Indicadores de convergência e diversidade em algoritmos evolutivos para otimização multiobjetivo

Abstract

The convergence of Multiobjective Evolutionary Algorithms (MOEA’s) is an important area in the study of this type algorithm, all the same, it is a topic that is currently not adequately represented in the literature, but this fact seems to be a changing one. This relevant importance is highlighted, as convergence is directly linked to the ability of an MOEA to obtain a solution to a problem. Current studies use indicators to observe characteristics in the set of non-dominated solutions of the algorithm, in order to analyze a certain aspect, which aids in the study of convergence. This work proposes two indicators, Concentration Rate (CR) and Diversity Rate (DR), to analyze behavioral characteristics and determine a stopping criteria for MOEA's, in addition to an indicator that can be used to determine the convergence point of a MOEA - Indicator of Stability in Solution Space (S3). To perform the necessary experiments, two MOEA's were proposed, the Simple Estimation of Distribution Algorithm (SEDA) and the Simple Estimation of Distribution Algorithm with Swarm Intelligence (SEDASI), to deal with the Flexible Job Shop Problem. The experiments, which included the MOEA's along with the proposed indicators, as well as those of the literature, were performed with the Flexible Job Shop Problem and the benchmark ZDT. The results showed the effectiveness of the indicators in presenting the proposed characteristics, while assisting in a process that determines the stopping and convergence point of MOEA's, with results that are competitive with those of methods already established in the literature.