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The traveling salesman problem: A hierarchical model

Abstract

Our review of prior literature on spatial information processing in perception, attention, and memory indicates that these cognitive functions involve similar mechanisms based on a hierarchical architecture. The present study extends the application of hierarchical models to the area of problem solving. First, we report results of an experiment in which human subjects were tested on a Euclidean traveling salesman problem (TSP) with 6 to 30 cities. The subject’s solutions were either optimal or near-optimal in length and were produced in a time that was, on average, a linear function of the number of cities. Next, the performance of the subjects is compared with that of five representative artificial intelligence and operations research algorithms, that produce approximate solutions for Euclidean problems. None of these algorithms was found to be an adequate psychological model. Finally, we present a new algorithm for solving the TSP, which is based on a hierarchical pyramid architecture. The performance of this new algorithm is quite similar to the performance of the subjects.

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Correspondence to Anupam Joshi or Zygmunt Pizlo.

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This study was reported at annual meetings of the Society for Mathematical Psychology at Irvine, 1995, and Chapel Hill, 1996 (an abstract is published in the Journal of Mathematical Psychology, 40, 356, 1996), and at the Annual Interdisciplinary Conference in Jackson Hole, 1999. This work was partially supported by NSF Awards ASC 9404859 and CCR 9202536, AFOSR Award F49620-92-J-0069, and ARPA ARO Award DAAH04-94-G-0010.

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Graham, S.M., Joshi, A. & Pizlo, Z. The traveling salesman problem: A hierarchical model. Memory & Cognition 28, 1191–1204 (2000). https://doi.org/10.3758/BF03211820

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Keywords

  • Convex Hull
  • Problem Size
  • Travel Salesman Problem
  • Travel Salesman Problem
  • Near Neighbor