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A DBSCAN-enhanced niching differential evolution algorithm for solving nonlinear equations
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DOI：10.1016/j.ins.2025.122996.png)
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Abstract
En 中文
Nonlinear problems are frequently encountered in engineering fields, and most of the nonlinear problems can be modeled as nonlinear equations (NEs). Accordingly, quickly and correctly obtaining the solutions of NEs becomes particularly critical. However, most NEs have multiple roots, and efficiently locating all roots remains a challenging task. To address this issue, this work proposes a density-based spatial clustering of applications with noise (DBSCAN)-enhanced niche differential evolution (DBNDE) algorithm for solving NEs. By integrating a density-based clustering technique with niching technology, the proposed DBNDE algorithm achieves effective coordination between global exploration and local refinement. Specifically, the DBNDE algorithm dynamically partitions the population using density clustering, categorizing individuals into noise points, suboptimal solution clusters, and optimal solution clusters, thereby enhancing the efficiency of root identification. Additionally, it incorporates migration strategies to optimize solution distribution and employs an archive mechanism to preserve optimal solutions, improving the quality and stability of results. To substantiate the superiority of DBNDE, we carried out head-to-head comparisons with several classical algorithms on a benchmark set comprising thirty widely used and ten newly added NEs. Then, we conducted performance evaluations on two high-dimensional nonlinear problems. Results demonstrate that the proposed DBNDE algorithm effectively locates multiple roots of the NEs in a single run. Furthermore, the core parameter sensitivity analysis of the proposed DBNDE algorithm reveals its strong robustness to parameter settings, ensuring its stable performance across diverse problem sets.
Keywords:
Nonlinear equations
Transformation techniques
Niching strategies
Differential evolution
Clustering techniques
Migration strategies
Journal
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6.8
Papers:
540
Citations:
6.2W