Solving multi-objective structural optimization problems using GDE3 and NSGA-II with reference points

Structural optimization problems can be described as multi-objective optimization problems (MOOPs) due to the presence of multiple conflicting objectives. Recently, procedures based on the decision-maker's preferences have attracted the interest of researchers. This type of information allows for the search technique to focus only on regions of interest instead of all possible solutions. Despite its advantage, incorporating these preferences into the search engine remains scarcely explored in multi-objective structural optimization design problems (MOSOPs). We propose here solving MOSOPs using multi-objective meta-heuristics guided by reference points. Particularly, variants where the decision-maker's preferences drive the search of the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the third evolution step of Generalized Differential Evolution (GDE3), and GDE3 + APM, which is GDE3 equipped with a constraint handling technique called Adaptive Penalty Method (APM), are considered. These approaches are labelled respectively as R-NSGA-II, R-GDE3, and R-GDE3 + APM. It is relevant to highlight that the R-GDE3 and R-GDE3 + APM are proposed in this paper. The results indicate that all were competitive and generated good solutions when solving the MOSOPs considered here. In addition, R-NSGA-II outperformed the remaining techniques in the computational experiments.