Desenvolvimento de métodos para solução de problemas de otimização multiobjetivo com incertezas

Abstract

The multiobjective optimization is rather used on the design phase of a system, whereby a set of approximated Pareto-optimal solutions is obtained for the system model under design. However, many sources of uncertainties in real world may jeopardize the solutions optimal condition reach so far. These uncertainties must be identified, measured, and taken into account on the design phase, aiming to minimize their impact on the following phases. Thus, multiobjective robust optimization methods have been widely employed on design phases in order to reduce the harmful effects of uncertainties. This thesis presents the different types of uncertainties, the concept of robust solutions, the most common methods of robust optimization in the literature, and the proposal of a set of test functions for robust optimization, a set of new robust metrics and robust optimization methods, which were combined for developing new algorithms for multiobjective robust optimization. Three novel algorithms are highlighted in this thesis for solving problems with interval parametric uncertainties: 1) Worst Case Estimation Multiobjective Evolutionary Algorithm (WCEMOEA), uses the minimax formulation jointly with a worst case scenario estimator to find solutions that minimize the worst case; 2) Robust Hypercube Space Partitioning Evolutionary Algorithm (RHySPEA), combines the use of two new robustness metrics with the use of an external database to measure and minimize the solutions sensitivity against uncertainties with few resampling; 3) Minimum Deviation Evolutionary Algorithm based on Robustness Factor (MDEA-RF), which is a novel iterative method aiming to minimize the maximum deviation of a perturbed solution based on the definition of a robustness factor by the decision maker. The algorithms were applied to test functions, and to real engineering problems, being successful to find robust solutions efficiently, with few model evaluations.