Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Convex-hull or crossing-avoidance? : solution heuristics in the travelling salesperson problem.
AU - MacGregor, James N.
AU - Chronicle, Edward P.
AU - Ormerod, Thomas C.
PY - 2004/3
Y1 - 2004/3
N2 - Untrained adults appear to have access to cognitive processes that allow them to perform well in the Euclidean version of the traveling salesperson problem (E-TSP). They do so despite the famous computational intractability of the problem, which stems from its combinatorial complexity. A current hypothesis is that humans' good performance is based on following a strategy of connecting boundary points in order (the convex hull hypothesis). Recently, an alternative has been proposed, that performance is governed by a strategy of avoiding crossings. We examined the crossing avoidance hypothesis from the perspectives of its capacity to explain existing data, its theoretical adequacy, and its ability to explain the results of three new experiments. In Experiment 1, effects on the solution quality of number of points versus number of interior points were compared. In Experiment 2, the distributions of observed paths were compared with those predicted from the two hypotheses. In Experiment 3, figural effects were varied to induce crossings. The results of the experiments were more consistent with the convex hull than with the crossing avoidance hypothesis. Despite its simplicity and intuitive appeal, crossing avoidance does not provide a complete alternative to the convex hull hypothesis. Further elucidation of human strategies and heuristics for optimization problems such as the E-TSP will aid our understanding of how cognitive processes have adapted to the demands of combinatorial difficulty.
AB - Untrained adults appear to have access to cognitive processes that allow them to perform well in the Euclidean version of the traveling salesperson problem (E-TSP). They do so despite the famous computational intractability of the problem, which stems from its combinatorial complexity. A current hypothesis is that humans' good performance is based on following a strategy of connecting boundary points in order (the convex hull hypothesis). Recently, an alternative has been proposed, that performance is governed by a strategy of avoiding crossings. We examined the crossing avoidance hypothesis from the perspectives of its capacity to explain existing data, its theoretical adequacy, and its ability to explain the results of three new experiments. In Experiment 1, effects on the solution quality of number of points versus number of interior points were compared. In Experiment 2, the distributions of observed paths were compared with those predicted from the two hypotheses. In Experiment 3, figural effects were varied to induce crossings. The results of the experiments were more consistent with the convex hull than with the crossing avoidance hypothesis. Despite its simplicity and intuitive appeal, crossing avoidance does not provide a complete alternative to the convex hull hypothesis. Further elucidation of human strategies and heuristics for optimization problems such as the E-TSP will aid our understanding of how cognitive processes have adapted to the demands of combinatorial difficulty.
KW - Psychology
KW - Experiments
KW - Cognition & reasoning
M3 - Journal article
VL - 32
SP - 260
EP - 270
JO - Memory and Cognition
JF - Memory and Cognition
SN - 0090-502X
IS - 2
ER -