计算机科学 ›› 2019, Vol. 46 ›› Issue (3): 30-38.doi: 10.11896/j.issn.1002-137X.2019.03.004
张晓凤,王秀英
ZHANG Xiao-feng, WANG Xiu-ying
摘要: 灰狼优化(Grey Wolf Optimization,GWO)算法是一种新兴的群体智能优化算法,因简单高效而被成功应用于诸多领域。文章阐述了灰狼优化算法的搜索机制和实现过程,分析灰狼优化算法的特性,对目前GWO算法的相关改进及应用进行综述。重点对GWO算法的改进策略,包括种群初始化的改进、搜索机制的改进、参数的改进等进行了描述,对GWO算法在参数优化、复杂函数优化和组合优化等方面的应用进行了讨论。最后,对GWO算法的未来改进策略和实际应用进行了展望。
中图分类号:
[1]WHITLEY D.A genetic algorithm tutorial[J].Statistics and Computing,1994,4(2):65-85. [2]TRELEA I C.The particle swarm optimization algorithm:convergence analysis and parameter selection[J].Information Processing Letters,2003,85(6):317-325. [3]STORN R,PRICE K.Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces[J].Journal of Global Optimization,1997,11(4):341-359. [4]DORIGO M,BIRATTARI M,STUTZLE T.Ant colony optimization[J].Computational Intelligence Magazine IEEE,2007,1(4):28-39. [5]PAN W T.A new fruit fly optimization algorithm:taking the financial distress model as an exampl[J].Knowledge-Based Systems,2012,26(2):69-74. [6]MIRJALILI S,MIRJALILI S M,LEWIS A.Grey Wolf Optimizer[J].Advances in Engineering Software,2014,69(3):46-61. [7]ZHANG S,ZHOU Y Q,LI Z M,et al.Grey wolf optimizer for unmanned combat aerial vehicle path planning[J].Advances in Engineering Software,2016,99(C):121-136. [8]ZHANG S,ZHOU Y Q.Grey wolf optimizer based on Powell local optimization method for clustering analysis[J/OL].Discrete Dynamics in Nature and Society,2015,http://dx.doi.org/10.1155/2015/481360. [9]EMARY E,ZAWBAA H M,GROSAN C,et al.Feature Subset Selection Approach by Gray-Wolf Optimization[M]∥Afro-European Conference for Industrial Advancement.Cham:Springer,2014:1-13. [10]SONG H M,SULAIMAN M H,MOHAMED M R.An application of Grey Wolf optimizer for solving combined economic emission dispatch problems[J].International Review on Modelling & Simulations,2014,7(5):838-844. [11]MADADI A,MOTLAGH M M.Optimal control of DC motor using grey wolf optimizer algorithm[J].Technical Journal of Engineering and Applied Science,2014,4(4):373-379. [12]EIGAAFARY A A M,MOHAMED Y S,HEMEIDA A A M,et al.Grey wolf optimization for multi input multi output system[J].Universal Journal of Communications and Networks,2015,3(1):1-6. [13]LUO Q,ZHANG S,LI Z,et al.A Novel Complex-Valued Encoding Grey Wolf Optimization Algorithm[J].Algorithms,2015,9(1):1-23. [14]MADHIARASAN M,DEEPA S N.Long-Term Wind Speed Forecasting using Spiking Neural Network Optimized by Improved Modified Grey Wolf Optimization Algorithm[J].International Journal of Advanced Research,2016,4(7):356-368. [15]LONG W,ZHAO D Q,XU S J.Improved grey wolf optimization algorithm for constrained optimization problem[J].Journal of Computer Applications,2015,35(9):2590-2595.(in Chinese) 龙文,赵东泉,徐松金.求解约束优化问题的改进灰狼优化算法[J].计算机应用,2015,35(9):2590-2595. [16]MUANGKOTE N,SUNAT K,CHIEWCHANWATTANA S.An improved grey wolf optimizer for training q-Gaussian Radial Basis Functional-link nets[C]∥Computer Science and Engineering Conference.IEEE,2014:209-214. [17]SAREMI S,MIRJALILI S Z,MIRJALILI S M.Evolutionary population dynamics and grey wolf optimizer[J].Neural Computing & Applications,2015,26(5):1257-1263. [18]GHOLIZADEH S.Optimal design of double layer grids consi- dering nonlinear behaviour by sequential grey wolf algorithm[J].Journal of Optimization