Abstract
We present an application of the Kohonen algorithm to the traveling salesman problem: Using only this algorithm, without energy function nor any parameter choosen “ad hoc”, we found good suboptimal tours. We give a neural model version of this algorithm, closer to classical neural networks. This is illustrated with various numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bearwood J, Halton JH, Hammersley JM (1959) The shortest path through many points. Proc Cambridge Phil Soc 55
Bonomi E, Lutton JL (1984) The n-city traveling salesman problem: statistical mechanics and Metropolis algorithm. SIAM Rev 26
Cottrell M, Fort JC (1987) Etude d'un processus d'autoorganisation. Ann IHP 23
Durbin R, Willishaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Science 326
Kirkpatrick S, Gelatt CD, Vecchi MP (1982) Optimization by simulated annealing. Res Rep 9335, IBM Thomas J. Watson Center, NY
Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43
Kohonen T (1984) Self-organization and associative memory. Springer, Berlin Heidelberg New York
Ritter H, Shulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping. Biol Cybern 54:99–106
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fort, J.C. Solving a combinatorial problem via self-organizing process: An application of the Kohonen algorithm to the traveling salesman problem. Biol. Cybern. 59, 33–40 (1988). https://doi.org/10.1007/BF00336888
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00336888