工程科学学报，第40卷，第7期：871-881,2018年7月 Chinese Journal of Engineering,Vol.40,No.7:871-881,July 2018 DOI:10.13374/j.issn2095-9389.2018.07.014;http://journals.ustb.edu.cn 一种改进的人工蜂群算法—粒子蜂群算法 王继超)，李擎)回，崔家瑞，左文香)，赵越飞 1)北京科技大学自动化学院，北京1000832)河北水利电力学院，沧州061001 ☒通信作者，E-mail:liqing@(ics.usth.cdu.cm 摘要针对经典人工蜂群算法收敛速率较慢，后期易陷入局部最优解的不足，本文将粒子群算法中“全局最优”的思想引入 到人工蜂群算法的改进过程，从而形成了一种新的人工蜂群改进算法一粒子蜂群算法.首先，提出了趋优度的概念，用来衡 量引领蜂在有限次迭代过程中向全局最优解靠近或远离的程度，趋优度值可以评价个体的“发展潜力”，趋优度值越低的个 体，越需要增大变异的程度，以便找到质量更优的解.其次，专门设计了一种新的蜜蜂群体一粒子蜂，在引领蜂变异阶段根 据趋优度的大小将引领蜂变异为侦查蜂和粒子蜂，粒子蜂的出现在很大程度上增加了种群的多样性，拓展了算法的搜索范 围.然后，通过粒子蜂群算法种群序列是一个有限齐次马尔科夫链和种群进化单调性的分析，验证了本文所提算法的种群序 列依概率1收敛于全局最优解集.最后，将本文所提算法应用于多个常见测试函数，并与经典蜂群算法、近年其他文献改进蜂 群算法进行了仿真对比研究，仿真结果表明本文所提算法确实加大了种群的分散度、扩宽了搜索范围，从而具有更快的收敛 速度和更高的寻优精度 关键词人工蜂群算法：趋优度：粒子蜂；马尔科夫链；种群分散度 分类号TP18 An improved artificial bee colony algorithm:particle bee colony WANG Ji-chao,LI Qing,CUI Jia-rui),ZUO Wen-xiang),ZHAO Yue-fei) 1)School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)Hebei University of Water Resources and Electric Engineering,Cangzhou 061001.China Corresponding author,E-mail:liqing@ies.ustb.edu.en ABSTRACT With an aim to address the disadvantages of the artificial bee colony algorithm of slow convergence speed and ease of falling into the local optimum in the later period of the evolution process as well as to improve the traditional artificial bee colony algo- rithm,the concept of the "global optimum"in particle swarm optimization is introduced.Therefore,an improved artificial bee colony algorithm,called particle bee colony (PBC),is proposed herein.First,the concept of degree toward optimum is proposed for measur- ing the degree to which the leader approaches or is removed from the "global optimum"in a limited iteration process.The individuals' values of degree toward optimum denote their"development potentials."The individuals that have a low degree toward optimum require a great mutation extent to find a good solution.Second,a new colony of bees,initiated by the particle bee,is uniquely developed.In mutation period,the leader will be changed into the scout or the particle bee according to the value of the degree toward optimum.The appearance of particle bees can increase the population diversity and expand the search area to a large extent.Next,analysis reveals that the sequence of population of the PBC is a finite homogeneous Markov chain and the population evolution process is monotonous. On the basis of the above observations,it can be proved that the population sequence of the proposed algorithm converges to the global optimum solution set with probability 1.Last,the algorithm proposed in this study is applied to numerical simulations of several classi- cal test functions.Furthermore,the proposed algorithm is compared with the traditional artificial bee colony algorithm and other im- proved bee colony algorithms.The simulation results show that PBC increases the population dispersion and broadens the search area, 收稿日期：2017-05-14 基金项目：国家自然科学基金资助项目(61673098)工程科学学报,第 40 卷,第 7 期:871鄄鄄881,2018 年 7 月 Chinese Journal of Engineering, Vol. 40, No. 7: 871鄄鄄881, July 2018 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2018. 