Abstract
The Crested Porcupine Optimizer (CPO), an emerging intelligent optimization algorithm, exhibits considerable potential for addressing complex engineering problems, yet its capabilities remain insufficiently investigated. Nevertheless, the original CPO is susceptible to premature convergence and suffers from insufficient population diversity. To effectively address these limitations, this paper proposes a multi-mechanism enhanced Crested Porcupine Optimizer (SDHCPO). Its core innovation lies in the integration of four key strategies: a Sobol-Opposition-Based Learning (Sobol-OBL) initialization strategy, which combines the Sobol sequence with opposition-based learning to generate an initial population that is more uniformly distributed in the high-dimensional search space; a cosine-annealing-based dynamic adjustment strategy that replaces the original random weights and substantially enhances convergence stability; the incorporation of the DE/rand/1 strategy in the first defense phase to disrupt positional dependence and prevent premature convergence; and a horizontal-vertical crossover strategy employed in the second defense phase to eliminate dimensional stagnation. Experimental results on two authoritative benchmark suites, CEC2017 and CEC2022, demonstrate that the proposed algorithm outperforms seven representative metaheuristic algorithms in terms of global exploration capability, local exploitation accuracy, and convergence robustness. Furthermore, empirical studies on five representative engineering design optimization problems show that SDHCPO consistently attains either the best-known solutions or highly competitive results reported in the literature, thereby further confirming its effectiveness and broad application potential for complex real-world engineering optimization tasks.
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This study is a benchmark based algorithm study and does not rely on any proprietary or externally collected dataset. All data generated or analyzed during this study are included in this published article . The implementation code and analysis scripts used to reproduce the reported tables, figures, and statistical analyses are available from the corresponding author upon reasonable request.
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H. Xie led the algorithm design and improvement, performed code implementation, experimental design, and statistical analysis, and drafted the manuscript. X. Wan created the visualization for the engineering application section (Figs. 19, 20, 21 and 22) using AutoCAD. J. Mao was responsible for coordination and communication management. Y. Bai contributed to the validation process by providing constructive suggestions and feedback. All authors have read and agreed to the published version of the manuscript.
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Xie, H., Mao, J., Wan, X. et al. Adaptive multi mechanism integration in the crested porcupine optimizer for global optimization and engineering design problems. Sci Rep (2026). https://doi.org/10.1038/s41598-026-39222-y
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DOI: https://doi.org/10.1038/s41598-026-39222-y
