From penalty function to learning-driven: evolution and perspectives of constrained multi-objective evolutionary algorithm

With the increasing prevalence of constrained multi-objective optimization problems (CMOPs) in complex systems such as engineering design and intelligent manufacturing, reconciling constraints and multi-objective conflicts in dynamic environments has become a key challenge in evolutionary algorithm research. Traditional optimization methods often exhibit limitations such as insufficient robustness and search efficiency when dealing with complex, high-dimensional, and multi-constraint problems. To address these challenges, learning-driven constraint handling techniques (CHTs) have gradually emerged in recent years, adapting search strategies through the combination of various learning strategies and evolutionary algorithms to explore the feasible solution space more efficiently. This paper systematically reviews the development of constrained multi-objective evolutionary algorithms (CMOEAs), focusing on the evolution from traditional penalty-based methods to learning-driven methods for handling complex CMOPs. It also explores in-depth how learning strategies achieve efficient constraint handling in areas such as adaptive learning, deep learning, and knowledge transfer. To further illustrate the unique advantages of learning-driven methods, the paper compares and analyzes them with traditional optimization methods in terms of applicability, computational complexity, and robustness. Finally, the article reviews various application examples of CMOEAs in CMOPs and discusses the potential of next-generation intelligent, learning-driven CHTs in more complex scenarios, providing a systematic framework for related research from traditional methods to learning-driven strategies and outlining future research directions.