Constrained multiobjective optimization with dynamic Manhattan–Harmony hybrid distance

Abstract In constrained multi-objective optimization problems, the discontinuity of the target space and the fragmentation of the feasible solution space caused by complex constraints make the optimization algorithm face irreconcilable conflicts between convergence, diversity, and feasibility. To this end, this paper proposes a dual population co-evolution algorithm based on a dynamic Manhattan–Harmony hybrid distance. The algorithm constructs a main and auxiliary population with complementary structures: the main population focuses on deep search in the feasible domain, the auxiliary population conducts global exploration in the infeasible area, and introduces an evolutionary stage perception mechanism for differentiated environmental selection. In particular, the proposed dynamic Manhattan–Harmony hybrid distance can effectively characterize the convergence and diversity characteristics of individuals and guide the auxiliary population to adopt adaptive selection strategies at different stages. In addition, the algorithm draws on the theory of biological potential energy diffusion and designs a dynamic resource allocation mechanism that combines three types of potential energy: goal orientation, constraint recovery, and structural diversity, to achieve adaptive scheduling of offspring resources. Furthermore, the constructed bidirectional knowledge transfer channel realizes information sharing and co-evolution between the main and auxiliary populations. Experimental results on 33 standard test functions and 12 real-world problems show that HDCMO outperforms many existing representative constrained multi-objective evolutionary algorithms in terms of convergence, feasibility, and distribution balance, and has significant performance advantages and adaptability.