A knowledge driven two-stage co-evolutionary algorithm for constrained multi-objective optimization - Zhang, Wei; Liu, Jianchang; Li, Lin; Liu, Yuanchao; Wang, Honghai (Expert systems with applications, 2025)
In recent years, constrained multi-objective optimization problems (CMOPs) have received wide attention. However, most solving methods for CMOPs still cannot balance objectives and constraints well since constraints make CMOPs have the complicated constrained Pareto front (CPF). This implies that utilizing the related CPF information may be helpful to solve CMOPs. Inspired by the human ability that summarizes the information into different knowledge to address different problems, a knowledge driven two-stage co-evolutionary algorithm (KTCOEA) for CMOPs is developed, including knowledge generation and knowledge application stages. The knowledge generation stage aims at generating two kinds of knowledge: explicit knowledge and implicit knowledge. To this end, main and auxiliary populations co-evolve towards the CPF and unconstrained Pareto front in turn, and then two kinds of knowledge are generated by storing non-dominated solutions and analyzing the correlation of two populations, respectively. Based on the implicit knowledge, reasonable evolution strategies and environmental selection manners are designed for the knowledge application stage, where the explicit knowledge acts as the main population. In this way, the main population can find the complete CPF (i.e., well balance objectives and constraints). In addition, to ensure the generated knowledge quality, a dynamic cooperation mechanism is proposed, which can dynamically adjust the focus of two populations on objectives and constraints based on the performance requirement and evolution status. Experimental results on five benchmark test suites and five real-world applications demonstrate that KTCOEA is better than seven state-of-the-art algorithms on most test problems. •A knowledge driven two-stage co-evolutionary algorithm is developed.•Two kinds of knowledge are generated to guide the population evolution.•Different evolution strategies and selection manners are designed.•A dynamic cooperation mechanism is proposed.