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<p>To address the challenge of balancing convergence and diversity in many-objective optimization problems (MaOPs), this paper introduces a novel evolutionary algorithm named reference vectors and hyper-distance based evolutionary algorithm (RHEA). RHEA leverages reference vectors to divide the population into multiple clusters. To evaluate convergence, it employs a hyper-distance metric, which measures the Euclidean distance of solutions within each cluster to their respective local hyperplane. To assess diversity, RHEA utilizes the sine function of the angle between each solution and its associated reference vector. By combining these two components into a fitness value, RHEA selects solutions from each cluster that exhibit balanced convergence and diversity. If the selected solutions do not meet the population size, RHEA employs a max–min-angle strategy to fill the gap by selecting unselected solutions based on their angles to the already selected solutions. Extensive empirical experiments against ten algorithms on DTLZ, WFG, and MaF test suites demonstrate the effectiveness and competitiveness of RHEA in handling MaOPs.</p>

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A many-objective evolutionary algorithm based on reference vectors and hyper-distance

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Xujian Wang,
  • Yongjin Jing,
  • Fenggan Zhang,
  • Minli Yao

摘要

To address the challenge of balancing convergence and diversity in many-objective optimization problems (MaOPs), this paper introduces a novel evolutionary algorithm named reference vectors and hyper-distance based evolutionary algorithm (RHEA). RHEA leverages reference vectors to divide the population into multiple clusters. To evaluate convergence, it employs a hyper-distance metric, which measures the Euclidean distance of solutions within each cluster to their respective local hyperplane. To assess diversity, RHEA utilizes the sine function of the angle between each solution and its associated reference vector. By combining these two components into a fitness value, RHEA selects solutions from each cluster that exhibit balanced convergence and diversity. If the selected solutions do not meet the population size, RHEA employs a max–min-angle strategy to fill the gap by selecting unselected solutions based on their angles to the already selected solutions. Extensive empirical experiments against ten algorithms on DTLZ, WFG, and MaF test suites demonstrate the effectiveness and competitiveness of RHEA in handling MaOPs.