Thermodynamical approach to the travelling salesman problem: An efficient simulation algorithm
We present a Monte Carlo algorithm to find approximate solutions of the travelling salesman problem. The algorithm generates randomly the permutations of the stations of the travelling salesman trip, with probability depending on the length of the corresponding route. Reasoning by analogy with statistical thermodynamics, we use the probability given by the Boltzmann-Gibbs distribution. Surprisingly enough, using this simple algorithm, one cat get very close to the optimal solution of the problem or even find the true optimum. We demonstrate this on several examples. We conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.
scientific article; zbMATH DE number 3849000