in Civil Engineering,2015,5(4):511-523. [19]MALIK M R S,MOHIDEEN E R,ALI L.Weighted distance Grey wolf optimizer for global optimization problems[C]∥IEEE International Conference on Computational Intelligence and Computing Research.IEEE,2016:1-6. [20]LONG W,LIANG X,CAI S,et al.A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems[J].Neural Computing & Applications,2016,28(S1):1-18. [21]MITTAL N,SINGH U,SOHI B S.Modified Grey Wolf Optimizer for Global Engineering Optimization[J].Applied Computational Intelligence and Soft Computing,2016,2016(4598):1-16. [22]YANG J C,LONG W.Improved Grey Wolf Optimization Algorithm for Constrained Mechanical Design Problems[J].Applied Mechanics & Materials,2016,851:553-558. [23]ZHANG S,LUO Q F,ZHOU Y Q.Hybrid grey wolf optimizer using elite opposition-based learning strategy and simplex me-thod[J].International Journal of Computational Intelligence and Applications,2017,16(2):1750012. [24]ZHU A,XU C,LI Z,et al.Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC[J].Journal of Systems Enginee-ring and Electronics,2015,26(2):317-328. [25]ElGAYYAR M,EMARY E,SWEILAM N H,et al.A Hybrid Grey Wolf-Bat Algorithm for Global Optimization[C]∥International Conference on Advanced Machine Learning Technologies and Applications.Cham:Springer,2018:3-12. [26]SINGH N,HACHIMI H.A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization[J].Mathematical and Computational Applications,2018,23(1):1-32. [27]ZHANG X,KANG Q,CHENG J,et al.A Novel Hybrid Algorithm Based on Biogeography-Based Optimization and Grey Wolf Optimizer[J].Applied Soft Computing,2018,67:197-214. [28]KOHLI M,ARORA S.Chaotic grey wolf optimization algorithm for constrained optimization problems[J].Journal of Computational Design & Engineering,2017,5(4):458-472. [29]TAWHID M A,ALI A F.A Hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function[J].Memetic Computing,2017,9(4):1-13. [30]MOSTAFA E,ABDEL-NASSER M,MAHMOUD K.Applica- tion of mutation operators to grey wolf optimizer for solving emission-economic dispatch problem[C]∥International Confe-rence on Innovative Trends in Computer Engineering.2018:278-282. [31]SINGH N,SINGH S B.Hybrid Algorithm of Particle Swarm Optimization and Grey Wolf Optimizer for Improving Convergence Performance[J/OL].Journal of Applied Mathematics,http://doi.org/10.1155/2017/2030489. [32]LAL D K,BARISAL A K,TRIPATHY M.Grey Wolf Optimizer Algorithm Based Fuzzy PID Controller for AGC of Multi-areaPower System with TCPS[J].Procedia Computer Science,2016,92:99-105. [33]SHARMA Y,SAIKIA L C.Automatic generation control of a multi-area ST-Thermal power system using Grey Wolf Optimizer algorithm based classical controllers[J].International Journal of Electrical Power & Energy Systems,2015,73:853-862. [34]YADAV S,VERMA S K,NAGAR S K.Optimized PID Controller for Magnetic Levitation System[J].Ifac Papersonline,2016,49(1):778-782. [35]MEDEIROS A B L D.Application of the Gray Wolf (GWO) algorithm in the tuning of a PID controller in a feedback control system[J].Journal of Engineering and Technology for Industrial Applications,2017,3(12):56-62. [36]SWEIDAN A H,EI-BENDARY N,HASSANIEN A E,et al. Water quality classification approach based on bio-inspired Gray Wolf Optimization[C]∥Soft Computing and Pattern