Solving Multimodal Multi-objective Optimization Problems in Limited Time

In recent years, many multimodal multi-objective evolutionary algorithms (MMOEAs) have been proposed for the widely existing multimodal multi-objective optimization problems (MMOPs) in real-world applications. However, these methods, developed based on artificial benchmark problems with a small number of decision variables, ignore the time efficiency and are ineffective for real-world MMOPs with high-dimensional decision space. To address this issue, this work proposes a time-efficient MMOEA based on SPEA2 by modifying its diversity measure and solution truncation strategy to reduce time complexity to enable solving MMOPs in limited time. Moreover, unlike the common practice in experiments for assessing MMOEAs, we set a limit on the run time rather than sufficient function evaluations as the termination condition. The results show that our algorithm obtains competitive performance on benchmark MMOPs but significantly better performances on real-world applications, including map-based location and feature selection problems, over representative and advanced MMOEAs.