Surrogate-based methods for black-box and preference-based optimization in control systems

Black-Box and Preference-Based Optimization (BBO and PBO) algorithms look for the global solutions of an optimization problem using, respectively, the least amount of function evaluations or sample comparisons as possible. In BBO, the objective function is unknown (i.e. a black-box) and can only be measured through expensive experiments. In PBO, the objective function is the subjective criterion of an individual (unknown): a human decision-maker compares two calibrations of the decision vector at a time and states which of the two is preferred. Lastly, BBO and PBO problems can include a variety of constraints that define the decision space: some are a-priori known, others may be black-box. BBO and PBO problems are present in disparate control systems applications, e.g. when controller tuning is done via the optimization of a performance indicator or by a human calibrator. Surrogate-Based Methods (SBMs) for BBO and PBO build approximations (i.e. surrogates) of the unknown objective and constraints functions and use them to drive the search. At each iteration, SBMs propose a new calibration to try based on an infill sampling criterion, i.e. a strategy that trades off exploration of the decision space and exploitation of the surrogates. This Book extends four recent SBMs: GLIS (BBO), GLISp (PBO), C-GLIS (BBO) and C-GLISp (PBO). The proposed extensions iteratively vary the emphasis put on exploration and exploitation, and are proven to be globally convergent when no black-box constraints are present. In the presence of black-box constraints, a Probabilistic Support Vector Machine classifier, tailored for BBO and PBO, estimates the probability of feasibility of a calibration. The latter, together with a novel infill sampling criterion, is used in the proposed extensions, which are shown to be more efficient than the original algorithms on several benchmarks. Lastly, the proposed procedures are employed for tuning the position controller of a hydraulic forming press.