Assessment of Robust Multi-objective Evolutionary Algorithms on Robust and Noisy Environments

Abstract

Robust optimization considers uncertainty in the decision variables while noisy optimization concerns with uncertainty in the evaluation of objective and constraint functions. Although many evolutionary algorithms have been proposed to deal with robust or noisy optimization problems, the research question approached here is whether these methods can deal with both types of uncertainties at the same time. In order to answer this question, we extend a test function generator available in the literature for multi-objective optimization to incorporate uncertainties in the decision variables and in the objective functions. It allows the creation of scalable and customizable problems for any number of objectives. Three evolutionary algorithms specifically designed for robust or noisy optimization were selected: RNSGA-II and RMOEA/D, which utilize Monte Carlo sampling, and the C-RMOEA/D, which is a coevolutionary MOEA/D that uses a deterministic robustness measure. We did experiments with these algorithms on multi-objective problems with (i) uncertainty in the decision variables, (ii) noise in the output, and (iii) with both robust and noisy problems. The results show that these algorithms are not able to deal with simultaneous uncertainties (noise and perturbation). Therefore, there is a need for designing algorithms to deal with simultaneously robust and noisy environments.