基于双目标的MNSGA-Ⅱ算法求解非线性方程组
MNSGA-Ⅱ algorithm based on bi-objective for solving nonlinear equation systems
李侦瑷 1韦慧 1陈馨1
作者信息
- 1. 安徽理工大学数学与大数据学院,安徽淮南 232001
- 折叠
摘要
通过MONES转换技术将非线性方程组转换为双目标优化问题,利用MNSGA-Ⅱ算法中的动态拥挤距离策略提高Pareto解集的多样性,在种群选择过程中动态计算个体的拥挤距离.为了验证算法的性能,选择30个非线性方程组进行测试,对比了基于MONES转换技术的NSGA-Ⅱ、动态NSGA-Ⅱ和MNSGA-Ⅱ算法.实验结果表明,基于MONES转换技术的MNSGA-Ⅱ算法在寻根率和成功率方面更具优势.最后,将3个算法得到的Pareto前沿进行对比,且验证本文算法所得Pareto前沿在均匀性和收敛性方面表现较好.
Abstract
MONES transformation technique is applied to transform the problem of solving nonlinear equation systems into a bi-objec-tive optimization problem,and a dynamic crowding distance strategy of MNSGA-Ⅱ algorithm is included to dynamically calculate indi-vidual crowding distance in the process of population selection,which improves the diversity of Pareto front.In order to verify the per-formance of algorithm,thirty nonlinear equation systems are selected for testing NSGA-Ⅱ,dynamic NSGA-Ⅱ and MNSGA-Ⅱ algo-rithm based on MONES transformation technique.Experimental results show that MNSGA-Ⅱ algorithm based on MONES transforma-tion technique has a better root-found ratio and success rate.Finally,the Pareto front of three algorithms mentioned above is compared,and the uniformity and convergence of Pareto front of the proposed algorithm performs better than others'.
关键词
非线性方程组/MONES转换技术/动态拥挤距离/非支配排序遗传算法Key words
nonlinear equation system/MONES transformation technique/dynamic crowding distance/non-dominated sorting ge-netic algorithm引用本文复制引用
基金项目
安徽省自然科学基金资助项目(2108085MA14)
国家自然科学基金资助项目(11601007)
出版年
2024
NETL
NSTL
万方数据