Prostor vyplňující křivky a jejich využití v optimalizaci

Abstract

This thesis deals with the use of space-filling curves in solving global optimization problems. By means of these curves, the original multidimensional optimization problem can be transformed into the problem of minimizing a function of a single variable. The thesis focuses specifically on the Hilbert curve as a representative of space-filling curves. The text describes the construction of the 2D and 3D Hilbert curve iterations, their arithmetic representation, and the related Hölder continuity. Furthermore, an algorithm for the optimization of one-dimensional Hölder functions is presented, together with numerical experiments focused on the influence of parameters on the efficiency of the algorithm and on the achieved results. This algorithm is also compared with the differential evolution method.