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

TL;DR

This paper introduces a variable reduction strategy (VRS) integrated with evolutionary algorithms to efficiently solve nonlinear equation systems by reducing problem complexity and enhancing search performance.

Contribution

It proposes a novel VRS approach that leverages problem domain knowledge and incorporates it into EAs, improving their effectiveness in solving NESs.

Findings

VRS significantly improves EA performance on NESs.

Integrated methods outperform original EAs and other benchmarks.

Experimental results confirm enhanced solution quality and efficiency.

Abstract

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.