Data-Driven Spatial Branch-And-Bound Algorithms For Black-Box Optimization

Abstract The use of high fidelity simulations is becoming more common in computer-aided design and optimization. Due to the complexity of the simulation models and the lack of closed-form mathematical formulations, the direct use of traditional deterministic optimization tools is prohibitive for such problems. Therefore, data-driven decision-making has become increasingly important, with surrogate-based optimization being one of the most popular approaches. Two of the most important challenges in surrogate-based optimization are the lack of consistent convergence metrics, and the variability in the quality of the incumbent solution when a different sampling set or a different surrogate model is used to guide the search. In this work, we propose a strategy to mitigate this uncertainty in the performance of such algorithms. A novel data-driven spatial branch-and-bound framework is proposed that uses stochastic bounds on different surrogate models and partitioning of the search space. The convergence properties of this algorithm are studied through a large set of benchmark problems.