Global Optimization for Black-Box Simulation via Sequential Intrinsic Kriging

Abstract

In this paper we investigate global optimization for black-box simulations using metamodels to guide this optimization. As a novel metamodel we introduce intrinsic Kriging, for either deterministic or random simulation. For deterministic simulation we study the famous `efficient global optimization' (EGO) method, substituting intrinsic Kriging for universal Kriging. For random simulation we investigate a state-of-the-art two-stage algorithm accounting for heteroscedastic variances of the simulation responses, and introduce a new variant with the following two features: (1) this variant uses intrinsic Kriging; (2) this variant uses a different procedure to allocate the total available number of replications over simulated points. We perform several numerical experiments with deterministic and random simulations, to compare (1) the classic EGO and our EGO with intrinsic Kriging; (2) the classic two-stage algorithm and our modified version. We conclude that in most experiments (1) EGO with intrinsic Kriging outperforms classic EGO; (2) there is no significant difference between the classic algorithm and our modifed two-stage algorithm.