Growing Neural Gas Network-based surrogate-assisted Pareto set learning for multimodal multi-objective optimization

The key issue in handling multimodal multi-objective optimization problems (MMOPs) is to find multiple Pareto sets (PSs) corresponding to one Pareto front (PF). Therefore, learning the PSs is critical to facilitate solving MMOPs while unfortunately, current research only focuses on PF learning which is helpless in finding multiple PSs by the information of one PF. Moreover, since the PSs of an MMOP are usually non-functional, traditional approximative function model-based PF learning is inapplicable. Consequently, developing new PS learning techniques is desired. Inspired by data-driven evolutionary algorithms, data can be used to train surrogate models to assist the algorithm. This article proposes an online data-driven PSs learning technique that aims to learn the topologies of PSs through a surrogate model to facilitate the search for PSs. Specifically, the Growing Neural Gas network is trained using non-dominated solutions to learn the topologies of PSs during the evolutionary process. Then, the nodes of the network are used to generate new solutions and adopted as reference points for environmental selection. A new algorithm is developed based on the PS learning technique for MMOPs. Experimental studies on three benchmark test suites and two different real-world applications demonstrate the superiority of our method over six state-of-the-art algorithms dedicated to MMOPs. The PSs learning technique can obtain the topologies of PSs and facilitate the search for them.