Algoritmo evolutivo multiobjetivo coevolutivo baseado em cluster para problemas de otimização robusta e ruidosa

Abstract

Optimization plays a fundamental role in engineering; however, uncertainty is a constant in the real world. Recently, evolutionary optimization under uncertainty has emerged as a research field. One segment is robust optimization, which deals with uncertainty in decision variables, and another area is noisy optimization, which addresses uncertainty in objective functions. Both scenarios have significant practical relevance. Although evolutionary algorithms have been developed to handle robust or noisy optimization problems, a fundamental research question is whether these methods can effectively address uncertainties simultaneously. This research addresses this question by extending a function generator available in the literature for multi-objective optimization, incorporating uncertainties in decision variables and objective functions. This allows the creation of customized, scalable problems with any number of objectives. Three specific evolutionary algorithms for robust or noisy optimization were selected: RNSGA-II, RMOEA/D, and CRMOEA/D. The first two use Monte Carlo sampling, while the third is a coevolutionary MOEA/D employing a deterministic robustness measure. Another test was conducted with a function that changes the Pareto Front shape with a parameter. The highlight of this test was the Global Pareto Front having a different shape from the Robust Pareto Front. In this test set, besides CRMOEA/D, RMOEA and MOEA-RE were chosen, two recent robust algorithms with two phases: the first aims to find the global optimum and then the robust solutions. The results demonstrate that these algorithms are not suitable for simultaneously handling noise and perturbation. This work presents a new approach based on the Coevolutionary Robust MOEA/D (CRMOEA/D), enhanced with clustering techniques for offspring generation. Notably, the algorithm eliminates the need for sampling, reducing the number of objective function evaluations and effectively handling both perturbations and noise in optimization problems. The experimental evaluations cover various noise intensities, revealing the impact of different noise levels on the algorithms’ performance. The results indicate that the proposed approach outperforms existing methods in handling simultaneous uncertainties, presenting itself as a promising solution for optimization problems where other methods are insufficient.