Extension of the direct optimization algorithm for noisy functions

DIRECT (Dividing RECTangles) is a deterministic global optimization algorithm for bound-constrained problems. The algorithm, based on a space-partitioning scheme, performs both global exploration and local exploitation. In this paper, we modify the deterministic DIRECT algorithm to handle noisy function optimization. We adopt a simple approach that replicates multiple function evaluations per point and takes an average to reduce functional uncertainty. Particular features of the DIRECT method are modified using acquired Bayesian sample information to determine appropriate numbers of replications. The noisy version of the DIRECT algorithm is suited for simulation-based optimization problems. The algorithm is a sampling approach, that only uses objective function evaluations. We have applied the new algorithm in a number of noisy global optimizations, including an ambulance base simulation optimization problem.