  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.
