Learning Enabled Constrained Black-Box Optimization

This chapter looks at the issue of black-box constrained optimization where both the objective function and the constraints are unknown and can only be observed pointwise. Both deterministic and probabilistic surrogate models are considered: the latter, more specifically analysed, are based on Gaussian Processes and Bayesian Optimization to handle the exploration–exploitation dilemma and improve sample efficiency. Particularly challenging is the case when the feasible region might be disconnected and the objective function cannot be evaluated outside the feasible region; this situation, known as “partially defined objective function” or “non-computable domains”, requires a novel approach: a first phase is based on the SVM classification in order to learn the feasible region, and a second phase, optimization, is based on a Gaussian Process. This approach is the main focus of this chapter that analyses modelling and computational issues and demonstrates the sample efficiency of the resulting algorithms.