Memory & Cognition

, Volume 28, Issue 7, pp 1191–1204 | Cite as

The traveling salesman problem: A hierarchical model

  • Scott M. Graham
  • Anupam Joshi
  • Zygmunt PizloEmail author


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.


Convex Hull Problem Size Travel Salesman Problem Travel Salesman Problem Near Neighbor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Burt, P. J. (1981). Fast filter transforms for image processing.Computer Graphics & Image Processing,16, 20–51.CrossRefGoogle Scholar
  2. Christofides, N. (1976).Worst-case analysis of a new heuristic for the traveling salesman problem (Tech. Rep. No. 388). Pittsburgh, PA: Carnegie-Mellon University, Graduate School of Industrial Administration.Google Scholar
  3. Durbin, R., &Willshaw, D. (1987). An analogue approach to the travelling salesman problem using an elastic net method.Nature,326, 689–691.CrossRefPubMedGoogle Scholar
  4. Golden, B., Bodin, L., Doyle, T., &Stewart, W. (1980). Approximate traveling salesman algorithms.Operations Research,28, 694–711.CrossRefGoogle Scholar
  5. Jolion, J. M., &Rosenfeld, A. (1994).A pyramid framework for early vision. Boston: Kluwer.Google Scholar
  6. Karp, R. M. (1977). Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane.Mathematics of Operations Research,2, 209–224.CrossRefGoogle Scholar
  7. Krolak, P., Felts, W., &Marble, G. (1971). A man—machine approach toward solving the traveling salesman problem.Communications of the ACM,14, 327–334.CrossRefGoogle Scholar
  8. Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., &Shmoys, D. B. (1992).The traveling salesman problem. Chichester, U.K.: Wiley.Google Scholar
  9. Lin, S., &Kernighan, B. W. (1973). An effective heuristic algorithm for the traveling-salesman problem.Operations Research,21, 498–516.CrossRefGoogle Scholar
  10. Logan, G. D. (1996). The CODE theory of visual attention: An integration of space-based and object-based attention.Psychological Review,103, 603–649.CrossRefPubMedGoogle Scholar
  11. MacGregor, J. N., &Ormerod, T. (1996). Human performance on the traveling salesman problem.Perception & Psychophysics,58, 527–539.CrossRefGoogle Scholar
  12. McNamara, T. P., Hardy, J. K., &Hirtle, S. C. (1989). Subjective hierarchies in spatial memory.Journal of Experimental Psychology: Learning, Memory, & Cognition,15, 211–227.CrossRefGoogle Scholar
  13. Michie, D., Fleming, J. G., &Oldfield, J. V. (1968). A comparison of heuristic, interactive, and unaided methods of solving a shortestroute problem.Machine Intelligence,2, 245–255.Google Scholar
  14. Ormerod, T. C., &Chronicle, E. P. (1999). Global perceptual processing in problem solving: The case of the traveling salesperson.Perception & Psychophysics,61, 1227–1238.CrossRefGoogle Scholar
  15. Pizlo, Z., Rosenfeld, A., &Epelboim, J. (1995). An exponential pyramid model of the time-course of size processing.Vision Research,35, 1089–1107.CrossRefPubMedGoogle Scholar
  16. Pizlo, Z., Salach-Golyska, M., &Rosenfeld, A. (1997). Curve detection in a noisy image.Vision Research,37, 1217–1241.CrossRefPubMedGoogle Scholar
  17. Platzman, L. K., &Bartholdi, J. J. (1989). Spacefilling curves and the planar traveling salesman problem.Journal of the Association for Computing Machinery,36, 719–737.Google Scholar
  18. Ramachandran, V. S. (1990). Visual perception in people and machines. In A. Blake & T. Troscianko (Eds.),AI and the eye (pp. 21–77). New York: Wiley.Google Scholar
  19. Rosenfeld, A., &Thurston, M. (1971). Edge and curve detection for visual scene analysis.IEEE Transactions on Computers,20, 562–569.CrossRefGoogle Scholar
  20. Scheessele, M. R., Graham, S. M., &Pizlo, Z. (1996). Exponential pyramid as a model of the human visual system. In E. J. Delp, J. P. Allebach, & J. Kovacevic (Eds.),IEEE and IS&T Proceedings of the Ninth Workshop in Image and Multidimensional Signal Processing (pp. 108–109). Los Alamitos, CA: IEEE Computer Society Press.Google Scholar
  21. Van Essen, D. C., &Anderson, C. H. (1995). Information processing strategies and pathways in the primate visual system. In S. F. Zornetzer, J. L. Davis, & C. Lau (Eds.),An introduction to neural and electronic networks (2nd ed., pp. 45–76). New York: Academic Press.Google Scholar
  22. van Oeffelen, M. P., &Vos, P. G. (1982). Configurational effects on the enumeration of dots: Counting by groups.Memory & Cognition,10, 396–404.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2000

Authors and Affiliations

  1. 1.Department of Computer Science and Electrical EngineeringUniversity of MarylandBaltimore
  2. 2.Department of Psychological SciencesPurdue UniversityWest Lafayette

Personalised recommendations