Traveling Salesman Problem and Statistical Physics

Abstract

We introduce statistical physics approaches to the traveling salesman problem (TSP). TSP is a kind of combinatorial optimization problem which is known to be difficult to solve exactly for large size systems. We develop a new method for solving the TSP based on an idea of real space renormalization theory. It will be shown that the TSP has self similar characteristics, hence the renormalization frame works well for solving the problem. Statistical physics formalism is also presented on solving the TSP by simulated annealing (SA) algorithm. Analytic expression for temperature dependence of the path length is given and compared to numerical simulation. Throughout this work we will provide a new insight to this kind of optimization problem from a viewpoint of statistical physics.