Solving nonlinear equation systems with multiple roots is challenging due to complex basin structures, uneven root distributions, premature population convergence, and repeated search around already discovered roots. Although differential evolution (DE) algorithm has been widely applied to nonlinear equation solving due to its derivative-free global search capability, standard DE often lacks an effective mechanism for maintaining multiple search branches and reallocating search resources among different potential root regions. To address these issues, this paper proposes a hierarchical cluster-guided adaptive differential evolution (HCADE) algorithm. This method employs a neighborhood-based differential evolution strategy to guide individuals toward potential root regions while preserving local search diversity; introduces a success-history-based parameter adaptation mechanism to dynamically adjust the mutation factor and crossover probability, reducing the dependence on manually fixed parameters; in the later search stage, utilizes hierarchical clustering to analyze the spatial distribution of the population and classify individuals into promising clusters, non-promising clusters, and scattered individuals; on this basis, an adaptive migration mechanism reallocates individuals from low-contribution clusters to more promising regions, while an archive-based reinitialization strategy preserves discovered roots and releases population capacity for further exploration. Experimental results on benchmark nonlinear equation systems demonstrate that HCADE achieves competitive performance in terms of multiple-root detection, convergence stability, and robustness.
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