Recognition.IEEE,2015:1-6. [37]ESWARAMOORTHY S,SIVAKUMARAN N,SEKARAN S.Grey wolf optimization based parameter selection for support vector machines[J].Compel International Journal for Computation & Mathematics in Electrical & Electronic Engineering,2016,35(5):1513-1523. [38]MUSTAFFA Z,SULAIMAN M H,KAHAR M N M.Training LSSVM with GWO for price forecasting[C]∥International Conference on Informatics,Electronics & Vision.IEEE,2015:1-6. [39]MUSTAFFA Z,SULAIMAN M H,KAHAR M N M.LS-SVM hyper-parameters optimization based on GWO algorithm for time series forecasting[C]∥International Conference on Software Engineering and Computer Systems.IEEE,2015:183-188. [40]MIRJALILI S.How effective is the Grey Wolf optimizer in training multi-layer perceptrons[J].Applied Intelligence,2015,43(1):150-161. [41]AMIRSADRI S,MOUSAVIRAD S J,EBRAHPOUR-KOM- LEH H.A Levy flight-based grey wolf optimizer combined with back-propagation algorithm for neural network training[J].Neural Computing & Applications,2017(3-4):1-14. [42]HASSANIN M F,SHOEB A M,HASSANIN A E.Grey wolf optimizer-based back-propagation neural network algorithm[C]∥Computer Engineering Conference.IEEE,2018,30(12):3707-3720. [43]AHMED H M,YOUSSEF B A B,EIKORANY A S,et al.Hybrid gray wolf optimizer-artificial neural network classification approach for magnetic resonance brain images[J].Applied Optics,2018,57(7):B25. [44]SEEMA,KUMAR V.Modified Grey Wolf Algorithm for optimization problems[C]∥International Conference on Inventive Computation Technologies.IEEE,2017:1-5. [45]BAI Y,CHEN J R,ZHAN Z C.Analysis and Research of Improved Grey Wolf Optimization Algorithm[J].Computer Science and Application,2017,7(6):562-571.(in Chinese) 白媛,陈京荣,展之婵.改进灰狼优化算法的研究与分析[J].计算机科学与应用,2017,7(6):562-571. [46]GUPTA S,DEEP K.A novel Random Walk Grey Wolf Optimizer[J].Swarm & Evolutionary Computation,2018,3(4):217-241. [47]LONG W,CAI S H,JIAO J J,et al.Hybrid grey wolf optimization algorithm for high-dimensional optimization[J].Control and Decision,2016,31(11):1991-1997.(in Chinese) 龙文,蔡绍洪,焦建军,等.求解高维优化问题的混合灰狼优化算法[J].控制与决策,2016,31(11):1991-1997. [48]WANG M,TANG M Z.Novel grey wolf optimization algorithm based on nonlinear convergence factor[J].Application Research of Computers,2016,33(12):3648-3653.(in Chinese) 王敏,唐明珠.一种新型非线性收敛因子的灰狼优化算法[J].计算机应用研究,2016,33(12):3648-3653. [49]SONG H M,SULAIMAN M H,MOHAMED M R.An application of Grey Wolf optimizer for solving combined economicemission dispatch problems[J].International Review on Modelling & Simulations,2014,7(5):838-844. [50]WONG L I,SULAIMAN M H,MOHAMED M R.Solving Economic Dispatch Problems with Practical Constraints Utilizing Grey Wolf Optimizer[J].Applied Mechanics & Materials,2015,785(1):511-515. [51]SIVARAJAN G,SUBRAMANIAN S,JAYAKUMAR N,et al.Dynamic Economic dispatch for wind-combined heat and power systems using grey wolf optimization[J].International Journal of Applied Mathematics & Computer Science,2015,2(3):24-32. [52]SULEIMAN M H,MUSTAFA Z,MOHMED M R.Grey Wolf optimizer For solving Economic Dispatch Problem With Valve-Loading Effects[J].APRN Journal of Engineering and Applied Sciences,2015,10(21):1619-1628. [53]MORADI M,BADRIA,GHANDEHARI R.Non-convex con- strained economic dispatch with valve point loading effect using a grey wolf optimizer algorithm[C]∥Thermal Power Plants.IEEE,2016:96-104. [54]JAYABARATHI T,RAGHUNATHAN T,ADARSH B R,et al.Economic dispatch using hybrid grey wolf optimizer[J].Energy,2016,111:630-641. [55]KOMAKI G M,KAYVANFAR V.Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time[J].Journal of Computational Science,2015,8:109-120. [56]LV X Q,LIAO T L.Permutation flow-shop scheduling based on the grey wolf optimizer[J].Journal of Wuhan University of Technology,2015,37(5):111-116.(in Chinese) 吕新桥,廖天龙.基于灰狼优化算法的置换流水线车间调度[J].武汉理工大学学报,2015,37(5):111-116. [57]YANG Z,LIU C,QIAN W.An improved multi-objective grey wolf optimization algorithm for fuzzy blocking flow shop sche-duling problem[C]∥Advanced Information Technology,Electronic and Automation Control Conference.IEEE,2017:661-667. [58]JIANG T H.Flexible job shop scheduling problem with hybrid grey wolf optimization algorithm[J].Control and Decision,2018,33(3):503-508.(in Chinese) 姜天华.混合灰狼优化算法求解柔性作业车间调度问题[J].控制与决策,2018,33(3):503-508. [59]YAO Y Y,YE C M.Solving Job-Shop scheduling problem using improved hybrid grey wolf optimizer[J].Application Research of Computers,2017,35(5):1-6.(in Chinese) 姚远远,叶春明.求解作业车间调度问题的改进混合灰狼优化算法[J].计算机应用研究,2017,35(5):1-6. [60]DZUNG P Q,TIEN N T,TUYEN N D,et al.Selective harmo- nic elimination for cascaded multilevel inverters using grey wolf optimizer algorithm[C]∥2015 9th International Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia).IEEE,2015:2776-2781. [61]SONG X,TANG L,ZHAO S,et al.Grey Wolf Optimizer for parameter estimation in surface waves[J].Soil Dynamics & Earthquake Engineering,2015,75:147-157. [62]MUSTAFFA Z,SULAIMAN M H,YUSOF Y.An Application of Grey Wolf Optimizer for Commodity Price Forecasting[J].Applied Mechanics & Materials,2015,785(1):473-478. [63]YILDIZ B S,YILDIZ A R.Comparison of grey Wolf,whale,water cycle,ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod[J].Materialprufung,2018,60(3):311-315. [64]HASSAN H A,ZELLAGUI M.Application of Grey Wolf Optimizer Algorithm for Optimal Power Flow of Two-Terminal HVDC Transmission System[J].Advances in Electrical & Electronic Engineering,2017,15(5):701-712. [65]WEI Y,NI N,LIU D,et al.An Improved Grey Wolf Optimization Strategy Enhanced SVM and Its Application in Predicting the Second Major[J].Mathematical Problems in Engineering,2017,2017(1):1-12. [66]EMARY E,YAMANY W,HASSANIEN A E,et al.Multi-objective Gray-Wolf Optimization for Attribute Reduction.Procedia Computer Science,2015,65:623-632. [67]RAMESHKUMAR J,GANESAN S,SUBRAMANIAN S,et al.Short-term unit consignment solution using real-coded grey wolf algorithm[J].Australian Journal of Electrical & Electronics Engineering,2015,13(1):54-66. [68]RADMANESH M,KUMAR M,SARIM M.Grey wolf optimization based sense and avoid algorithm in a Bayesian framework for multiple UAV path planning in an uncertain environment [J].Aerospace Science & Technology,2018,77:168-179. [69]LIU H,WU H,LI Y.Smart wind speed forecasting using EWT decomposition,GWO evolutionary optimization,RELM learning and IEWT reconstruction[J].Energy Conversion & Management,2018,161:266-283. [70]SINGHAL R,KUMAR R.Receding horizon based greenhouse air temperature control using grey wolf optimization algorithm[C]∥IEEE Uttar Pradesh Section International Conference on Electrical,Computer and Electronics Engineering.IEEE,2017:32-37. [71]GUO Z Z,LIU R,GONG C Q,et al.Study on improvement of gray wolf algorithm[J].Application Research of Computers,2017,34(12):3603-3606.(in Chinese) 郭振洲,刘然,拱长青,等.基于灰狼算法的改进[J].计算机应用研究,2017,34(12):3603-3606. |
