However, it is difficult or even impossible to create a dark voxel in space immediately after a focused bright voxel, because it is physically infeasible to have the phase of light changed rapidly during the free space propagation over a very small distance. For this reason, the reconstruction of the voxel distribution method usually suffers from severe noise and greatly degraded image quality 132 . The focal stack method, as is shown in Fig. 8b , constructs 3D volume by rendering focal stacks at different propagation depths 133 , 153 . These computationally generated focal stacks at multiple depths are jointly involved in optimization together with the target object, which enables the diffractive reconstruction to better imitate the natural defocus blur, especially in holographic display 194 . The light field method originates from holographic stereograms which reconstruct an array of directional views of the object with a single hologram 139 , 195 , 196 , 197 , as is shown in Fig. 8c . Although some strategies of light field computation without hogel-based structure have been developed 198 , the application of the light field method is still relatively limited in 3D hologram optimization due to current band limitation existing in the pixelized holographic media like SLMs 199 , 200 .

a voxel distribution method. b focal stack method. c light field method

Here we provide a computational comparison between different optimization frameworks. As presented in Fig. 9a , the optimization of CHs and POHs is demonstrated by basic frameworks of the alternating projections, the SGD method (implemented by the Adam algorithm), and the quasi-Newton method (implemented by the L-BFGS algorithm), respectively. The object phase is initialized with a random matrix. The 512 × 512 holograms are computed on a PC with an Intel Core i9-9900K 3.6 GHz CPU and 32.0 GB of RAM, and an NVIDIA GeForce RTX 2080Ti GPU. Two diffractive propagation methods including the FFT and the ASM are compared, where the propagation distance of ASM is 50 mm. In general, the quasi-Newton method outperforms other optimization frameworks in reconstructing accuracy, which is measured by root-mean-square error (RMSE, ${E}_{{\rm{RMSE}}}=\sqrt{{\sum }_{m,n}{[{a}^{2}({{\bf{r}}}_{m,n})-{I}_{{\rm{obj}}}({{\bf{r}}}_{m,n})]}^{2}}$ ). However, much more computation time is required for the convergence. Compared with the alternating projections, the holograms optimized by SGD present a slightly lower RMSE and longer time. However, the flexibility in editing the loss functions and the superiority in computing efficiency make SGD unreplaceable in a number of implementations of CGH, especially for the training stage of hologram synthesis based on deep learning methods. The different performances of the first-order and second-order gradient descent methods while approaching convergence are also illustrated. Since SGD is a first-order gradient descent method, biased moment vectors are continuously introduced into the optimization when the algorithm approaches its convergence, resulting in the fluctuation around the optimal solution. On the other hand, the second-order gradient descent method searches for the optimal direction of gradient descent, the output of optimization varies at a limited range around the optimal solution. For this reason, the RMSE curves of SGD optimization in Fig. 9a bounce up when relatively weaker constraints are imposed on the optimization. The optimization convergence is also related to the diffractive calculation approaches utilized. It should be noted that the optimization of FFT-based holograms gives slightly worse quality of reconstruction here. This is because the bandwidth constraint imposed on FFT-based holograms is merged with spatial scale constraint, and thus the searching range of the FFT-based hologram optimization is less restricted around the optimal solution when approaching the convergence. Table 1 provides a review of the performance of these algorithms based on the equal testing of different frameworks.

a 2D reconstruction of the optimized complex holograms (CHs) and phase-only holograms (POHs) based on FFT and ASM diffraction model. b 3D reconstruction of the optimized complex holograms (CHs) and phase-only holograms (POHs) based on the superposition method and the global method

The performance of different frameworks for 3D holography is presented in Fig. 9b . Both the superposition method and the global method are demonstrated with the reconstructions of CHs and POHs. Three optimization frameworks perform similarly with 3D holograms generated with the superposition method. As predicted, the diffractive cues for different layers are well preserved after superposition, enabling the generation of defocus dispersion for 3D display. For the global method, however, different optimization frameworks present distinct differences in reconstruction. The quasi-Newton method and SGD are better at breaking the crosstalk between layers and showing more uniform energy distributions, among which SGD performs better at suppressing severe speckle noise. Yet, the multi-depth reconstructions by the alternating projections cannot avoid the disturbance from adjacent layers. This impact is more severe with the sequential method, which is currently only applicable to alternating projection algorithms.

