深度学习萤火虫算法
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摘要
为克服萤火虫算法全局寻优精度不高和过早收敛的缺点,本文提出深度学习萤火虫算法.算法采用随机吸引模型,萤火虫随机选择一个粒子学习,根据历史最优位置构建广义中心粒子,对其进行一定次数的单维深度学习,学习后的粒子引导种群进化.实验发现,深度学习策略及粒子深度学习次数对算法优化性能的改善起着重要作用.12个基准测试函数的实验结果表明,算法的综合寻优性能优于其它8种最近提出的萤火虫算法.
In order to overcome lowprecision and premature convergence of firefly algorithm,this paper proposes a newmethod,called firefly algorithm with deep learning. First,firefly algorithm selects a particle to learn according to the random attraction model; second,the method constructs a general center particle based on the best historical position; third,the particle leads the evolution of the population after a certain times of one-dimensional deep learning. Experiments showthat the deep learning strategy and the number of deep learning of particles play an important role in optimizing the performance of the algorithm. The experimental results of 12 benchmark functions demonstrate that the comprehensive optimization performance of the proposed algorithm outperforms eight other recently firefly algorithm variants.
In order to overcome lowprecision and premature convergence of firefly algorithm,this paper proposes a newmethod,called firefly algorithm with deep learning. First,firefly algorithm selects a particle to learn according to the random attraction model; second,the method constructs a general center particle based on the best historical position; third,the particle leads the evolution of the population after a certain times of one-dimensional deep learning. Experiments showthat the deep learning strategy and the number of deep learning of particles play an important role in optimizing the performance of the algorithm. The experimental results of 12 benchmark functions demonstrate that the comprehensive optimization performance of the proposed algorithm outperforms eight other recently firefly algorithm variants.
引文
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[3]LEE H M,YOO D G,SADOLLAH A,et al. Optimal cost design of water distribution networks using a decomposition approach[J]. Engineering Optimization,2016,48(12):2141-2156.
[4] MASHAYEKHY L,NEJAD M M,GROSU D,et al. An online mechanism for resource allocation and pricing in clouds[J]. IEEE Transactions on Computers,2016,65(4):1172-1184.
[5]YEH W C. A novel node-based sequential implicit enumeration method for finding all d-M Ps in a multistate flownetwork[J]. Information Sciences,2015,297:283-292.
[6] BHATI D,SINGH P. Branch and bound computational method for multi-objective linear fractional optimization problem[J]. Neural Computing and Applications,2017,28(11):3341-3351.
[7] MATHIEU L,OLIVIER P. Dynamic programm-ing for mean-field type control[J]. Journal of Optimization Theory&Applications,2016,169(3):902-924.
[8]KENNEDY J,EBERHART R. Particle swarm optimization[A]. Proceedings of International Conference on Neural Networks[C]. Piscataway:IEEE,1995. 1942-1948.
[9]陈侃松,阮玉龙,戴磊,等.区域分割的自适应变异粒子群算法[J].电子学报,2017,45(8):1849-1855.CHEN Kan-song,RUAN Yu-long,DAI Lei,et al. Regional-segmentation self-adapting variation particle swarm optimization[J]. Acta Electronica Sinica,2017,45(8):1849-1855.(in Chinese)
[10]周凌云,丁立新,彭虎,等.一种邻域重心反向学习的粒子群优化算法[J].电子学报,2017,45(11):2815-2824.ZHOU Ling-yun,DING Li-xin,PENG Hu et al. Neighborhood centroid opposition-based particle swarm optimization[J]. Acta Electronica Sinica,2017,45(11):2815-2824.(in Chinese)
[11]YANG X S,DEB S. Cuckoo search via Lévy flights[A].Proceedings of World Congress on Nature and Biologically Inspired Computing[C]. Piscataway:IEEE,2010. 210-214.
[12]马卫,孙正兴.采用搜索趋化策略的布谷鸟全局优化算法[J].电子学报,2015,43(12):2429-2439.M A Wei,SUN Zheng-xing. A global cuckoo optimization algorithm using coarse-to-fine search[J]. Acta Electronica Sinica,2015,43(12):2429-2439.(in Chinese)
[13]KARABOGA D. An Idea Based on Honey Bee Swarm for Numerical Optimization[R]. Kayseri,Turkey:Erciyes University,Engineering Faculty,Computer Engineering Department,2005. 1-10.
[14] YANG X S. Nature-inspired Metaheuristic Algorithms[M]. London:Luniver Press,2008.
[15]杜鹏桢,唐振民,陆建峰,等.不确定环境下基于改进萤火虫算法的地面自主车辆全局路径规划方法[J].电子学报,2014,42(3):616-624.DU Peng-zhen,TANG Zhen-min,LU Jian-feng,et al.Global path planning for ALV based on improved glowworm swarm optimization under uncertain environment[J]. Acta Electronica Sinica,2014,42(3):616-624.(in Chinese)
[16]LECUN Y,BENGIO Y,HINTON G. Deep learning[J].Nature,2015,521(7553):436-444.
[17]马世龙,乌尼日其其格,李小平.大数据与深度学习综述[J].智能系统学报,2016,11(6):728-742.M A Shi-long,WUNIRI Qi-qi-ge,LI Xiao-ping. Deep learning with big data:state of the art and development[J]. CAII Transactions on Intelligent Systems,2016,11(6):728-742.(in Chinese)
[18]LIU Y,QIN Z,SHI Z,et al. Center particle swarm optimization[J]. Neurocomputing,2007,70(4):672-679.
[19]汤可宗,柳炳祥,杨静宇,等.双中心粒子群优化算法[J].计算机研究与发展,2012,49(5):1086-1094.TANG Ke-zong,LIU Bing-xiang,YANG Jing-yu,et al.Double center particle swarm optimization algorithm[J].Journal of Computer Research and Development,2012,49(5):1086-1094.(in Chinese)
[20]孙志远,鲁成祥,史忠植,等.深度学习研究与进展[J].计算机科学,2016,43(2):1-8.SUN Zhi-yuan,LU Chen-xiang,SHI Zhong-zhi,et al. Research and advances on deep learning[J]. Computer Science,2016,43(2):1-8.(in Chinese)
[21] YANG X S. Engineering Optimization:An Introduction with M etaheuristic Applications[M]. Hoboken:Wiley Publishing,2010.
[22]FISTER I,FISTER I,BREST J,et al. Memetic firefly algorithm for combinatorial optimization[A]. Proceedings of International Conference on Bioinspired Optimization M ethods and their Applications[C]. Piscataway:IEEE Press,2012. 76-86.
[23]GANDOMI A H,YANG X E,TALATAHARI S,et al.Firefly algorithm with chaos[J]. Communications in Nonlinear Science&Numerical Simulation,2013,18(1):89-98.
[24]YU S,SU S,LU Q,et al. A novel wise step strategy for firefly algorithm[J]. International Journal of Computer M athematics,2014,91(12):2507-2513.
[25]YU S,ZHU S,MA Y,et al. A variable step size firefly algorithm for numerical optimization[J]. Applied M athematics&Computation,2015,263:214-220.
[26] WANG H,WANG W,SUN H,et al. Firefly algorithm with random attraction[J]. International Journal of BioInspired Computation,2016,8(1):33-41.
[27]WANG H,ZHOU X,SUN H,et al. Firefly algorithm with adaptive control parameters[J]. Soft Computing,2017,21(17):5091-5102.