TwoArchRH: Enhanced Two-Archive Algorithm for Many-Objective Optimization

Abstract

Multi-objective optimization is a cornerstone of modern engineering and management, tackling challenges in complex system design, resource allocation, and financial portfolio optimization. Effective multi-objective optimization algorithms must strike a balance between convergence and diversity, a process that inherently reflects the symmetry in objectives and their trade-offs. However, real-world complexities introduce significant hurdles: the exponential increase in Pareto optimal solutions diminishes the effectiveness of dominance-based selection, while escalating problem complexity heightens the tension between convergence and diversity. To address these issues, we propose a two-archive evolutionary algorithm that integrates reference vectors and a novel hypervolume contribution strategy. This approach employs two complementary archives—convergence and diversity—for parallel optimization. Within the diversity archive, candidate solutions are first filtered using angular relationships to maintain uniform distribution. A novel hypervolume contribution evaluation strategy (HVindex) then determines whether updating solutions can improve the overall quality of the neighborhood population. For the convergence archive, we first select all the non-dominated solutions through non-dominated sorting. These solutions are further refined using reference vectors, and the final archive is completed by adding some opposite characteristic solutions based on distance measurements. The experimental results demonstrate that the proposed algorithm outperforms existing methods in multi-objective optimization.