基于邻域交叉的双变异差分进化算法求解非线性方程组  

Solving nonlinear equation systems with neighborhood crossover-based dual-mutation differential evolution algorithm

作　　者：赵世杰[1,2] 赵秋丽 陈淼 崔倩倩 ZHAO Shi-jie;ZHAO Qiu-li;CHEN Miao;CUI Qian-qian(College of Science,Liaoning Technical University,Fuxin 123000,China;Institute for Optimization and Decision Analytics,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000 [2]辽宁工程技术大学运筹与优化研究院,辽宁阜新123000

出　　处：《控制与决策》2025年第2期546-552,共7页Control and Decision

基　　金：辽宁省教育厅基本科研项目(JYTMS20230802);辽宁省自然科学基金面上项目(2023-MS-317);辽宁省研究生教育教学改革研究资助项目(LNYJG2023119)。

摘　　要：非线性方程组问题的求解难点在于多根联解的同步解出,针对邻域拥挤差分进化算法存在的多根解出不完整、丢根及易陷入局部最优等问题,提出一种基于邻域交叉的双变异差分进化算法.双变异策略基于个体适应度值综合学习邻域和全局的进化信息,以提高种群多样性并同步增强其局部最优规避性能;邻域交叉策略通过种群分组与不同交叉操作实现进化个体的差异性引导,以规避多根的联解丢失并改善计算资源的利用效率.实验结果表明,所提算法能够有效实现非线性方程组的多根联解,且在找根率和成功率指标上表现优异.The difficulty of solving nonlinear equation systems(NESs)lies in how to achieve the synchronous parsing of multiple-root joint solution.Since neighborhood-based crowding differential evolution algorithm has many problems such as incomplete solution of multiple roots,loss of roots and easy to fall into local optimality,a neighborhood crossover-based dual-mutation differential evolution algorithm is proposed.The dual-mutation strategy is based on individual fitness values to learn both neighborhood and global evolutionary information,which results in improving population diversity and simultaneously enhancing the local optimum avoidance performance.The neighborhood crossover strategy employs the population grouping mechanism and different crossover operations to achieve differential guidance of evolutionary individuals,which contributes to avoiding the loss of joint solution of multiple roots and improving the computing resources utilization efficiency.The experimental results show that the proposed algorithm can effectively realize the multi-root joint solution of NESs and has outstanding capacity on the index of root rate and success rate.

关 键 词：智能优化算法 非线性方程组 差分进化算法 双变异策略 邻域交叉策略 种群多样性 多根联解 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]