| Abstract [eng] |
In this thesis, Direct (DIviding RECTangles) type algorithms based on Lipschitz objective function models with unknown Lipschitz constant, which are often applied for practical black-box optimization problems, are considered. The main goal of this thesis is set - to propose a global optimization algorithm for Lipschitz functions with unknown Lipschitz constants in order to efficiently spend potentially expensive function evaluations. For the considered class of algorithms, a new simplicial optimization algorithm Libre (LIpschitz Bound Rough Estimation) is proposed, which is based on Disimpl (DIviding SIMPLices) algorithms. The novelty of the proposed algorithm is that a single estimate of the Lipschitz constant is used instead of a set to select potential simplices for division. Experimental analysis is conducted and the competitiveness of the proposed algorithm to other best algorithms from this algorithm class is shown. In addition, various modifications of the Libre algorithm are proposed and experimentally investigated; the impact of the tightness of the surogate Lipschitz bounds on the efficiency of the Libre algorithm is demonstrated. Moreover, a strategy to generalize Lipschitzian global optimization algorithms for multi-objective problems is proposed. Libre algorithm is generalized for multi-objective problems by applying the proposed strategy and then experimentally investigated. |
