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Method to solve the travelling salesman problem using the inverse of diffusion process

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  • Ugajin, Ryuichi

Abstract

The travelling salesman problem, in which the best route between cities to be visited is chosen from a large number of possible routes, is reconsidered using the time reversal of physical dynamics, e.g. an inverse of the diffusion process. Information mediators assigned to every city diffuse as time passes, eventually merging into a single peak. When the time reversal of the dynamics is performed, the single peak splits into two peaks, each of which splits into two peaks, eventually resulting in peaks at all the cities. The hierarchy of the above bifurcations tells us how the distribution of the cities looks as the level of focus changes. This scheme is applied to a travelling salesman problem involving 532 US cities, the result of which is a 17% longer path than the optimal path.

Suggested Citation

  • Ugajin, Ryuichi, 2002. "Method to solve the travelling salesman problem using the inverse of diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 260-268.
    • Handle: RePEc:eee:phsmap:v:307:y:2002:i:1:p:260-268
    DOI: 10.1016/S0378-4371(01)00571-4
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