Initialization

The initialization condition is a crucial factor affecting the optimum solution sought out by an optimization algorithm. Specifically in a hologram synthesis problem, the object phase $\varphi ({\bf{r}})$ is the only free parameter floating in the optimization. Given that the hologram optimization is non-convex, as is depicted in Fig. 10a , the initial value of this free parameter decides at which point the optimization path starts and to which local optimum point the optimization path is heading. Since the closet local optimal solution differs with different initialization conditions, illustrated in Fig. 10b , the choice of the object phase is closely associated with the performance of the in-focus reconstrued intensity. And the initial object phase determines the defocus pattern through the reconstructed phase. Various attempts are made to manipulate the object phase for initialization of the optimization, adapting computer-generated holograms for diverse applications. In this section, different object phase initializations, such as random phase, constant phase, and quadratic phase, and their corresponding reconstructing performances are discussed.

a A schematic diagram of the non-convex optimization in an actual hologram synthesis problem. Different optimization paths are triggered by different initialization conditions. b The variation of the loss function when a local optimal solution is searched. The closest optimum point is decided by the start point of optimization. c A rendered ideal reconstruction for a 3D scene. The reconstructions of CHs optimized with different initialization conditions. d Random object phase. e Constant object phase. f Quadratic object phase

Random phase

In the experiments of conventional optical holography, the real-world objects that generate the object waves to be recorded have scattering surfaces 201 . This is based on the fact that most materials encountered in the real world are rough on the scale of object wavelength. Various microscopic facets of the rough scattering surfaces of an object contribute randomly distributed phases to the recorded object wave. The random phase is widely used in CGH because the scattering surfaces of real-world objects produce scattered wavelets, which in turn leads to speckles 202 . Although CGH generates holograms through wave computation instead of optical interferometry, the phase term of the object wave needs to be defined according to the phase generated by the real-world object. An artificial object wave computed with a random phase distribution is thus more in line with the real object wave generated from scatterers.

It can be seen that the phase of the object wave is closely related to the defocus effects in reconstruction. Initialized with a random object phase, as shown in Fig. 10d , the reconstructed wave of optimization can generate a natural blur of defocus like that of the scatterers in the real world, which slowly varies on spatial distribution. This capability is essential because reconstructing a 3D scene is the core strength of holography and reproducing the object image faithfully at various positions in space is necessary. From this perspective, random or to some extent random distributions conform better to the phases of waves modulated by real-world objects in most cases. Since scattering materials occupy a considerable proportion in the natural world 203 , preserving the propagating characteristic of a scattered wave and at the same time removing speckles is unavoidable for CGH.

Apart from this consideration, there is an additional reason to use a random phase. In a great number of applications, holograms need to be encoded onto phase-only elements, such as DOEs, metasurfaces, and liquid crystal on silicon (LCoS). The POH operates only on the phase of an incident wave and is generated based on the assumption that a scattered wavefront can be reconstructed with only the phase information. Therefore, using random phase is also an essential procedure to enable the encoding of POHs in specific applications of holography.

