《计算机应用研究》|Application Research of Computers

多模态多目标差分进化算法求解非线性方程组

Multimodal multi-objective differential evolution algorithm for solving nonlinear equations

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作者 许伟伟,梁静,岳彩通,瞿博阳
机构 1.郑州大学 电气工程学院,郑州 450001;2.中原工学院 电子信息学院,郑州 450007
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文章编号 1001-3695(2019)05-006-1305-06
DOI 10.19734/j.issn.1001-3695.2017.11.0734
摘要 针对当前算法在求解非线性方程组时面临解的个数不完整、精确度不高、收敛速度慢等问题,提出一种多模态多目标差分进化算法。首先将非线性方程组转换为多模态多目标优化问题,初始化一个随机种群,并对种群中全部个体进行评价;然后通过非支配解排序和决策空间拥挤距离选择机制,挑选种群中的一半优质个体进行变异,在变异过程中采用一种新的变异策略和边界处理方法以增加解的多样性;最后通过交叉和选择机制使优质个体进行进化,直到搜索到全部最优解。在所选测试函数集和工程实例上的实验结果表明,该算法能够有效地搜索到非线性方程组的解,并通过与当前四种算法进行比较,该算法在解的数量和成功率上具有优越性。
关键词 非线性方程组; 多模态; 多目标; 差分进化; 非支配解排序
基金项目 国家自然科学基金资助项目(61473266,61673404)
河南省高校优秀青年教师研究奖励基金资助项目(2014GGJS-004)
河南省大学创新人才科技计划资助项目(16HASTIT041)
本文URL http://www.arocmag.com/article/01-2019-05-006.html
英文标题 Multimodal multi-objective differential evolution algorithm for solving nonlinear equations
作者英文名 Xu Weiwei, Liang Jing, Yue Caitong, Qu Boyang
机构英文名 1.School of Electrical Engineering,Zhengzhou University,Zhengzhou 450001,China;2.School of Electronic & Information Engineering,Zhongyuan University of Technology,Zhengzhou 450007,China
英文摘要 Aiming at the problems such as incomplete solutions, low accuracy and slow convergence speed of current algorithms in solving nonlinear equations, this paper proposed a multimodal multi-objective differential evolution algorithm. Firstly, it transformed the nonlinear equations into multimodal multi-objective optimization problems, and initialized a random population and evaluated all individuals in the population. Through the non-dominated sorting and decision space crowding distance selection mechanism, it selected half of the individuals in the population to mutate. Then it used a new mutation strategy and boundary processing method to increase the diversity of solutions. Finally, it evolved the high-quality individuals through crossover and selection mechanism until it found all the optimal solutions. The experimental results on selected test function sets and engineering examples show that the algorithm can effectively search for optimal solutions and it is superior to the other four algorithms in the number of solutions and success rate.
英文关键词 nonlinear equations; multimodal; multi-objective; differential evolution; non-dominated sorting
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收稿日期 2017/11/4
修回日期 2018/1/5
页码 1305-1310
中图分类号 TP183
文献标志码 A