Integration of preferences in multimodal multi-objective optimization

Abstract

Various existing multimodal multi-objective evolutionary algorithms (MMEAs) efficiently search for an approximation to the Pareto optimal front (PF), which consists of multiple equivalent Pareto optimal sets (PSs), when tackling multimodal multi-objective optimization problems (MMOPs). However, in practical applications, the Decision-maker (DM) often seeks specific portions of the PF, known as the Region of Interest (ROI), corresponding to particular instances rather than the whole PF. Existing MMEAs only focus on the whole PF and lack exploration of the ROI. Consequently, we propose an innovative MMEA that incorporates the DM’s preferences and local convergence quality (MMEA-PLC). The proposed algorithm integrates the DM’s preferences into the traditional Pareto-dominance relationship, enabling the search for multiple equivalent Pareto optimal set subsets (PSSs) within the ROI. Due to the influence of local PFs, accurately representing the ROI can be challenging when expressed across different PFs. Therefore, we design a preference-based Pareto-dominance relationship to accurately convey the preferences on different PFs by mapping solutions onto a hyperplane in the objective space. Then, we further develop a scheme for assessing local convergence quality (LCQ) to ensure that the algorithm can identify multiple equivalent PSSs within the same ROI. To verify the effectiveness of the proposed algorithm, MMEA-PLC was experimentally compared with eight state-of-the-art MMEAs on 28 benchmark functions and a real-life application problem. Experimental results show that MMEA-PLC has significant competitive advantages in different preference scenarios.