07. 014; http: / / journals. ustb. edu. cn 一种改进的人工蜂群算法———粒子蜂群算法 王继超1) , 李 擎1) 苣 , 崔家瑞1) , 左文香2) , 赵越飞1) 1) 北京科技大学自动化学院, 北京 100083 2) 河北水利电力学院, 沧州 061001 苣通信作者, E鄄mail: liqing@ ies. ustb. edu. cn 摘 要 针对经典人工蜂群算法收敛速率较慢,后期易陷入局部最优解的不足,本文将粒子群算法中“全局最优冶的思想引入 到人工蜂群算法的改进过程,从而形成了一种新的人工蜂群改进算法———粒子蜂群算法. 首先,提出了趋优度的概念,用来衡 量引领蜂在有限次迭代过程中向全局最优解靠近或远离的程度,趋优度值可以评价个体的“发展潜力冶,趋优度值越低的个 体,越需要增大变异的程度,以便找到质量更优的解. 其次,专门设计了一种新的蜜蜂群体———粒子蜂,在引领蜂变异阶段根 据趋优度的大小将引领蜂变异为侦查蜂和粒子蜂,粒子蜂的出现在很大程度上增加了种群的多样性,拓展了算法的搜索范 围. 然后,通过粒子蜂群算法种群序列是一个有限齐次马尔科夫链和种群进化单调性的分析,验证了本文所提算法的种群序 列依概率 1 收敛于全局最优解集. 最后,将本文所提算法应用于多个常见测试函数,并与经典蜂群算法、近年其他文献改进蜂 群算法进行了仿真对比研究,仿真结果表明本文所提算法确实加大了种群的分散度、扩宽了搜索范围,从而具有更快的收敛 速度和更高的寻优精度. 关键词 人工蜂群算法; 趋优度; 粒子蜂; 马尔科夫链; 种群分散度 分类号 TP18 收稿日期: 2017鄄鄄05鄄鄄14 基金项目: 国家自然科学基金资助项目(61673098) An improved artificial bee colony algorithm: particle bee colony WANG Ji鄄chao 1) , LI Qing 1) 苣 , CUI Jia鄄rui 1) , ZUO Wen鄄xiang 2) , ZHAO Yue鄄fei 1) 1) School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) Hebei University of Water Resources and Electric Engineering,Cangzhou 061001, China 苣Corresponding author, E鄄mail: liqing@ ies. ustb. edu. cn ABSTRACT With an aim to address the disadvantages of the artificial bee colony algorithm of slow convergence speed and ease of falling into the local optimum in the later period of the evolution process as well as to improve the traditional artificial bee colony algo鄄 rithm, the concept of the “global optimum冶 in particle swarm optimization is introduced. Therefore, an improved artificial bee colony algorithm, called particle bee colony (PBC), is proposed herein. First, the concept of degree toward optimum is proposed for measur鄄 ing the degree to which the leader approaches or is removed from the “global optimum冶 in a limited iteration process. The individuals爷 values of degree toward optimum denote their “development potentials. 冶 The individuals that have a low degree toward optimum require a great mutation extent to find a good solution. Second, a new colony of bees, initiated by the particle bee, is uniquely developed. In mutation period, the leader will be changed into the scout or the particle bee according to the value of the degree toward optimum. The appearance of particle bees can increase the population diversity and expand the search area to a large extent. Next, analysis reveals that the sequence of population of the PBC is a finite homogeneous Markov chain and the population evolution process is monotonous. On the basis of the above observations, it can be proved that the population sequence of the proposed algorithm converges to the global optimum solution set with probability 1. Last, the algorithm proposed in this study is applied to numerical simulations of several classi鄄 cal test functions. Furthermore, the proposed algorithm is compared with the traditional artificial bee colony algorithm and other im鄄 proved bee colony algorithms. The simulation results show that PBC increases the population dispersion and broadens the search area