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<p>To rapidly track the dynamic evolution of the Pareto-optimal front (PF) in dynamic multiobjective optimization problems (DMOPs), this paper proposes a dividing-line–hyperplane-intersection-based and associated subpopulation prediction strategy (ISPP). The strategy infers the changes in the Pareto-optimal set (PS) in the decision space from the dynamic characteristics of the PF in the objective space. First, hyperplane fitting and dividing-line setting strategy are used to locate and segment the PF, and to characterize the changing trend of the PF through intersection point sequences at different time steps. Subsequently, the PF is partitioned into multiple subsets through local association operations at the intersection points, establishing a mapping relationship between the PF subsets and the PS subpopulations, where each subpopulation is modeled by a subcenter and a submanifold. When environmental changes occur, the sequences of subcenters are used to estimate the new subcenters, and historical submanifolds are utilized to estimate the new submanifolds, thereby constructing the initial population. In addition, six new test functions are designed, incorporating PS rotation and translation patterns as well as discontinuous PF characteristics. The proposed ISPP-DMOEA is compared with PPS, MDP, KTM, and RNN on 16 test problems, and the results show that the proposed algorithm performs well on the majority of test functions. In particular, it demonstrates distinct advantages on test functions characterized by discontinuous PFs and those undergoing translational or rotational changes at varying frequencies.</p>

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A dividing lines-hyperplane intersection points and associated subpopulations prediction strategy for evolutionary dynamic multiobjective optimization

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Zhao-jun Sheng,
  • Er-chao Li,
  • Li-sen Wei,
  • Chen-miao Liu

摘要

To rapidly track the dynamic evolution of the Pareto-optimal front (PF) in dynamic multiobjective optimization problems (DMOPs), this paper proposes a dividing-line–hyperplane-intersection-based and associated subpopulation prediction strategy (ISPP). The strategy infers the changes in the Pareto-optimal set (PS) in the decision space from the dynamic characteristics of the PF in the objective space. First, hyperplane fitting and dividing-line setting strategy are used to locate and segment the PF, and to characterize the changing trend of the PF through intersection point sequences at different time steps. Subsequently, the PF is partitioned into multiple subsets through local association operations at the intersection points, establishing a mapping relationship between the PF subsets and the PS subpopulations, where each subpopulation is modeled by a subcenter and a submanifold. When environmental changes occur, the sequences of subcenters are used to estimate the new subcenters, and historical submanifolds are utilized to estimate the new submanifolds, thereby constructing the initial population. In addition, six new test functions are designed, incorporating PS rotation and translation patterns as well as discontinuous PF characteristics. The proposed ISPP-DMOEA is compared with PPS, MDP, KTM, and RNN on 16 test problems, and the results show that the proposed algorithm performs well on the majority of test functions. In particular, it demonstrates distinct advantages on test functions characterized by discontinuous PFs and those undergoing translational or rotational changes at varying frequencies.