工程科学学报，第39卷，第1期：125-132.2017年1月 Chinese Journal of Engineering,Vol.39,No.1:125-132,January 2017 DOI:10.13374/j.issn2095-9389.2017.01.016;http://journals.ustb.edu.cn 基于自适应搜索的免疫粒子群算法 张超)，李擎)四，王伟乾)，陈鹏)，冯毅南) 1)北京科技大学自动化学院，北京1000832)中国电子科技集团第二研究所.太原030024 ☒通信作者，E-mail:liqing@ics.usth.cdu.cn 摘要经典粒子群算法由于多样性差而陷入局部最优，从而造成早熟停滞现象.为克服上述缺点，本文结合人工免疫算 法，提出一种基于自适应搜索的免疫粒子群算法.首先，该算法改善了浓度机制：然后由粒子最大浓度值来控制子种群数目 以充分利用粒子种群资源：最后对劣质子种群进行疫苗接种，利用粒子最大浓度值调节接种疫苗的搜索范围，不仅避免了种 群退化现象，而且提高了算法的收敛精度和全局搜索能力.仿真结果表明该算法求解复杂函数优化问题的有效性和优越性 关键词粒子群算法：人工免疫算法；自适应搜索；海明距离 分类号TP18 Immune particle swarm optimization algorithm based on the adaptive search strategy ZHANG Chao,LI Qing),WANG Wei-gian?),CHEN Peng),FENG Yi-nan) 1)School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)The Second Research Institute of China Electronics Technology Group Corporation,Taiyuan 030024,China Corresponding author,E-mail:liging@ies.ustb.edu.cn ABSTRACT The particle swarm algorithm is often trapped in a local optimum due to poor diversity,resulting in a premature stagna- tion phenomenon.In order to overcome this shortcoming,an immune particle swarm optimization algorithm based on the adaptive search strategy was proposed in this paper.Firstly,the concentration mechanism was improved.Secondly,in order to make full use of the resources of the particle population,the number of particles of sub-populations was controlled by the maximum concentration of particles.Finally,the inferior sub-populations were vaccinated,and the maximum concentration of particles was used to control the search range of the vaccine,so the population degradation was avoided,and the convergence accuracy and the global search ability of the algorithm were improved.Simulation results show the effectiveness and superiority of the proposed algorithm in solving the complex function optimization problems. KEY WORDS particle swarm optimization;artificial immune algorithm;adaptive search;Hamming distance 粒子群优化算法(particle swarm optimization,应用过程中往往会出现陷入局部最优而导致的早熟停 PS0))是模仿鸟类飞行觅食过程的算法，以其速度更滞现象，造成算法得不到理想最优解，尤其是在解决复 新公式使种群中的粒子迅速向种群历史最优值靠拢， 杂的多峰多谷问题时更为突出2-).因此，研究者开始 搜索速度快、效率高且算法简单，适合处理实数编码问 尝试将一些其他智能仿生算法与经典粒子群优化算法 题.该算法一经提出，便受到众多学者的关注和研究. 相融合，以弥补粒子群优化算法多样性不足的缺点. 目前已被广泛应用于工程技术、科学研究等领域.但 如蚁群粒子群算法[]、遗传粒子群算法[]和免疫粒子 是粒子群优化算法与其他群智能算法类似，算法后期 群算法[6] 多样性差，进化速度大幅降低，容易出现停滞现象，在 人工免疫优化算法(artificial immune algorithm, 收稿日期：2016-01-29 基金项目：国家自然科学基金青年基金资助项目(61603362,61603034)工程科学学报,第 39 卷,第 1 期:125鄄鄄132,2017 年 1 月 Chinese Journal of Engineering, Vol. 39, No. 1: 125鄄鄄132, January 2017 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2017. 01. 016; http: / / journals. ustb. edu. cn 基于自适应搜索的免疫粒子群算法 张 超1) , 李 擎1) 苣 , 王伟乾2) , 陈 鹏1) , 冯毅南1) 1) 北京科技大学自动化学院, 北京 100083 2) 中国电子科技集团第二研究所, 太原 030024 苣 通信作者, E鄄mail: liqing@ ies. ustb. edu. cn 摘 要 经典粒子群算法由于多样性差而陷入局部最优,从而造成早熟停滞现象. 为克服上述缺点,本文结合人工免疫算 法,提出一种基于自适应搜索的免疫粒子群算法. 首先,该算法改善了浓度机制;然后由粒子最大浓度值来控制子种群数目 以充分利用粒子种群资源;最后对劣质子种群进行疫苗接种,利用粒子最大浓度值调节接种疫苗的搜索范围,不仅避免了种 群退化现象,而且提高了算法的收敛精度和全局搜索能力. 仿真结果表明该算法求解复杂函数优化问题的有效性和优越性. 关键词 粒子群算法; 人工免疫算法; 自适应搜索; 海明距离 分类号 TP18 Immune particle swarm optimization algorithm based on the adaptive search strategy ZHANG Chao 1) , LI Qing 1) 苣 , WANG Wei鄄qian 2) , CHEN Peng 1) , FENG Yi鄄nan 1) 1) School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) The Second Research Institute of China Electronics Technology Group Corporation, Taiyuan 030024, China 苣 Corresponding author, E鄄mail: liqing@ ies. ustb. edu. cn ABSTRACT The particle swarm algorithm is often trapped in a local optimum due to poor diversity, resulting in a premature stagna鄄 tion phenomenon. In order to overcome this shortcoming, an immune particle swarm optimization algorithm based on the adaptive search strategy was proposed in this paper. Firstly, the concentration mechanism was improved. Secondly, in order to make full use of the resources of the particle population, the number of particles of sub鄄populations was controlled by the maximum concentration of particles. Finally, the inferior sub鄄populations were vaccinated, and the maximum concentration of particles was used to control the search range of the vaccine, so the population degradation was avoided, and the convergence accuracy and the global search ability of the algorithm were improved. Simulation results show the effectiveness and superiority of the proposed algorithm in solving the complex function optimization problems. KEY WORDS particle swarm optimization; artificial immune algorithm; adaptive search; Hamming distance 收稿日期: 2016鄄鄄01鄄鄄29 基金项目: 国家自然科学基金青年基金资助项目(61603362,61603034) 粒 子 群 优 化 算 法 ( particle swarm optimization, PSO) [1]是模仿鸟类飞行觅食过程的算法,以其速度更 新公式使种群中的粒子迅速向种群历史最优值靠拢, 搜索速度快、效率高且算法简单,适合处理实数编码问 题. 该算法一经提出,便受到众多学者的关注和研究. 目前已被广泛应用于工程技术、科学研究等领域. 但 是粒子群优化算法与其他群智能算法类似,算法后期 多样性差,进化速度大幅降低,容易出现停滞现象,在 应用过程中往往会出现陷入局部最优而导致的早熟停 滞现象,造成算法得不到理想最优解,尤其是在解决复 杂的多峰多谷问题时更为突出[2鄄鄄3] . 因此,研究者开始 尝试将一些其他智能仿生算法与经典粒子群优化算法 相融合,以弥补粒子群优化算法多样性不足的缺点. 如蚁群粒子群算法[4] 、遗传粒子群算法[5] 和免疫粒子 群算法[6] . 人工免疫优化算法 ( artificial immune algorithm