Balancing Search and Estimation in Random Search Based Stochastic Simulation Optimization

Stochastic simulation optimization involves two fundamental steps: 1) searching the solution space to generate candidate solutions for comparison and 2) estimating the performance of each candidate solution via multiple simulations and selecting a solution as the best solution found. Comparisons of solutions via simulation estimation are subject to error due to the stochastic noise in simulation output. While estimation errors can be reduced by increasing the number of simulation replications, it would in turn limit the number of candidate solutions that can be generated for comparison in a fixed computation budget. Under a random search framework, we derive an analytical formula to (approximately) optimally determine the number of candidate solutions generated in the search step and simulation replications in the estimation step to maximize the quality of the solution selected as the best by the random search algorithm. We then propose a practical method based on this formula and test the method on several common benchmark problems. Experiment results show that our method is quite effective and leads to significant improvement in the quality of the best solution found.