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<p>Over the past few decades, the field of optimization has witnessed the emergence of numerous meta-heuristic algorithms. However, most of these algorithms primarily mimic animal-inspired search behaviors and lack a solid theoretical foundation. Based on the well-known Newton method, this study introduces a novel swarm intelligence optimization algorithm, termed the Fractional Newton-Derived Optimizer (FNDO). The FNDO comprises three core stages: update rules, vector combination, and local search. In the update rule stage, the Newton method is enhanced using fractional derivatives, leading to the development of the Fractional Newton Explore Strategy (FNES), which is integrated with the Best Solution Tendency (BST) to generate new vectors. During the vector combination stage, the generated vectors are integrated to refine the solution quality. In the local search phase, the Solution Improvement Operator (SIO) is employed to strengthen the algorithm’s local exploitation capability. The synergy among these three stages significantly improves both the global exploration and local exploitation capabilities of FNDO. First, ablation study was conducted on benchmark functions to evaluate the contribution of each component and compare FNDO against seven other metaheuristic algorithms. Radar chart and Friedman test results indicate that FNDO consistently ranks first. Furthermore, the Friedman, Quade, and Wilcoxon rank-sum tests collectively demonstrate statistically significant differences between FNDO and the other algorithms. In performance evaluations on the two-dimensional CEC2017 test functions and five real-world engineering problems, FNDO once again ranked first, exhibiting remarkable performance and strong robustness. In summary, the FNDO algorithm offers superior exploration and exploitation capabilities, rapid convergence, and a strong ability to avoid local optima. The source code of the FNDO algorithm is publicly available at <a href="https://github.com/YyangGu/FNDO.git">https://github.com/YyangGu/FNDO.git</a>.</p>

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Fractional Newton-derived optimizer: a novel metaheuristic for global optimization problems

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Yangyang Gu,
  • Yaqian Mao,
  • Yuqiu Shen,
  • Haixin Wu,
  • Yue Yu,
  • Jianhong Wang

摘要

Over the past few decades, the field of optimization has witnessed the emergence of numerous meta-heuristic algorithms. However, most of these algorithms primarily mimic animal-inspired search behaviors and lack a solid theoretical foundation. Based on the well-known Newton method, this study introduces a novel swarm intelligence optimization algorithm, termed the Fractional Newton-Derived Optimizer (FNDO). The FNDO comprises three core stages: update rules, vector combination, and local search. In the update rule stage, the Newton method is enhanced using fractional derivatives, leading to the development of the Fractional Newton Explore Strategy (FNES), which is integrated with the Best Solution Tendency (BST) to generate new vectors. During the vector combination stage, the generated vectors are integrated to refine the solution quality. In the local search phase, the Solution Improvement Operator (SIO) is employed to strengthen the algorithm’s local exploitation capability. The synergy among these three stages significantly improves both the global exploration and local exploitation capabilities of FNDO. First, ablation study was conducted on benchmark functions to evaluate the contribution of each component and compare FNDO against seven other metaheuristic algorithms. Radar chart and Friedman test results indicate that FNDO consistently ranks first. Furthermore, the Friedman, Quade, and Wilcoxon rank-sum tests collectively demonstrate statistically significant differences between FNDO and the other algorithms. In performance evaluations on the two-dimensional CEC2017 test functions and five real-world engineering problems, FNDO once again ranked first, exhibiting remarkable performance and strong robustness. In summary, the FNDO algorithm offers superior exploration and exploitation capabilities, rapid convergence, and a strong ability to avoid local optima. The source code of the FNDO algorithm is publicly available at https://github.com/YyangGu/FNDO.git.