An efficient simulated annealing algorithm for stochastic systems

In the fields of management and administrative science, operations research and industrial engineering, many practical problems can be modeled as discrete stochastic optimization problems where the objective function can be evaluated only through Monte Carlo simulation. In this paper we present a modification of the simulated annealing algorithm (SA) for solving discrete stochastic optimization problems where the acceptance probability depends on whether the objective function values indicate a statistically significant difference at each iteration. Similar to the original SA algorithm, the proposed approach has the hill climbing feature to escape the trap of local optima. However, our method uses constant temperature rather than decreasing temperature, and selects the estimated optimal solution as the state with the best average estimated objective function value obtained from all the previous estimates of the objective function value. We show that the proposed modification converges almost surely to the set of optimal solutions. Computational results and comparisons with other variants are given to demonstrate the performance of the proposed modified SA algorithm.