[1] | 王兵, 吴洪亮, 牛新征. 基于改进势场法的机器人路径规划 Robot Path Planning Based on Improved Potential Field Method 计算机科学, 2022, 49(7): 196-203. https://doi.org/10.11896/jsjkx.210500020 |
[2] | 储安琪, 丁志军. 基于灰狼优化算法的信用评估样本均衡化与特征选择同步处理 Application of Gray Wolf Optimization Algorithm on Synchronous Processing of Sample Equalization and Feature Selection in Credit Evaluation 计算机科学, 2022, 49(4): 134-139. https://doi.org/10.11896/jsjkx.210300075 |
[3] | 殷子樵, 郭炳晖, 马双鸽, 米志龙, 孙怡帆, 郑志明. 群智体系网络结构的自治调节:从生物调控网络结构谈起 Autonomous Structural Adjustment of Crowd Intelligence Network: Begin from Structure of Biological Regulatory Network 计算机科学, 2021, 48(5): 184-189. https://doi.org/10.11896/jsjkx.210200161 |
[4] | 周益旻, 刘方正, 王勇. 基于混合方法的IPSec VPN加密流量识别 IPSec VPN Encrypted Traffic Identification Based on Hybrid Method 计算机科学, 2021, 48(4): 295-302. https://doi.org/10.11896/jsjkx.200700189 |
[5] | 邓丽, 武金达, 李科学, 卢亚康. 基于TPE的SpaRC算法超参数优化方法 SpaRC Algorithm Hyperparameter Optimization Methodology Based on TPE 计算机科学, 2021, 48(2): 70-75. https://doi.org/10.11896/jsjkx.200500156 |
[6] | 张志强, 鲁晓锋, 隋连升, 李军怀. 集成随机惯性权重和差分变异操作的樽海鞘群算法 Salp Swarm Algorithm with Random Inertia Weight and Differential Mutation Operator 计算机科学, 2020, 47(8): 297-301. https://doi.org/10.11896/jsjkx.190700063 |
[7] | 李欣, 段詠程. 基于改进隐马尔可夫模型的网络安全态势评估方法 Network Security Situation Assessment Method Based on Improved Hidden Markov Model 计算机科学, 2020, 47(7): 287-291. https://doi.org/10.11896/jsjkx.190300045 |
[8] | 李建军, 汪校铃, 杨玉, 付佳. 基于CQPSO移动群智感知紧急任务分配方法研究 Emergency Task Assignment Method Based on CQPSO Mobile Crowd Sensing 计算机科学, 2020, 47(6A): 273-277. https://doi.org/10.11896/JsJkx.190700040 |
[9] | 武玉坤,肖杰,李伟,楼吉林. 融合渐近性的灰狼优化支持向量机模型 Support Vector Machine Model Based on Grey Wolf Optimization Fused Asymptotic 计算机科学, 2020, 47(2): 37-43. https://doi.org/10.11896/jsjkx.190100092 |
[10] | 吴文峻, 于鑫, 蒲彦均, 汪群博, 于笑明. 微服务时代的复杂服务软件开发 Development of Complex Service Software in Microservice Era 计算机科学, 2020, 47(12): 11-17. https://doi.org/10.11896/jsjkx.200700181 |
[11] | 吴英杰, 黄鑫, 葛晨, 孙岚. 差分隐私流数据实时发布中的自适应参数优化 Adaptive Parameter Optimization for Real-time Differential Privacy Streaming Data Publication 计算机科学, 2019, 46(9): 99-105. https://doi.org/10.11896/j.issn.1002-137X.2019.09.013 |
[12] | 胡鑫楠. 基于改进型混沌粒子群优化算法的FIR高通数字滤波器设计 FIR High Pass Digital Filter Design Based on Improved Chaos Particle Swarm Optimization Algorithm 计算机科学, 2019, 46(6A): 601-604. |
[13] | 孙博文, 韦素媛. 基于自适应调整策略灰狼算法的DV-Hop定位算法 DV-Hop Localization Algorithm Based on Grey Wolf Optimization Algorithm with Adaptive Adjutment Strategy 计算机科学, 2019, 46(5): 77-82. https://doi.org/10.11896/j.issn.1002-137X.2019.05.012 |
[14] | 赵宏伟, 田力威. 基于改进细菌觅食算法的云计算资源调度策略 Cloud Computing Resource Scheduling Strategy Based on Improved Bacterial Foraging Algorithm 计算机科学, 2019, 46(11): 309-314. https://doi.org/10.11896/jsjkx.181002000 |
[15] | 廖湖声, 黄珊珊, 徐俊刚, 刘仁峰. Spark性能优化技术研究综述 Survey on Performance Optimization Technologies for Spark 计算机科学, 2018, 45(7): 7-15. https://doi.org/10.11896/j.issn.1002-137X.2018.07.002 |
|