The N-city travelling salesman problem: Statistical mechanics and the Metropolis algorithm. (English) Zbl 0551.90095

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.


90C35 Programming involving graphs or networks
90C10 Integer programming
65K05 Numerical mathematical programming methods
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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