Nonlinear equations systems (NESs) are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots. Evolutionary algorithms (EAs) are one of the methods for solving NESs, given their global search capabilities and 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, problem domain knowledge of NESs is investigated in this study, where we propose the incorporation of a variable reduction strategy (VRS) into EAs to solve NESs. The 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 variable relationships that exist in the equation systems. It enables the reduction of partial variables and equations and shrinks 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 mainly integrates the VRS into two existing state-of-the-art EA methods (i.e., MONES and DR-JADE) according to the integration framework of the VRS and EA, respectively. Experimental results show that, with the assistance of the VRS, the EA methods can produce better results than the original methods and other compared methods. Furthermore, extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.

Aijuan Song

School of Traffic and Transportation Engineering,Central South University,Changsha 410075,China;Department of Electrical and Computer Engineering,University of Alberta,Edmonton,AB T6G 2V4,Canada;Department of Electrical and Computer Engineering,Faculty of Engineering,King Abdulaziz University,Jeddah 21589 Saudi Arabia;Systems Research Institute,Polish Academy of Sciences,Warsaw 01447,Poland;Department of Automation,Tsinghua University,Beijing 100084,China

自动化学报（英文版）

[1]Aijuan Song-.Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems)[J].自动化学报（英文版）,2022(01):75-89

NESs,MONES

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