Decision space dynamic niching-based method for constrained multiobjective evolutionary optimization

Finding a set with a good approximation to the Pareto-optimal solutions in the multiobjective optimization problem (MOP) is a challenging task in terms of convergence toward and diversity across the Pareto optimal front (PoF). In some cases, solving MOPs requires satisfying certain constraints, which significantly increases the complexity of the problem. Such problems are constrained multiobjective optimization problems (CMOPs) and pose considerable computational challenges. Many constrained multiobjective evolutionary algorithms (CMOEAs) face challenges in avoiding becoming trapped in local optima, which impacts convergence, and offer solutions that lack good coverage of the PoF, implying weak diversity. All these nonoptimal or partially optimal solutions in the objective space are essentially clustered in local optimality dilemmas in the decision space. To better eliminate the convergence and diversity challenges caused by clustered solutions, this paper proposes a decision space dynamic niching-based (DSDN) method to better address CMOPs. Specifically, the DSDN method adds a dynamic decision space niche as an additional criterion to the traditional Pareto-constrained dominance principle (Pareto-CDP). The better preserved solutions must satisfy the Pareto-CDP and the condition within the niche radius of other solutions, which strictly meets the original dominance relationship requirement while relaxing the nondominance threshold. As a result, the dynamic adjustment of the niche radius (NR) effectively balances the exploitation and exploration of solutions in the decision space while enhancing both convergence and diversity in the objective space. Experiments conducted on four widely recognized test suites and three real-world case studies have demonstrated that the DSDN method yields significantly better results than the original Pareto-CDP algorithms. Furthermore, the proposed approach is competitive with or comparable to seven other state-of-the-art CMOEAs.