Problem solving

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The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of the problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires abstract thinking or coming up with a creative solution.

Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered.

Problem solving in psychology refers to the process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding, in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an end goal to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.

Mental health professionals study the human problem-solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods. Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills.

Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems. Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia.

Computer science is centered around solving problems. Computer Scientist must have solving-problem skills. Problem-Solving in Computer Science is a complex mental process. Therefore it requires; cognitive skills, professional skills, and social skills. Much of computer science and artificial intelligence involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs. These Algorithms are common factors within problem-solving.

Steps for designing such systems include problem determination, heuristics, root cause analysis, de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems, and simulation.

Solving problems within the algorithm begins with problem analysis; identifying the input and output categories within the problems. The next step is solution design, which consists of the determining the best strategy for solving a problem based on the complexity of it. This step also includes; problem decomposition, as well as algorithm development, correctness, and efficiency.

A large, perennial obstacle is to find and fix errors in computer programs: debugging. Debugging uses problem solving skills to enhance programs, and fix issues throughout the process. The debugging process consists of understanding code, editing code, examining code, and testing the code.

Formal logic concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution.

The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the 1950s. It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine, developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the resolution principle developed by John Alan Robinson.

In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science. In 1958, John McCarthy proposed the advice taker, to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning.

The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking.

When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems.

In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypotheses (asking "how?"); deduction evaluates and refines hypotheses based on other plausible premises (asking "why?"); and induction justifies a hypothesis with empirical data (asking "how much?"). The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert. In the Peircean logical system, the logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details (empirical substantiation) to our conceptual knowledge.

Forensic engineering is an important technique of failure analysis that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

Reverse engineering attempts to discover the original problem-solving logic used in developing a product by disassembling the product and developing a plausible pathway to creating and assembling its parts.

In physics, problem solving refers to the process by which one transforms an initial physical situation into a goal state by applying physics-specific reasoning and analysis. This involves identifying the relevant physical principles, making assumptions, formulating and manipulating equations, and checking whether the results are reasonable.

A physics problem is not simply the application or recall of a formula, but requires understanding the underlying concepts and navigating through a “problem space” of possible knowledge states toward the goal.

In military science, problem solving is linked to the concept of "end-states", the conditions or situations which are the aims of the strategy. Ability to solve problems is important at any military rank, but is essential at the command and control level. It results from deep qualitative and quantitative understanding of possible scenarios. Effectiveness in this context is an evaluation of results: to what extent the end states were accomplished. Planning is the process of determining how to effect those end states.

Some models of problem solving involve identifying a goal and then a sequence of subgoals towards achieving this goal. Andersson, who introduced the ACT-R model of cognition, modelled this collection of goals and subgoals as a goal stack in which the mind contains a stack of goals and subgoals to be completed, and a single task being carried out at any time.

Knowledge of how to solve one problem can be applied to another problem, in a process known as transfer.

• A3 problem solving – Structured problem improvement approach
• Design thinking – Processes by which design concepts are developed
• Eight Disciplines Problem Solving – Eight disciplines of team-oriented problem solving methodPages displaying short descriptions of redirect targets
• GROW model – Method for goal setting and problem solving
• Help-seeking – Theory in psychology
• How to Solve It – 1945 book on problem solving by George Pólya
• Lateral thinking – Manner of solving problems
• OODA loop – Observe–orient–decide–act cycle
• PDCA – Iterative design and management method
• Root cause analysis – Method of identifying the fundamental causes of faults or problemsPages displaying short descriptions of redirect targets
• RPR problem diagnosis
• TRIZ – Problem-solving tools
• Scientific method – is an empirical method for acquiring knowledge that has characterized the development of science.
• Swarm intelligence – Collective behavior of decentralized, self-organized systems
• System dynamics – Study of non-linear complex systems

Common barriers to problem solving include mental constructs that impede an efficient search for solutions. Five of the most common identified by researchers are: confirmation bias, mental set, functional fixedness, unnecessary constraints, and irrelevant information.

Functional fixedness is the tendency to view an object as having only one function, and to be unable to conceive of any novel use, as in the Maier pliers experiment described above. Functional fixedness is a specific form of mental set, and is one of the most common forms of cognitive bias in daily life.

As an example, imagine a person wants to kill a bug in their house, but the only thing at hand is a can of air freshener. They may start searching for something to kill the bug instead of squashing it with the can, thinking only of its main function of deodorizing.

Tim German and Clark Barrett describe this barrier: "subjects become 'fixed' on the design function of the objects, and problem solving suffers relative to control conditions in which the object's function is not demonstrated." Their research found that young children's limited knowledge of an object's intended function reduces this barrier Research has also discovered functional fixedness in educational contexts, as an obstacle to understanding: "functional fixedness may be found in learning concepts as well as in solving chemistry problems."

There are several hypotheses in regards to how functional fixedness relates to problem solving. It may waste time, delaying or entirely preventing the correct use of a tool.

Unnecessary constraints are arbitrary boundaries imposed unconsciously on the task at hand, which foreclose a productive avenue of solution. The solver may become fixated on only one type of solution, as if it were an inevitable requirement of the problem. Typically, this combines with mental set—clinging to a previously successful method. Such problems are typically solved via a sudden insight which leaps over the mental barriers, often after long toil against them. This can be difficult depending on how the subject has structured the problem in their mind, how they draw on past experiences, and how well they juggle this information in their working memory. In the example, envisioning the dots connected outside the framing square requires visualizing an unconventional arrangement, which is a strain on working memory.