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Nonlinear equations systems (NESs) are widely used in real-world problemswhile they are also difficult to solve due to their characteristics ofnonlinearity and multiple roots. Evolutionary algorithm (EA) is one of themethods for solving NESs, given their global search capability and an abilityto locate multiple roots of a NES simultaneously within one run. Currently, themajority of research on using EAs to solve NESs focuses on transformationtechniques and improving the performance of the used EAs. By contrast, theproblem 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 NESand uses some variables (i.e., core variable) to represent other variables(i.e., reduced variables) through the variable relationships existing in theequation systems. It enables to reduce partial variables and equations andshrink the decision space, thereby reducing the complexity of the problem andimproving the search efficiency of the EAs. To test the effectiveness of VRS indealing with NESs, this paper integrates VRS into two existing state-of-the-artEA methods (i.e., MONES and DRJADE), respectively. Experimental results showthat, with the assistance of VRS, the EA methods can significantly producebetter results than the original methods and other compared methods.

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