Global and preference-based optimization using surrogate-based methods

This thesis explores methodologies in black-box and preference-based optimization, addressing three key research questions. Firstly, it introduces a semi-automated calibra- tion approach that eliminates the need for an explicit per- formance index by relying on human calibrator preferences. Secondly, the thesis delves into preference-based global op- timization algorithms that address optimization problems where the analytic expression of the objective function is unknown and the optimization is subject to unknown con- straints. The proposed algorithm, C-GLISp, extends the active preference learning framework to handle these un- known constraints. Lastly, the thesis tackles the challenge of optimization problems involving mixed variables and lin- ear constraints. To address this challenge, we present a novel surrogate-based global optimization algorithm, named PWAS. The algorithm constructs a piecewise affine surrogate of the objective function over feasible samples and utilizes ex- ploration functions to efficiently navigate the feasible domain using mixed-integer linear programming solvers. Addition- ally, a preference-based version of the algorithm, PWASp, is introduced to handle situations where only pairwise compar- isons between samples are available instead of direct objec- tive function evaluations. The efficiency and effectiveness of the proposed approaches are demonstrated via benchmark studies. Additionally, the practical applicability of PWAS is discussed via experimental design case stuides.