The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate.

解决非线性方程组的挑战是如何在一次运行中同时定位多个最优解。为了解决这个问题，本文提出了一种将多样性指标，多目标优化技术和聚类技术相结合的新颖算法。首先，设计多样性指标来维持人口的多样性。然后，引入了一种基于K均值聚类的选择策略，以找到有前途的解决方案。最后，使用局部搜索来加速人口收敛。在30个非线性方程组上的实验结果表明，该算法在收敛速度和成功率方面都优于6种最新算法。