Optimization by simulated annealing: A preliminary computational study for the TSP

In recent papers by Kirkpatrick et al.(1982,1983), an analogy between the statistical mechanics of large multivariate physical systems and combinatorial optimization is 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 be found in a moderate amount of computer time. This paper applies an implementation of the proposed algorithm to the TSP for various size networks. The results show the algorithm to be inferior to several well-known heuristics in terms of both solution quality and computer time expended. In addition, set-up time for parameter selection constitutes a major burden for the user. Sensitivity of the algorithm to changes in stopping rules and parameter selection is demonstrated through extensive computational experiments.