Non-Euclidean Traveling Salesman Problem
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.
KeywordsShort Path Travel Salesman Problem Travel Salesman Problem Visibility Graph Visual Noise
Unable to display preview. Download preview PDF.
- 1.S. M. Graham, A. Joshi, and Z. Pizlo. The traveling salesman problem: A hierarchical model. Memory and Cognition, 28:1191–1204, 2000.Google Scholar
- 4.Human problem solving difficult optimization tasks workshop. http://psych.purdue.edu/tsp/workshop/downloads.html. Last accessed January 2008.
- 5.J. M. Jolion and A. Rosenfeld. A Pyramid Framework for Early Vision. Kluwer, Dordrecht, 1994.Google Scholar
- 7.K. Koffka. Principles of Gestalt Psychology. Harcourt, Brace, New York, 1935.Google Scholar
- 15.Z. Pizlo, E. Stefanov, J. Saalwaechter, Z. Li, Y. Haxhimusa, and W. G. Kropatsch. Traveling salesman problem: A foveating algorithm. Journal of Problem Solving, 1:83–101, 2006.Google Scholar
- 17.H. A. Simon. The Sciences of the Artificial. MIT Press., Cambridge, MA, 1996.Google Scholar
- 19.The Journal of Problem Solving. http://docs.lib.purdue.edu/jps/. Last accessed January 2008.
- 20.J. von Neumann and O. Morgenstern. The Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ, 1944.Google Scholar
- 21.R. J. Watt. Scanning from coarse to fine spatial scales in the human visual system after the onset of a stimulus. Journal of the Optical Society of America, A4:2006–2021, 1987.Google Scholar