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Non-Euclidean Traveling Salesman Problem

In: Decision Modeling and Behavior in Complex and Uncertain Environments

Author

Listed:
  • John Saalweachter

    (Purdue University)

  • Zygmunt Pizlo

    (Purdue University)

Abstract

The traveling salesman problem (TSP) is usually studied on a Euclidean plane. When obstacles are placed on the plane, the distances are no longer Euclidean, but they still satisfy the metric axioms. Three experiments are reported in which subjects were tested on the TSP and on the shortest-path problem with obstacles. When the obstacles were simple, and they did not change the global structure of the problem, the subjects were able to produce near-optimal solutions, but the complexity of the mental mechanisms was higher than in the case of the Euclidean TSP. When obstacles were complex and changed the problem's global structure, the solutions were no longer near-optimal. Several computational models are proposed that can account for the psychophysical results.

Suggested Citation

  • John Saalweachter & Zygmunt Pizlo, 2008. "Non-Euclidean Traveling Salesman Problem," Springer Optimization and Its Applications, in: Tamar Kugler & J. Cole Smith & Terry Connolly & Young-Jun Son (ed.), Decision Modeling and Behavior in Complex and Uncertain Environments, pages 339-358, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-77131-1_14
    DOI: 10.1007/978-0-387-77131-1_14
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    Cited by:

    1. Enrico Maria Fenoaltea & Izat B. Baybusinov & Jianyang Zhao & Lei Zhou & Yi-Cheng Zhang, 2021. "The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective," Papers 2103.11458, arXiv.org.

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