High-dimensional Black-box Optimization Under Uncertainty

Limited informative data remains the primary challenge for optimization the expensive complex systems. Learning from limited data and finding the set of variables that optimizes an expected output arise practically in the design problems. In such situations, the underlying function is complex yet unknown, a large number of variables are involved though not all of them are important, and the interactions between the variables are significant. On the other hand, it is usually expensive to collect more data and the outcome is under uncertainty. Unfortunately, despite being real-world challenges, exiting works have not addressed these jointly. We propose a new surrogate optimization approach in this article to tackle these challenges. We design a flexible, non-interpolating, and parsimonious surrogate model using a partitioning technique. The proposed model bends at near-optimal locations and identifies the peaks and valleys for optimization purposes. To discover new candidate points an exploration-exploitation Pareto method is implemented as a sampling strategy. Furthermore, we develop a smart replication approach based on hypothesis testing to overcome the uncertainties associated with the black-box outcome. The Smart-Replication approach identifies promising points to replicate rather than wasting evaluation on less informative data points. We conduct a comprehensive set of experiments on challenging global optimization test functions to evaluate the performance of our proposal.