Zhang Wenning, Jiao Chongyang, Zhou Qinglei
Zhongyuan University of Technology, Zhengzhou, 450000, China.
State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, 450000, China.
Sci Rep. 2025 Aug 4;15(1):28400. doi: 10.1038/s41598-025-09523-9.
The Firefly Algorithm (FA), while effective for complex optimization, suffers from inherent limitations such as search oscillation and low convergence precision. To address these issues, a firefly algorithm with multiple learning ability based on gender difference (MLFA-GD) is proposed. Firstly, the algorithm evenly divides the randomly initialized population into male and female subgroups. Then a male firefly learning strategy which incorporated a partial attraction model combining with an escape mechanism, and a female firefly learning strategy guided by both the generalized centroid of the male subgroup and the global optimal individual are designed separately. Additionally, a random walk strategy is further incorporated to refine the optimization accuracy. Different from existing gender-based FA variants, male fireflies either fly toward brighter female fireflies or move away from weaker individuals to enhance exploration capability. Meanwhile, female fireflies update positions guided by two elite male individuals, effectively leveraging historical search information to improve exploitation capability. The performance is evaluated on 23 numerical functions, 30 CEC 2017 benchmark functions and an automatic test data generation problem. The experiment comparison results with six FA variants and ten popular meta heuristic algorithms confirm its enhanced search capability and significantly higher optimization precision, validating its effectiveness in balancing exploration and exploitation.
萤火虫算法（FA）虽然在复杂优化方面有效，但存在搜索振荡和收敛精度低等固有局限性。为了解决这些问题，提出了一种基于性别差异的具有多种学习能力的萤火虫算法（MLFA-GD）。首先，该算法将随机初始化的种群均匀划分为雄性和雌性子群体。然后分别设计了一种结合部分吸引模型和逃逸机制的雄性萤火虫学习策略，以及一种由雄性子群体的广义质心和全局最优个体共同引导的雌性萤火虫学习策略。此外，进一步引入随机游走策略以提高优化精度。与现有的基于性别的萤火虫算法变体不同，雄性萤火虫要么飞向更亮的雌性萤火虫，要么远离较弱的个体以增强探索能力。同时，雌性萤火虫由两个精英雄性个体引导更新位置，有效利用历史搜索信息以提高开发能力。在23个数值函数、30个CEC 2017基准函数和一个自动测试数据生成问题上对其性能进行了评估。与六种萤火虫算法变体和十种流行的元启发式算法的实验比较结果证实了其增强的搜索能力和显著更高的优化精度，验证了其在平衡探索和开发方面的有效性。
