Metodi basati su surrogati per l'ottimizzazione black-box e a preferenze nell'ambito dei sistemi di controllo

Black-Box Optimization (BBO) and Preference-Based Optimization (PBO) algorithms are global optimization procedures that aim to find the global solutions of an optimization problem using, respectively, the least amount of function evaluations or sample comparisons as possible. In the black-box setting, the analytical expression of the objective function is unknown (i.e. it is a black-box) and it can only be measured through expensive computer simulations or real-world experiments. Instead, in the preference-based framework, the objective function is still unknown, but it corresponds to the subjective criterion of an individual, which cannot be quantified reliably. Therefore, PBO algorithms seek global solutions using only comparisons between couples of different calibrations of the decision vector, for which a human decision-maker indicates 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 are black-box constraints. In preference-based optimization, the feasibility of a calibration could even be assessed directly by the decision-maker, giving rise to a decision-maker-based constraint. In control systems applications, black-box and preference-based optimization methods are valuable tools for controller tuning purposes. BBO algorithms can be employed whenever there is the need to optimize performance indicators that can only be assessed by performing experiments on the system. Instead, PBO methods can assist a human calibrator during the controller tuning process, potentially replacing the trial-and-error industry practice. Surrogate-based methods are the de facto standard algorithms for BBO and PBO. These methods build approximations (i.e. surrogates) of the unknown objective and constraints functions and use them to drive the search for the global solutions. At each iteration, surrogate-based methods propose a new calibration to try based on a so-called infill sampling criterion, which is a strategy that trades off exploration of the decision space and exploitation of the surrogates. This Thesis extends four recent surrogate-based methods: GLIS (BBO), GLISp (PBO), C-GLIS (BBO) and C-GLISp (PBO). The former two only consider a-priori known constraints, while the latter two also handle black-box (or decision-maker-based) constraints. Differently from the original methods, the proposed extensions of GLIS and GLISp iteratively vary the emphasis put on exploration and exploitation, and are proven to be globally convergent. Notably, in the preference-based optimization literature, no other surrogate-based method is shown to be globally convergent. Additionally, this Thesis derives a globally convergent general surrogate-based scheme, which can be employed either for BBO or PBO. Empirically, the proposed extension of GLISp proves to be more robust than the original method on several benchmark optimization problems. When black-box (or decision-maker-based) constraints are present, many surrogate-based methods estimate the probability of feasibility of a calibration through a Probabilistic Support Vector Machine (PSVM) classifier. In this Thesis, a revisited PSVM classifier, tailored for BBO and PBO, is presented. The latter, together with a novel infill sampling criterion, is employed in the proposed extensions of C-GLIS and C-GLISp to penalize the search in those zones of the decision space that are likely to contain infeasible calibrations. The revisited methods are shown to be more efficient than the original algorithms on several benchmark optimization problems. Lastly, all the proposed procedures are employed for the calibration of the position controller of a hydraulic forming press.