Um estudo de transformações matemáticas em pontos de referência em algoritmos de otimização com muitos objetivos

Abstract

Many-Objective Optimization Problems (MaOPs) are problems that have more than three objective functions to be optimized. Most Multi-Objective Evolutionary Algorithms scale poorly when the number of objective functions increases. To face this limitation, new strategies have been proposed. One of them is the use of reference points to enhance the search of the algorithms. NSGA-III is a reference point based algorithm that has been successfully applied to solve MaOPs. It uses a set of reference points placed on a normalized hyper-plane which is equally inclined to all objective axes and intercepts at 1.0 each axis. Despite the good results of NSGA-III, the shape of the hyper-surface that supports the search is not deeply explored in the literature. This work seeks to propose an algorithm capable of exploring the relation between reference points and the improvement of the search in the optimization of many objective problems. At first, we propose three different mechanisms to transform the set of reference points used by NSGA-III. In addition, the Vector Guided Adaptation (RVEA) procedure is applied to modify periodically the original NSGA-III set of reference points. In a second stage of the development, a new algorithm (K-Greedy) is presented, whose main characteristic is to perform the transformations of the reference points autonomously from a set of available transformations. In the experiments, the performance of the proposed transformations is evaluated both, in separated way (in the first stage) and also when integrated in a pool of the K-Greedy algorithm (in the second stage). In these experiments, the original and adapted versions of the NSGA-III are confronted considering several problems of benchmarking, observing the convergence and diversity through the analysis of statistical tests. The results show that the transformations, especially those alternately carried out by K-Greedy, are able to provide improvements in the NSGA-III without deteriorating the performance when the number of objectives increases.