The N-City Travelling Salesman Problem: Statistical Mechanics and the Metropolis Algorithm

In any N-city travelling salesman problem there are (N-1)!/2 possible tours. We use the Metropolis algorithm to generate a sequence of such tours. This sequence may be viewed as the random evolution of a physical system in contact with a heat-bath. As the temperature is lowered, the tours generated...

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Bibliographic Details
Published in:	SIAM review Vol. 26; no. 4; pp. 551 - 568
Main Authors:	Bonomi, Ernesto, Lutton, Jean-Luc
Format:	Journal Article
Language:	English
Published:	Philadelphia The Society for Industrial and Applied Mathematics 01-10-1984 Society for Industrial and Applied Mathematics
Subjects:	Algorithms Annealing Boltzmann distribution Combinatorial optimization Cost functions Entropy Linear programming Metropolitan areas Physics Probabilities Probability Probability distribution Statistical inference Statistical mechanics Statistics
Online Access:	Get full text
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Summary:	In any N-city travelling salesman problem there are (N-1)!/2 possible tours. We use the Metropolis algorithm to generate a sequence of such tours. This sequence may be viewed as the random evolution of a physical system in contact with a heat-bath. As the temperature is lowered, the tours generated approach the optimal tour. It appears that for large N one arrives within a few percent of the optimal solution in better than quadratic time.
ISSN:	0036-1445 1095-7200
DOI:	10.1137/1026105