Algoritmos determinístico e evolucionário intervalarespara otimização robusta multi-objetivo

Abstract

This thesis considers the presence of uncertainties in the modeling ofnonlinear multi-objective optimization problem. To solve these nonlinearmulti-objective robust optimization problems, three original search methods has been proposed using worst-case scenario strategies: [I]RMOA I and [I]RMOA II, that use interval deterministic techniques, and [I]RMOEA that uses evolutionary algorithms and deterministic interval techniques. The found efficient solutions in this context are called efficient robust solutions or non-dominated robust solutions. These algorithms are at great length described, as well as the analysis of their characteristics, advantages and disadvantages. Beyond these original contributions, this work also considers: a) one technique of niches, based on intervals, useful to keep diversity in the populations in evolutionary algorithms; b) a metric technique to measure uniformity in the non-dominated points distribution; c) a set of test functions, suitable for robust optimization; e d) the description and resolution of a multi-objective robust optimization problem about PID controller tuning. In addition, this text presents and argues the sources of uncertainties, as well as their probabilistic and deterministic interpretations in optimization problems.