基于鞅方法的鸡群优化算法收敛性分析

摘要：

针对鸡群优化(chickenswarmoptimization,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 convergenee analysis on chicken swarm optimization(CSO) algorithm belonged to weak conver-gence, and it cannot infer in general that the C'$0 algorithm would be convergent to a global optimum in a finite number of evo-lution steps. ln order to make up for this deficieney, a martingale method was proposed to study the global convergence of CS0 algorithm, Firstly, based on relevant definitions of Cs0 algorithm, the Markoy chain model of Cs0 algorithm was established.and its Markov properties were analyzed. $econdly, the chicken swarm state sequence with the minimum fitness value was transformed into a supermartingale. By using the supermartingalke convergence theorem and the Egorof's theorem, it was proved that the C$0 algorithm had almost surely strong convergence and uniform convergence, Furthermore, it was concluded that the C$0 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 experi-ment, and it was found that the C$0 algorithm had stronger ability to search for exeellenee and higher convergenee accuracy than PSO algorithm and DE algorithm.

作者：

周婷婷，戴家佳

Zhou Tingting,Dai Jiajia

机构地区：

贵州大学数学与统计学院

引用本文：

周婷婷,戴家佳,基于鞅方法的鸡群优化算法收敛性分析[]].betway官方app 学报(自然科学版),2024,52(6)。80-87.

(Zhou Tingting, Dai jiajia.Convergence analysis of chicken swarm optimization algorithm based on martingale method[j].Journal of Henan Normal University( Natural Seienee Edition),2024,52(6):80-87.DO1.10.16366/i.cki.1000-2367.2023.05.04.0002.)

基金：

国家自然科学基金；贵州省数据驱动建模学习与优化创新团队项目

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

chicken swarm optimizatio(CSO)algorithm;Markov chain;supermartingale convergence theorem;Egoroff's theorem;almost sure strong convergence;uniform convergence

分类号：

TP301.6；TP18

基于鞅方法的鸡群优化算法收敛性分析.pdf