An enhanced global evolutionary algorithm using filled functions and estimation of distribution for robust multiobjective optimization

In robust multiobjective optimization, the mean effective objective function (MEOF) is commonly used to evaluate the robustness of solutions. However, when the original objective functions are multimodal, the global Pareto front of the MEOF-based problem may correspond to a local Pareto front of the original problem, which poses a significant challenge for the search of robust solutions. Consequently, traditional multiobjective evolutionary algorithms (MOEAs) face challenges in identifying the global robust MEOF-based PFs, as their primary goal is to locate the global PFs of the original MOPs. In this paper, we introduce a novel global multiobjective evolutionary algorithm that incorporates a filled function and estimation of distribution algorithm (EDA), denoted by MO-EDA/FF, to approximate the global robust PFs of MEOF-based MOPs under the framework of MOEA/D. In our proposed algorithm, the filled functions facilitate the search to escape from local optima by detecting robustness-related multimodal decision variables and reinitializing the evolutionary population within MOEA/D. Moreover, the EDA based on multivariate Gaussian distribution is used to optimize a family of filled weighted sum subproblems, enabling the sampling of numerous offspring solutions within promising search regions. We conduct some experiments to compare the performance of our proposed algorithm with several other state-of-the art MOEAs based on MEOF evaluations on a benchmark set of multiobjective test instances with robustness challenges. Our experimental results demonstrate the competitiveness and advantages of our proposed algorithm in solving these test instances.