Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.[1] Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for.[2] Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices.[3]
Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution.
There are many specialized problem-solving techniques and methods in fields such as engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include confirmation bias, mental set, and functional fixedness.
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.[2] 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 in psychology refers to the process of finding solutions to problems encountered in life.[5] Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping, 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.[6]
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.[7] 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.[8]
Empirical research shows many different strategies and factors influence everyday problem solving.[9] 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.[10] 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,[11] 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.[12] In conceptualization,[clarification needed]human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills.[13] People's strategies cohere with their goals[14] and stem from the process of comparing oneself with others.
Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, such as Karl Duncker in The Psychology of Productive Thinking (1935).[15] Perhaps best known is the work of Allen Newell and Herbert A. Simon.[16]
Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks.[17][18] These simple problems, such as the Tower of Hanoi, admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic cognitive processes by which more complex "real world" problems are solved.
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.
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.[20] A large, perennial obstacle is to find and fix errors in computer programs: debugging.
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,[21] which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving[22] and computational logic to improve human thinking.[23]
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?").[24] The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert.[25] 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.[26]
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.[27]
Common steps in this cycle include recognizing the problem, defining it, developing a strategy to fix it, organizing knowledge and resources available, monitoring progress, and evaluating the effectiveness of the solution. Once a solution is achieved, another problem usually arises, and the cycle starts again.
Insight is the sudden aha! solution to a problem, the birth of a new idea to simplify a complex situation. Solutions found through insight are often more incisive than those from step-by-step analysis. A quick solution process requires insight to select productive moves at different stages of the problem-solving cycle. Unlike Newell and Simon's formal definition of a move problem, there is no consensus definition of an insight problem.[31]
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.
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