A Simulated Annealing Algorithm with Constant Temperature for Discrete Stochastic Optimization

Abstract

We present a modification of the simulated annealing algorithm designed for solving discrete stochastic optimization problems. Like the original simulated annealing algorithm, our method has the hill climbing feature, so it can find global optimal solutions to discrete stochastic optimization problems with many local solutions. However, our method differs from the original simulated annealing algorithm in that it uses a constant (rather than decreasing) temperature. We consider two approaches for estimating the optimal solution. The first approach uses the number of visits the algorithm makes to the different states (divided by a normalizer) to estimate the optimal solution. The second approach uses the state that has the best average estimated objective function value as estimate of the optimal solution. We show that both variants of our method are guaranteed to converge almost surely to the set of global optimal solutions, and discuss how our work applies in the discrete deterministic optimization setting. We also show how both variants can be applied for solving discrete optimization problems when the objective function values are estimated using either transient or steady-state simulation. Finally, we include some encouraging numerical results documenting the behavior of the two variants of our algorithm when applied for solving two versions of a particular discrete stochastic optimization problem, and compare their performance with that of other variants of the simulated annealing algorithm designed for solving discrete stochastic optimization problems.