| Abstract [eng] |
Due to its simplicity and efficiency, the derivative-free global-search DIRECT (DIviding RECTangles) algorithm has received much consideration from the optimization community, and various novel ideas and extensions have been proposed. However, the efficiency of many DIRECT-type algorithms solving multi-modal problems and also in cases when a solution with high accuracy is required has decreased. This thesis presents the new scheme for selecting potentially optimal hyper-rectangles in the DIRECT framework, which addresses two of its weaknesses. An extensive experimental investigation revealed the potential and competitiveness of the added enhancements in our recent proposals, especially for more challenging multi-modal optimization problems. Unfortunately, the original DIRECT algorithm addresses optimization problems only with bounds on the variables, and due to it, the application of the algorithm is limited, as various applied optimization problems often hold other types of constraints. The initial DIRECT extensions for problems with general constraints were not competitive, compared with other derivative-free global optimization methods. Only in recent years, a few promising DIRECT-type modifications were proposed. In this thesis, two different constraint handling techniques are presented, and one of these strategies can even be applied to solve problems with hidden constraints. The proposed algorithms effectively explore hyper-rectangles with infeasible midpoints close to the boundaries of feasibility and may cover feasible regions. An extensive experimental investigation revealed the potential of the proposed approaches compared with other existing DIRECT-type algorithms for constrained global optimization problems, including important engineering issues. Contemporary problems often can not be solved with algorithms reasonably fast using a single core on the fastest computers. However, most DIRECT-type algorithms present challenges for efficient parallel implementation, and only a few parallel versions of DIRECT are known. To the best of our knowledge, all the existing parallel DIRECT-type versions are focused on box-constrained global optimization problems. Since the newly proposed selection scheme per iteration selects a larger number of subdividing regions, the algorithms developed in this thesis look more promising for parallelization than DIRECT. Therefore, the first parallel DIRECT-type algorithms for constrained global optimization problems are also introduced in this thesis. |
