Solving a New Test Set of Nonlinear Equation Systems by Evolutionary Algorithm

During the past two decades, many evolutionary algorithms have been proposed to solve nonlinear equation systems (NESs). However, the benchmark test sets have not received enough attention. Some features of NESs (e.g., high dimension, large search range, the connectivity of the feasible region) are rarely considered in the original benchmark test sets, which results in that they cannot represent the real-world problems well. Thus, a general toolkit is proposed to generate artificial test problems and 18 test instances with diverse characteristics are constructed in this article, which is the first attempt to design NESs. The experimental results indicate that the current algorithms perform poorly on this new benchmark test set. Furthermore, we develop a transformation method that transforms a NES into a new single-objective optimization problem and design a two-phase method to solve this transformed multimodal optimization problem. Compared to other algorithms, the proposed method has a superior or at least competitive performance.

Automated summary

Many evolutionary algorithms have been proposed to solve nonlinear equation systems (NESs) in the past two decades. However, the benchmark test sets have been neglected, causing a lack of representation for real-world problems. This article introduces a general toolkit for generating artificial test problems and constructs 18 test instances with diverse characteristics, aiming to design NESs. The experimental results demonstrate the poor performance of current algorithms on this new benchmark test set. Additionally, a transformation method and a two-phase method are developed to solve the transformed multimodal optimization problem, outperforming other algorithms.