Complex problem-solving: a field in search of a definition?

Abstract

Complex problem-solving (CPS) is as an area of cognitive science that has received a good amount of attention, but theories in the field have not progressed accordingly. The reasons could be the lack of good definitions and classifications of the tasks (taxonomies). Although complexity is a term used pervasively in psychology and is operationalized in different ways, there are no psychological theories of complexity. The definition of problem-solving has been changed in the past to reflect the varied interests of the researchers and has lost its initial concreteness. These two facts together make it difficult to define CPS or make clear if CPS should reuse the theory and methods of classical problem-solving or on the contrary should build a theoretical structure starting from scratch. A taxonomy is offered of tasks using both formal features and psychological features that are theory-independent that could help compare the CPS tasks used in the literature. The adequateness is also reviewed of the most extended definitions of CPS and conclude that they are in serious need of review, since they cover tasks that are not considered problem-solving by their own authors or are not complex, but ignore others that should clearly be included.

Keywords:

• Problem solving
• Dynamic decision making
• Micro-worlds
• Expertise

Acknowledgments

About the authors

Walter Kintsch is Professor of Psychology and Director of the Institute of Cognitive Science at the University of Colorado in Boulder. He came to the University of Colorado in 1968 after receiving a PhD in psychology from the University of Kansas and faculty appointments at the University of Missouri and the University of California at Riverside. His research focus has been on the study of how people understand language, using both experimental methods and computational modelling techniques. In co-operation with the Dutch linguist Teun van Dijk, he formulated the first psychological process theory of discourse comprehension in 1978. In 1988, this work was reformulated as a constraint- satisfaction process. His latest book ‘Comprehension’ appeared in 1998 and argues that many cognitive processes can be usefully conceptualized as comprehension processes. Kintsch is a member of the National Academy of Education and received the Distinguished Scientific Contribution Award of the American Psychological Association in 1992 and an honorary doctorate from the Humboldt University in Berlin in 2001.

Jose Quesada is a graduate student in the University of Granada and a research associate at the institute of Cognitive Science, University of Colorado, Boulder. His main interest is in computational theories of knowledge representation and problem-solving. His theoretical work is around Latent Problem Solving Analysis (LPSA), a theory that proposes that when facing complex environments, people represent the task using huge amounts of simultaneous small constraints, in a similar way as when people learn the meaning of words in a natural language. The theory has been tested in several simulated, laboratory environments such as firefighting and thermodynamic systems and also in real-life tasks such as piloting and landing a Boeing 747. In 2002, he was granted an European project to develop an automatic landing technique assessing system based on LPSA, using a high fidelity flying simulator. He administers the Latent Semantic analysis (LSA) web-site (lsa.colorado.edu).

Emilio Gomez is professor of Psychology at the Department of Experimental Psychology of Granada University. He teaches Psychology of consciousness and Motor Processes. His main interests are spatial attention and the shift of mental set. His research focus has been on attentional capture and on how to determine when mental effort is useful or disturbs a problem-solving situation. The main idea of his theoretical work is to study how attention works in complex environments. Latent Problem Semantic Analysis (LPSA) can help to build a measure of strategies switching, a kind of multi-dimensional cost shift of mental set. In 2002 he was granted, together with Jose Quesada, a European grant to develop an automatic landing technique assessing system based on LPSA. In 2003, he was granted a Spanish Government grant to Apply LPSA to the complex relationships between (vote) intention and action (real vote) in national elections, where cost of intention switching has been found.

Notes

Memory retrieval is considered by some as a search activity that can be related to problem-solving as well.

Problem difficulty was initially thought to vary with the size of the problem space. However, some problems are hard even if the problem spaces are small. For example, the Chinese ring puzzle, which requires freeing a metal bar from a series of rings, has an unbranching problem space, so that the solution can be reached simply by never reversing the direction. Nevertheless, this problem, with seven rings, is seldom solved in less than 30 min.

However, Klein et al. (1993) have said that most complex, dynamic decision-making tasks are analytically intractable.

Biology Lab has four input variables (temperature, salt, oxygen and current) that are connected one-to-many to four output variables (prawns, sea bass, lobster and crabs). The objective of the task is to reach a particular level of the output variables.

Weak methods (Newell 1980) are those used by problem-solvers when little is known about the task. As their name indicates, they are not very powerful, but often suffice to solve a problem if the space is not large or if extensive search is undertaken. An example of weak method is ‘Generate and Test’: Generate in any way possible (e.g. systematically or haphazardly) a sequence of candidate states, testing each for whether it is the desired state.