However, a significant drawback of introducing a random phase into optimization is the degraded optical reconstruction severely affected by speckle noise. Careful studies have identified that speckles in CGH are closely associated with phase singularities and are regarded as the results of optical vortices 71 . Speckles in a scattered wavefront are found to be intertwined with optical vortices 204 , indicating the existence of phase singularities on which amplitudes are precisely zero and phases are indeterminate. Although scattered wavefronts are artificially generated in CGH, speckles can be suppressed optically when phase singularities are eliminated 205 . Computational approaches to suppress speckles are essentially making modifications to the random phase introduced in the generation of holograms. Optimization algorithms are able to restrict the scattering caused by the random phase to suppress speckles, which is achieved by feeding the object intensity and bandwidth limitation as constraints 67 , 68 . Some optimizing or training methods, such as camera-in-the-loop training 66 , 133 , 142 , can produce more remarkable results by involving optical systems in computation. However, it has been discovered that optimization algorithms are not inherently capable of eliminating all the speckles 205 . Given the connection between the random phase and speckles, intensive research is carried out to replace the random phase with other phase formats, including constant phase, quadratic phase, and some other artificially defined phase distributions, which will be introduced in the following sections.

Constant phase

Constant phase is increasingly utilized to synthesize holograms due to the invention of double-phase holograms 206 , delivering highly photorealistic reconstructions free from speckles 207 , 208 . As a choice of initialization, constant phase is more frequently used in 3D hologram optimization with the superposition method, especially for the synthesis of POHs optimized in virtue of middle complex amplitude planes 136 . The constant phase physically describes the phase distribution of extremely smooth surfaces in the natural world, like mirrors or objects with surfaces as smooth as mirrors. Suchlike objects cause less scattering and fewer speckles naturally even when they are illuminated by coherent beams. As is shown in Fig. 10e , when initialized with a constant object phase, the optimized object wave is reconstructed with undiffused diffracting patterns at defocus positions. This kind of defocus effect with diffracting patterns greatly differs from defocus blurs which are generated by scatterers. Constructing object waves with constant phases means replacing the materials of the object with the ones that naturally cannot cause light scattering and produce speckles. Consequently, the object wave would lose the propagating characteristic as a scattered wave and fail to provide a faithful appearance of the object in 3D space. Observed along the direction of propagation, however, constant phase generates diffracting outlines instead of defocus blurs, weakening the depth sensation of 3D scenes.

Quadratic phase

The quadratic phase enables the production of faithful, speckle-free, planer reconstructions, especially when it is coordinated with alternating projection algorithms. With the improvements enabled by the double freedoms 103 , 209 and proper bandwidth limitation 102 , 210 , alternating projection algorithms are able to overcome ring artifacts brought about by the quadratic phase, which highly promotes the reconstructing performance in holographic projection.

Nevertheless, the intensity pattern attached to the quadratic phase cannot keep its feature size with the propagation of light 172 , which strictly restricts its application within two-dimensional (2D) holographic projections and beam shaping 211 . As is shown in Fig. 10f , the object wave can be constructed by such a quadratic phase for 3D hologram optimization. In the optimization pipeline, the diffractive wavefronts are converted into CHs and reconstructed at various distances. With the convergent quadratic phase, the object wave is reconstructed with undiffused diffracting patterns at multiple defocus positions. And the reconstructed object intensity cannot maintain its feature size with the enlargement of the reconstructing distance. Because of this enlarging characteristic, the application of the reconstruction for the quadratic phase is limited within 2D holographic projection.

Defining the object phase directly as a quadratic phase has a huge advantage in that it can generate holograms efficiently with a single propagation and avoids speckles. And this quadratic phase approach is indeed applicable to 2D projection. However, it has a consequence that the object wave would lose the propagating characteristic as a scattered wave and fail to provide a faithful appearance of the object and maintain the feature size in 3D space. This is why random phase is still widely used in CGH even after such methods were proposed. Another drawback of introducing well-defined phases, like the constant phase and the quadratic phase, is that any perturbation in the optical configuration of reconstruction, including element damage, dust, or varying illumination, can cause severe degradation in the image quality 71 . This property is concluded as the “robustness” brought about by the initial phase and compared in Table 2 .

