Mode pursuing sampling method for discrete variable optimization on expensive black-box functions

Abstract

Based on previously developed Mode Pursuing Sampling (MPS) approach for continuous variables, a variation of MPS for discrete variable global optimization problems on expensive black-box functions is developed in this paper. The proposed method, namely, the discrete variable MPS (D-MPS) method, differs from its continuous variable version not only on sampling in a discrete space, but moreover on a novel double-sphere strategy. The double-sphere strategy features two hyperspheres whose radii are dynamically enlarged or shrunk in control of respectively, the degree of "exploration" and "exploitation " in the search of the optimum. Through testing and application to design problems, the proposed D-MPS method demonstrates excellent efficiency and accuracy as compared to the best results in literature on the test problems. The proposed method is believed a promising global optimization strategy for expensive black-box functions with discrete variables. The double-sphere strategy provides an original search control mechanism and has potential to be used in other search algorithms. Copyright © 2008 by ASME.