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arXiv 2008.04223cs.NEcs.AI
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变量约简策略与进化算法相结合求解非线性方程组

Integrating Variable Reduction Strategy with Evolutionary Algorithm for Solving Nonlinear Equations Systems

Central South University(中南大学);University of Alberta(阿尔伯塔大学);King Abdulaziz University(阿卜杜勒阿齐兹国王大学);Systems Research Institute, Polish Academy of Sciences(波兰科学院系统研究所)

Aijuan Song, Guohua Wu, Witold Pedrycz

摘要:

非线性方程组在实际问题中有着广泛的应用,但由于其非线性和多重根的特点,也给求解带来了困难。进化算法(EA)具有全局搜索能力和在一次运行中同时定位NES的多个根的能力,是求解NES的方法之一。目前,大多数关于使用进化算法解决非进化问题的研究集中在转换技术和提高所使用的进化算法的性能。相比之下,NES的问题域知识在这项研究中,特别是调查,利用它,我们建议将变量减少策略(VRS)到EA解决NES。VRS充分利用了NES的表达系统,并使用了一些变量(即,核心变量)来表示其它变量(即,减少的变量)通过方程系统中存在的变量关系。该算法减少了部分变量和方程,缩小了决策空间,从而降低了问题的复杂性,提高了进化算法的搜索效率。为了测试VRS在处理NES方面的有效性,本文将VRS集成到两种现有的最先进的EA方法中(即,MONES和DRJADE)。实验结果表明,在VRS的辅助下,EA方法可以产生明显优于原始方法和其他比较方法的结果。

英文摘要:

Nonlinear equations systems (NESs) are widely used in real-world problems while they are also difficult to solve due to their characteristics of nonlinearity and multiple roots. Evolutionary algorithm (EA) is one of the methods for solving NESs, given their global search capability and an ability to locate multiple roots of a NES simultaneously within one run. Currently, the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs. By contrast, the problem domain knowledge of NESs is particularly investigated in this study, using which we propose to incorporate the variable reduction strategy (VRS) into EAs to solve NESs. VRS makes full use of the systems of expressing a NES and uses some variables (i.e., core variable) to represent other variables (i.e., reduced variables) through the variable relationships existing in the equation systems. It enables to reduce partial variables and equations and shrink the decision space, thereby reducing the complexity of the problem and improving the search efficiency of the EAs. To test the effectiveness of VRS in dealing with NESs, this paper integrates VRS into two existing state-of-the-art EA methods (i.e., MONES and DRJADE), respectively. Experimental results show that, with the assistance of VRS, the EA methods can significantly produce better results than the original methods and other compared methods.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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