problem solving

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. Another classification 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. 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.

Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, and consultants are largely problem solvers for issues which 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. Additionally, the mental obstacles preventing people from finding solutions is a widely researched topic: problem solving impediments include confirmation bias, mental set, and functional fixedness.

Definition

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. Schacter, D.L. et al. (2009). Psychology, Second Edition. New York: Worth Publishers. pp. 376 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 the problem requires abstract thinking or coming up with a creative solution.

Psychology

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 and problem shaping, where 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 and 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.

Problem solving has two major domains: mathematical problem solving and personal problem solving. Both are seen in terms of some difficulty or barrier that is encountered.Bernd Zimmermann, ''On mathematical problem solving processes and history of mathematics'', University of Jena. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying individuals 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 the individual personal motivational and contextual components. One such component is the emotional valence of "real-world" problems and it 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 and impede problem resolution and likely lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization, human problem solving consists of two related processes: problem orientation and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. Studies conclude people's strategies cohere with their goals and stem from the natural process of comparing oneself with others.

Cognitive sciences

Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, e.g., Karl Duncker in ''The Psychology of Productive Thinking'' (1935). Perhaps best known is the work of Allen Newell and Herbert A. Simon.

Experiments the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi, admitted optimal solutions which could be found quickly, allowing observation of 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.

An outstanding problem solving technique found by this research is the principle of decomposition.

Computer science

Much of computer science and artificial intelligence involves designing automatic 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. A large, perennial obstacle is to find and fix errors in computer programs: debugging.

Logic

Formal logic is concerned with such issues as 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 als