Heuristics for Comparing the Lengths of Completed E-TSP Tours: Crossings and Areas

The article reports three experiments designed to explore heuristics used in comparing the lengths of completed Euclidean Traveling Salesman Problem (E-TSP) tours. The experiments used paired comparisons in which participants judged which of two completed tours of the same point set was shorter. The first experiment manipulated two factors, the presence/absence of crossed arcs, and the relative areas of the enclosed polygons. Both factors significantly influenced judgments, with the absence of crossings and smaller areas being associated with shorter tours. The second experiment examined the effects of crossings only, and compared stimulus pairs using all possible combinations of no, one, and more than one crossing. The results showed a significant tendency for tours with one or more crossings to be judged longer than tours with none, while tours with more crossings were not judged to be longer than tours with only one. Apparently the mere presence of a crossing is sufficient to cause a tour to be judged as longer. The third experiment examined the effects of area only, and consisted of two parts. In the first part, participants judged which of two tours that differed in area was shorter. The results supported those of the first experiment, by finding that tours with smaller areas tended to be judged as shorter. In the second part of the experiment, participants judged the relative areas of each pair, to determine whether people can reliably differentiate the areas of such complex polygons. The results confirmed that they can, thereby supporting the feasibility of using differences in area as a heuristic to judge relative lengths. The results were discussed in terms of Carruthers’s (2015) proposal of goal modification and the suggestion is made that applying heuristics of the type identified may represent a specific form of goal modification.