Abstract:The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human performance on the TSP and related problems, and discuss the main theoretical explanations that have been offered. We then review some related developments in animal studies, spatial cognition, and neuropsychology. The article closes with a brief look at possible future directions.

The article provides a review of recent research on insight problem-solving performance. We discuss what insight problems are, the different types of classic and newer insight problems, and how we can classify them. We also explain some of the other aspects that affect insight performance, such as hints, analogs, training, thinking aloud, and individual differences. In addition, we describe some of the main theoretical explanations that have been offered. Finally, we present some measures of insight and relevant neuroscience contributions to the area over the last decade.

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In this paper we conducted three experiments using the cheap necklace problem, which is regarded as an insight problem. The effects of two hints derived from two contemporary theoretical accounts of insight-Criterion for Satisfactory Progress theory (CSP) and Representational Change Theory (RCT)-were investigated. In Experiment 1, 78 participants made a single attempt at the problem, and significantly fewer participants given the CSP hint used an incorrect (maximizing) first move than participants given the RCT hint or control participants given no hint, Fisher's exact test for 2x3 table, p = .029, with an approximation in χ² effect size, phi = .340. Experiment 2 explored the performance of 60 participants in the same hint conditions over ten problem-solving trials. The number of trials to solution was significantly fewer in the CSP hint condition than in the control condition, t(30) = 2.23, p = .033, η² = .14; this was not so for the RCT hint condition, t(30) = .44, p = .666, η² = .006. Furthermore, there were significantly fewer incorrect (maximizing) first moves in the CSP hint condition than in the other two conditions, F(2, 59) = 15.31, p < .001, η² = .35. The CSP hint here appears to promote the exploration of the problem space, such that the correct move may be found. The lack of effect of the RCT hint suggests in preliminary fashion that representational change may not be the primary cognitive process required to solve the cheap necklace problem. However, in Experiment 3 with 110 participants, the CSP and RCT hints were combined yielding a 75% solution rate over a 34.88% solution rate in the control condition, χ²(1) = 16.03, p < .001, phi = .402. This result indicates that perhaps aspects from both theories are employed during the problem solving process.

Planning is fundamental to successful problem solving, yet individuals sometimes fail to plan even one step ahead when it lies within their competence to do so. In this article, we report two experiments in which we explored variants of a ball-weighing puzzle, a problem that has only two steps, yet nonetheless yields performance consistent with a failure to plan. The results fit a computational model in which a solver's attempts are determined by two heuristics: maximization of the apparent progress made toward the problem goal and minimization of the problem space in which attempts are sought. The effectiveness of these heuristics was determined by lookahead, defined operationally as the number of steps evaluated in a planned move. Where move outcomes cannot be visualized but must be inferred, planning is constrained to the point where some individuals apply zero lookahead, which with n-ball problems yields seemingly irrational unequal weighs. Applying general-purpose heuristics with or without lookahead accounts for a range of rational and irrational phenomena found with insight and noninsight problems.