An Empirical Review of Model-Based Adaptive Sampling for Global Optimization of Expensive Black-Box Functions

This paper reviews the state-of-the-art model-based adaptive sampling approaches for single-objective black-box optimization (BBO). While BBO literature includes various promising sampling techniques, there is still a lack of comprehensive investigations of the existing research across the vast scope of BBO problems. We first classify BBO problems into two categories of engineering design and algorithm design optimization and discuss their challenges. We then critically discuss and analyze the adaptive model-based sampling techniques focusing on key acquisition functions. We elaborate on the shortcomings of the variance-based sampling techniques for engineering design problems. Moreover, we provide in-depth insights into the impact of the discretization schemes on the performance of acquisition functions. We emphasize the importance of dynamic discretization for distance-based exploration and introduce EEPA+, an improved variant of a previously proposed Pareto-based sampling technique. Our empirical analyses reveal the effectiveness of variance-based techniques for algorithm design and distance-based methods for engineering design optimization problems.