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This paper reviews the state-of-the-art model-based adaptive samplingapproaches for single-objective black-box optimization (BBO). While BBOliterature includes various promising sampling techniques, there is still alack of comprehensive investigations of the existing research across the vastscope of BBO problems. We first classify BBO problems into two categories:engineering design and algorithm design optimization and discuss theirchallenges. We then critically discuss and analyze the adaptive model-basedsampling techniques focusing on key acquisition functions. We elaborate on theshortcomings of the variance-based sampling techniques for engineering designproblems. Moreover, we provide in-depth insights on the impact of thediscretization schemes on the performance of acquisition functions. Weemphasize the importance of dynamic discretization for distance-basedexploration and introduce EEPA+, an improved variant of a previously proposedPareto-based sampling technique. Our empirical analyses reveal theeffectiveness of variance-based techniques for algorithm design anddistance-based methods for engineering design optimization problems.

An Empirical Review of Model-based Adaptive Sampling for Global Optimization of Expensive Black-box Functions