  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:
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 on 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.
