A coevolutionary algorithm for constrained multi-objective optimization with dynamic relaxation

Abstract

To effectively address constrained multi-objective problems, algorithms need to strike a balance between objectives and constraints. This article introduces a method that utilizes two separate populations to investigate the exploration of the constrained Pareto front (CPF) and the unconstrained Pareto front (UPF). The fitness of each population is evaluated based on the information entropy of their positions, and suitable evolutionary operators are employed to improve solution quality in terms of convergence and diversity. Moreover, by adaptively relaxing constraint conditions, the auxiliary population can traverse large infeasible domains, thereby enhancing solution diversity. In the initial stages, the auxiliary population evolves alongside the main population, bringing it close to the CPF and minimizing computational resource wastage. A tournament environment selection model based on a dynamic relaxation (DR) function is utilized in the later stages, helping the auxiliary population relax constraints, retain promising solutions, and augment diversity. In addition, an entropy selection evolutionary strategy was designed to address the problem of populations easily falling into local optima during the evolution process. By calculating the entropy information of the population, the current state of the population can be determined, and then appropriate operators can be selected to enable the population to effectively escape from local optimal solutions. Compared against seven state-of-the-art algorithms, demonstrate that the proposed constrained multi-objective optimization evolutionary algorithm (CMOEA) surpasses the performance of existing CMOEAs.