Using simulated annealing to solve routing and location problems

In recent papers by Kirkpatrick et al., an analogy between the statistical mechanics of large multivariate physical systems and combinatorial optimization has been presented and used to develop a general strategy for solving discrete optimization problems. The method relies on probabilistically accepting intermediate increases in the objective function through a set of user‐controlled parameters. It is argued that by taking such controlled uphill steps, from time to time, a high quality solution can eventually be found in a moderate amount of computer time. In this paper, we implement this idea, apply it to the traveling salesman problem and the p‐median location problem, and test the approach extensively.