基于双目标的MNSGA-II算法求解非线性方程组

doi:10.6040/j.issn.1671-9352.0.2023.236

摘要/Abstract

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。

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

Abstract: MONES transformation technique is applied to transform the problem of solving nonlinear equation systems into a bi-objective optimization problem, and a dynamic crowding distance strategy of MNSGA-II algorithm is included to dynamically calculate individual crowding distance in the process of population selection, which improves the diversity of Pareto front. In order to verify the performance of algorithm, thirty nonlinear equation systems are selected for testing NSGA-II, dynamic NSGA-II and MNSGA-II algorithm based on MONES transformation technique. Experimental results show that MNSGA-II algorithm based on MONES transformation 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.

Key words: nonlinear equation system, MONES transformation technique, dynamic crowding distance, non-dominated sorting genetic algorithm

中图分类号:

O241

李侦瑷,韦慧,陈馨. 基于双目标的MNSGA-II算法求解非线性方程组[J]. 《山东大学学报(理学版)》, 2024, 59(10): 22-29.

LI Zhenai, WEI Hui, CHEN Xin. MNSGA-II algorithm based on bi-objective for solving nonlinear equation systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 22-29.

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