Bridging kriging believer and expected improvement using bump hunting for expensive black-box optimization

For several real-world optimization problems, the evaluation of response functions may be expensive, computationally or otherwise. The number of design evaluations one can afford for such problems are therefore severely limited. Surrogate models are commonly used to guide the search for such computationally expensive optimization problems (CEOP). The surrogate models built using a limited number of true evaluations are used to identify the next infill/sampling location. Expected improvement (EI) is a well known infill criteria which balances exploration and exploitation by accounting for both mean and uncertainties in the current model. However, recent studies have shown that, somewhat counter-intuitively, a greedy ("believer") strategy can compete well with EI in solving CEOPs. In this study, we are interested in examining the relative performance of the two infill methods across a range of problems, and identify the influencing factors affecting their performance. Based on the empirical analysis, we further propose an algorithm incorporating the strengths of the two strategies. The numerical experiments demonstrate that the proposed algorithm is able to achieve a competitive performance across a range of problems with diverse characteristics; making it a strong candidate for solving black-box CEOPs.