基于鞅方法的鸡群优化算法收敛性分析  

Convergence analysis of chicken swarm optimization algorithm based on martingale method

作　　者：周婷婷 戴家佳 Zhou Tingting;Dai Jiajia(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《河南师范大学学报（自然科学版）》2024年第6期80-87,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12361057);贵州省数据驱动建模学习与优化创新团队项目(黔科合平台人才[2020]5016)。

摘　　要：针对鸡群优化(chicken swarm optimization, CSO)算法已有的收敛性分析结果属于弱收敛,不能保证算法能在有限步内收敛到问题的全局最优这一不足,提出了运用鞅方法来研究CSO算法的全局收敛性.首先,基于CSO算法的相关定义,建立CSO算法的马尔可夫(Markov)链模型,分析其Markov性质;其次,将具有最小适应度值的鸡群状态序列转化成上鞅,利用上鞅收敛定理和Egoroff定理证明了CSO算法的几乎处处强收敛性和一致收敛性,进而得出了当鸡群状态空间有限时,CSO算法能确保在有限步内收敛到问题的全局最优这一结论;最后,在仿真实验中成功验证了理论证明的正确性,并发现CSO算法比其他算法具有更强的寻优能力和更高的收敛精度.The most convergence analysis on chicken swarm optimization(CSO)algorithm belonged to weak convergence,and it cannot infer in general that the CSO algorithm would be convergent to a global optimum in a finite number of evolution steps.In order to make up for this deficiency,a martingale method was proposed to study the global convergence of CSO algorithm.Firstly,based on relevant definitions of CSO algorithm,the Markov chain model of CSO algorithm was established,and its Markov properties were analyzed.Secondly,the chicken swarm state sequence with the minimum fitness value was transformed into a supermartingale.By using the supermartingale convergence theorem and the Egoroff's theorem,it was proved that the CSO algorithm had almost surely strong convergence and uniform convergence.Furthermore,it was concluded that the CSO algorithm can surely convergence to a global optimum in a finite number of evolution steps when the chicken swarm state space was finite.Finally,the validity of the theoretical proofs were verified successfully in the simulation experiment,and it was found that the CSO algorithm had stronger ability to search for excellence and higher convergence accuracy than PSO algorithm and DE algorithm.

关 键 词：CSO算法 MARKOV链 上鞅收敛定理 EGOROFF定理 几乎处处强收敛 一致收敛 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] TP18[自动化与计算机技术—计算机科学与技术]