Optimalizace na Grassmannových varietách pomocí hejnových algoritmů s aplikacemi ve výpočtech elektronových struktur

Abstract

The goal of this bachelor thesis is the modification of the Particle Swarm Optimization method in a way that is suitable for constrained optimization problems used in Electronic Structures Calculations. This work firstly introduces both the optimization problem and the original method. Then a two-step modification of the Particle Swarm Optimization is proposed, which consists of particle projection onto the tangent set and the following restoration back to the feasible set. The modified method was tested. Computations of the potential curve of $Be_2$ molecule yielded satisfactory results in comparison with benchmark data. The main contribution of this work is the invention of a new modification of Particle Swarm Optimization suitable for constrained optimization problems.