A systematic procedure for setting parameters in simulated annealing algorithms

Scope and Purpose—Simulated annealing (SA) algorithms have been successfully applied to various difficult combinatorial optimization problems. To apply an SA algorithm to a specific problem, one must design the algorithm by determining methods to represent solutions, to generate neighborhood solutions and to reduce temperature, etc., and then selecting values of parameters used in the algorithm. Since the performance of an SA algorithm generally depends on values of the parameters, it is important to select the most appropriate parameter values. In previous research, parameter values are often selected using experimental designs such as full factorial designs, which require excessive computation time and efforts and frequent human decisions during the design process. In this paper, we suggest a systematic procedure to find appropriate values for parameters quickly without much human intervention by using a nonlinear optimization method. Values of parameters used in simulated annealing (SA) algorithms must be carefully selected since parameter values may have a significant influence on the performance of the algorithm. However, it is not easy to find good parameter values because values of a wide range have to be considered for each parameter and some parameters may be correlated with each other. In this paper, we suggest a procedure which gives good parameter values quickly without much human intervention by using the simplex method for nonlinear programming. To show the performance of the procedure, computational tests are done on a graph partitioning problem, a permutation flowshop scheduling problem and a short-term production scheduling problem. We select values for parameters needed in SA algorithms for the problems using the suggested procedure. The SA algorithms designed with this procedure are compared with existing SA algorithms in which parameter values were selected after extensive experiments.