Other phase patterns

Some other attempts at adjusting random phase also include imposing constraints on the phase gradient, controlling the standard deviation of phase radius 212 , and limiting the range of phase radius 213 , 214 . A regularization term may be added to the objective function to restrict the variation of some parameters, like the gradient of the object phase, in optimization. With these modifications on the object phase, scattering characteristics of the object wave, which is ensured by sufficient randomness and fluctuating ranges, are weakened synchronously with the suppression of speckles, resulting in various distortions in depth dimension 138 . Table 2 provides a general comparison of 3D reconstructing performances of different initial phases.

In this review article, we have focused on the inverse problem in CGH and provided an overview of various frameworks based on non-convex optimization for appropriate hologram generation. The corresponding algorithms synthesize holograms by searching for optimal solutions within the feasible set restricted by physical models and implementation schemes. Although the computation of holograms is a numerical process, purely computational strategies cannot guarantee the generation of appropriate holograms with faithful reconstruction unless the underlying physics of holography is carefully considered in the calculation. Therefore, this review incorporates an understanding of the fundamental physics in CGH and provides an explanation of the various optimization frameworks, constraints imposed on optimization, 2D/3D optimization pipelines, and object phase initializations utilized in CGH algorithms. Recent advancements in calculation principles and computational strategies have further extended the capabilities of hologram optimization algorithms. By involving cameras or other hardware sets in optimization, the accuracy of planar reconstructions from CGH has been improved significantly. Furthermore, optimization-based hologram synthesis has been enhanced by introducing neural networks, resulting in a significant reduction in computation time to ~1 s 208 , 215 . Further improvement in the computing pipeline has made the optimization of 3D holograms feasible in practice, resulting in natural-like depth perceptions. These progresses have laid a foundation for the fast advance of CGH and been implemented on a wide range of holographic media, including digital micromirror devices, LCoS, DOEs 119 , 216 , and metasurfaces 217 , 218 , 219 , 220 . Overall, the optimization algorithms have significantly improved the accuracy and efficiency when generating appropriate holograms for faithful reconstruction, while considering the fundamental physics of holography, leading to their deployment in various fields.

Data availability

The open-source code for the above-mentioned numerical simulations on 2D and 3D hologram optimization is provided as supplemental materials 221 .

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This work is supported by the National Science Foundation of China (62035003) and the Tsinghua University Initiative Scientific Research Program (20193080075) as well as the Cambridge Tsinghua Joint Research Initiative.

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Sui, X., He, Z., Chu, D. et al. Non-convex optimization for inverse problem solving in computer-generated holography. Light Sci Appl 13 , 158 (2024). https://doi.org/10.1038/s41377-024-01446-w

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Received : 04 January 2024

Revised : 27 March 2024

Accepted : 07 April 2024

Published : 09 July 2024

DOI : https://doi.org/10.1038/s41377-024-01446-w

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Information & Contributors

Bibliometrics & citations, view options, recommendations, extending pareto dominance for multi-constraints satisfaction and multi-performance enhancement in constrained multi-objective optimization.

Multi-objective optimization problems (MOPs) in science and engineering frequently involve intricate multi-constraints. This paper extends the application of the Pareto dominance in MOPs on addressing complex multi-constraints and enhancing algorithmic ...

Dual-grid model of MOEA/D for evolutionary constrained multiobjective optimization

A promising idea for evolutionary constrained optimization is to efficiently utilize not only feasible solutions (feasible individuals) but also infeasible ones. In this paper, we propose a simple implementation of this idea in MOEA/D. In the proposed ...

A Method for Constrained Multiobjective Optimization Based on SQP Techniques

We propose a method for constrained and unconstrained nonlinear multiobjective optimization problems that is based on an SQP-type approach. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front ...

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Elsevier Science Inc.

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Idempotent semifield
Tropical optimization
Log-Chebyshev approximation
Constrained multiobjective optimization
Multiple criteria evaluation
Research-article

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Clearly define the problem

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Document everything

Bring a facilitator

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Design a great agenda

Save time and effort creating an effective problem solving process

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A guide to problem-solving techniques, steps, and skills

The 7 steps to problem-solving

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2. Disaggregate

3. Prioritize problem branches

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