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.

中文翻译：

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用进化算法求解一个新的非线性方程组测试集

在过去的二十年中，已经提出了许多进化算法来求解非线性方程系统（NES）。然而，基准测试集并没有得到足够的重视。NES 的一些特征（例如，高维、大搜索范围、可行区域的连通性）在原始基准测试集中很少被考虑，这导致它们不能很好地代表现实世界的问题。因此，本文提出了一个生成人工测试问题的通用工具包，并构建了 18 个具有不同特征的测试实例，这是设计 NES 的首次尝试。实验结果表明，目前的算法在这个新的基准测试集上表现不佳。此外，我们开发了一种将 NES 转换为新的单目标优化问题的转换方法，并设计了一种两阶段方法来解决这种转换后的多模态优化问题。与其他算法相比，所提出的方法具有优越的或至少具有竞争力的性能。