噪声环境下基于蒲丰距离的依概率多峰优化算法  

Probabilistic Multimodal Optimization Algorithm Based on the Buffon Distance in Noisy Environment

作　　者：王霞 王耀民 施心陵[1] 高莲[1] 李鹏[1] WANG Xia;WANG Yao-Min;SHI Xin-Ling;GAO Lian;LI Peng(School of Information Science and Engineering,Yunnan Uni-versity,Kunming 650500;School of Electrical and Informa-tion Engineering,Yunnan Minzu University,Kunming 650500)

机构地区：[1]云南大学信息学院,昆明650500 [2]云南民族大学电气信息工程学院,昆明650500

出　　处：《自动化学报》2021年第11期2691-2714,共24页Acta Automatica Sinica

基　　金：国家自然科学基金(61763046,61762093,61662089,61761048);云南省第十七批中青年学术和技术带头人资助项目(2014HB019);云南省高校科技创新团队支持计划资助,云南省教育厅科学研究基金(2017ZZX229);云南省应用基础研究重点项目(2018FA036)资助。

摘　　要：针对噪声环境下求解多个极值点的问题,本文提出了噪声环境下基于蒲丰距离的依概率多峰优化算法(Probabilistic multimodal optimization algorithm based on the Button distance,PMB).算法依据蒲丰投针原理提出噪声下的蒲丰距离和极值分辨度概念,理论推导证明了二者与算法峰值检测率符合依概率关系.在全局范围内依据蒲丰距离划分搜索空间,可以使PMB算法保持较好的搜索多样性.在局部范围内利用改进的斐波那契法进行探索,减少了算法陷入噪声引起的局部最优的概率.基于34个测试函数,从依概率特性验证、寻优结果影响因素分析、多极值点寻优和多维函数寻优四个角度进行实验.证明了蒲丰距离与算法的峰值检测率符合所推导的依概率关系.对比噪声环境下的改进蝙蝠算法和粒子群算法,PMB算法在噪声环境中可以依定概率更精确地定位多峰函数的更多极值点,从而证明了PMB算法原理的正确性和噪声条件下全局寻优的依概率性能,具有理论意义和实用价值.To solve the problem of multiple extremum points optimization in noisy environment,a probabilistic multimodal optimization algorithm based on the Buffon distance(PMB)is proposed in this paper.Based on the principle of Buffon needles,the concepts of Buffon distance and resolution of extreme value under noisy environment are put forward.The theoretical derivation proves that the relationship between peak detection rate of PMB algorithm and Buffon distance conforms to a probabilistic relation.In global scope,the search space is divided by Buffon distance for diversity maintenance.The improved Fibonacci method is used in local search to reduce the probability of falling into the local optimum caused by noise.Based on 34 test functions,experiments are carried out from four aspects,including probabilistic property verification,analysis of influencing factors of optimization results,multiple extremum points optimization and multidimensional optimization.It is proved that the relationship of Buffon distance and peak detection rate of PMB algorithm is in line with the deduced probabilistic relationship.Compared with the improved bat algorithm and particle swarm optimization(PSO),PMB algorithm can locate extremum points of multimodal function by a steady probability in noise environment,and gain more extremum points accurately.Thus,the correctness of PMB algorithm principle and probabilistic performance of global optimization under noise condition are proved,which has theoretical and practical significance.

关 键 词：噪声环境 多峰优化 蒲丰距离 依概率 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]