元知识辅助的小生境差分进化算法求解非线性方程组
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TP18

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国家自然科学基金项目(62362001,62403477,62576325);广西重点研发计划项目(桂科AB25069428);湖北省重点研发项目(2025BEB002);湖北省区域创新体系项目(2025EIA022);国家资助博士后研究人员计划项目(GZC20242271).


Solving nonlinear equation systems with meta-knowledge-based niching differential evolution algorithm
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    摘要:

    非线性方程组的多根联解是一项具有挑战性的任务, 尽管差分进化算法已被广泛应用于求解此类复杂问题, 但进化过程产生的差分向量所蕴含的个体进化信息往往未被充分利用, 影响了算法的性能. 鉴于此, 提出一种基于元知识的小生境差分进化算法. 将进化过程中生成的差分向量视为蕴含搜索经验的“元知识”, 设计神经网络模型对元知识进行学习与建模, 并将环境特征向量作为模型输入, 精准感知个体当前所处的环境, 进而提升所生成预测的差分向量, 高效引导后续种群进化. 同时提出两种基于元知识的变异策略, 以提升算法搜索效率. 实验结果表明, 所提出算法能够有效实现非线性方程组的多根联解, 并在找根率和成功率指标上表现优异.

    Abstract:

    The simultaneous solution of multiple roots of nonlinear equation systems is a challenging task. Although differential evolution algorithms have been widely applied to solve such complex problems, the individual evolutionary information contained in the differential vectors generated during the evolutionary process is often not fully utilized. To address this, this paper proposes a meta-knowledge-based niching differential evolution algorithm. Its main features are as follows: (1) The differential vectors generated in the evolutionary process are regarded as “meta-knowledge” that contains search experience; (2) A neural network model is designed to learn and model meta-knowledge, with environmental feature vectors taken as the model input. This enables accurate perception of the current environment of individuals, thereby improving the differential vectors generated by prediction and efficiently guiding the subsequent evolution of the population; (3) A mutation method based on meta-knowledge is proposed to improve the search efficiency of the algorithm. Experimental results show that the proposed algorithm can effectively realize the simultaneous solution of multiple roots of nonlinear equation systems and perform excellently in terms of the peak rate (PR) and success rate (SR) indicators.

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廖作文,覃慧琳,谷琼,等.元知识辅助的小生境差分进化算法求解非线性方程组[J].控制与决策,2026,41(4):1035-1043

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  • 收稿日期:2025-08-26
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  • 在线发布日期: 2026-03-24
  • 出版日期: 2026-04-10
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