Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution
Finding Multiple Roots of Nonlinear Equation Systems via a Repulsion-Based Adaptive Differential Evolution
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DOI：
10.1109/tsmc.2018.2828018
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Wenyin Gong;Yong Wang;Z. Cai;Ling Wang
中科院分区：
文献类型：
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作者：
Wenyin Gong;Yong Wang;Z. Cai;Ling Wang
在单次运行中查找非线性方程组 (NES) 的多个根是数值计算中最重要的挑战之一。我们通过结合排斥技术、多样性保存机制和自适应参数控制的优势来解决这一具有挑战性的任务。首先，排斥技术通过排斥先前发现的根周围的区域来激励种群寻找新的根。然而，为了找到尽可能多的根，算法设计者需要解决一个关键问题：如何保持种群的多样性。为此，我们的方法中融入了多样性保护机制，其中包括邻域突变和拥挤选择。此外，我们通过结合自适应参数控制进一步提高了性能。目的是增强搜索能力并纠正不同问题的差分进化（DE）参数的试错调整。通过将上述三个方面组合在一起，我们提出了一种基于斥力的自适应 DE，称为 RADE，用于在单次运行中查找 NES 的多个根。为了评估 RADE 的性能，从文献中选择了 30 个具有不同功能的 NES 作为测试套件。实验结果表明，RADE 能够在所有测试问题的单次运行中同时找到多个根。此外，在根率和成功率方面，RADE 能够提供比对比方法更好的结果。
Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate.