Constrained multi-objective optimization problems: Methodologies, algorithms and applications

Constrained multi -objective optimization problems (CMOPs) are widespread in practical applications such as engineering design, resource allocation, and scheduling optimization. It is high challenging for CMOPs to balance the convergence and diversity due to conflicting objectives and complex constraints. Researchers have developed a variety of constrained multi -objective optimization algorithms (CMOAs) to find a set of optimal solutions, including evolutionary algorithms and machine learning-based methods. These algorithms exhibit distinct advantages in solving different categories of CMOPs. Recently, constrained multi -objective evolutionary algorithms (CMOEAs) have emerged as a popular approach, with several literature reviews available. However, there is a lack of comprehensive-view survey on the methods of CMOAs, limiting researchers to track the cutting-edge investigations in this research direction. Therefore, this paper reviews the latest algorithms for handling CMOPs. A new classification method is proposed to divide literature, containing classical mathematical methods, evolutionary algorithms and machine learning methods. Subsequently, it reviews the modeling and algorithms of CMOPs in the context of practical applications. Lastly, the paper gives potential research directions with respect to CMOPs. This paper is able to provide guidance and inspiration for scholars studying CMOPs.