Um algoritmo híbrido entre Evolução Diferencial e Neder-Mead usando entropia para problemas de otimização não-linear inteiro misto

Abstract

Many problems in engineering are formulated as mixed integer non-linear optimization problems. Stochastic methods have been used due to their performance, flexibility, adaptability and robustness. On the one side, Differential Evolution can be used in any kind of functions and has global search ability. On the other side, the Nelder-Mead algorithm can be used to improve candidate solutions. This work proposes a hybrid approach between Differential Evolution and Nelder-Mead for mixed integer non-linear optimization problems, where the local search is activated by means of the population entropy. The Nelder-Mead algorithm was extended to handle integer variables. The first prototype was developed to solve integer non-linear optimization problems without constraint. The Alpha Constrained method was incorporated to deal with constrained integer non-linear optimization problems. Finally, the approach was aplied to constrained mixed integer non-linear optimization problems showing its effectiveness. The main advantage of this method is the ability to switch between global and local by means of the population entropy during the search.