纵横交叉和螺旋移动的萤火虫算法  

Firefly Algorithm with Vertical Horizontal Crossover and Spiral Movement

作　　者：刘丹 邢文来 张莹莹 陈涵婧 李陈思怡 吕莉[1,2] LIU Dan;XING Wenlai;ZHANG Yingying;CHEN Hanjing;LI Chensiyi;LYU Li(School of Information Engineering,Nanchang Institute of Technology,330099,Nanchang,PRC;Nanchang Key Laboratory of IoT Perception and Collaborative Computing for Smart City,330099,Nanchang,PRC)

机构地区：[1]南昌工程学院信息工程学院,南昌330099 [2]南昌市智慧城市物联感知与协同计算重点实验室,南昌330099

出　　处：《江西科学》2025年第2期321-329,共9页Jiangxi Science

基　　金：国家自然科学基金资助项目(62066030);2023年大学生创新创业训练计划项目(S202311319020)。

摘　　要：针对萤火虫算法寻优精度低和种群收敛速度慢等问题,提出纵横交叉和螺旋移动的萤火虫算法(CSMFA)。首先,引入黄金正弦搜索模式,使个体在搜索过程中结合正弦函数的周期性动态改变方向,并利用黄金分割系数缩小搜索空间,从而使个体能更有效逼近最优解,提升算法寻优精度;其次,加入纵横交叉策略:横向交叉使不同个体在相同维度上信息交互,有利于优良特征在子代个体中延续和组合,帮助算法快速收敛,纵向交叉令个体的2个不同维度进行算术交叉,并对其中1个维度进行更新,以增加种群多样性,防止出现集群集聚现象;最后,提出动态螺旋移动机制,使当前最优萤火虫以螺旋方式运动,减少随机性并逐渐靠近全局最优解。为验证所提算法的有效性,在12个经典测试函数上与FA及其改进算法进行仿真对比,实验结果证明,通过结合3种策略改进FA,不仅提升了算法的寻优能力,而且在寻优精度和收敛速度方面展现出优良的性能。To address issues such as low optimization accuracy and slow convergence speed in the Firefly Algorithm,this paper proposes the Firefly Algorithm with Vertical Horizontal Crossover and Spiral Movement(CSMFA).Firstly,it introduces the Golden Sine pattern,which combines the periodicity of the sine function with the golden ratio to dynamically adjust directions during the search process,reducing the search space and enabling individuals to approach the optimal solution more efficiently,thereby improving the algorithm’s optimization accuracy.Secondly,it adds the Vertical Horizontal Crossover strategy:horizontal crossover enables different individuals to interact with information on the same dimensions,which facilitates the continuation and combination of excellent features in the offspring individuals and helps the algorithm to converge quickly,and Vertical crossover enables arithmetic crossover of two different dimensions of an individual and updating of one of the dimensions in order to increase population diversity and to prevent clustering;Finally,a dynamic spiral movement mechanism is presented so that the current optimal firefly moves in a spiral fashion,reducing randomness and gradually approaching the global optimal solution.To verify the effectiveness of the proposed algorithm,a simulation comparison was conducted using 12 classic test functions against FA and its improved versions.The experimental results demonstrate that by integrating three strategies to enhance FA,not only is the optimization capability of the algorithm improved,but it also exhibits excellent performance in terms of optimization accuracy and convergence speed.

关 键 词：萤火虫算法 黄金分割率 纵向交叉 横向交叉 螺旋移动 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]