Computer Science ›› 2018, Vol. 45 ›› Issue (10): 212-216.

• Artificial Intelligence •

### Convergence Analysis of Artificial Bee Colony Algorithm:Combination of Number and Shape

HUO Jiu-yuan, WANG Ye, HU Zhuo-ya

1. School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China
• Received:2017-08-26 Online:2018-11-05 Published:2018-11-05

Abstract: The convergence analysis of existing methods for artificial bee colony algorithm(ABC) is based on the analysis method of global convergence.But these convergence analysis methods can’t show the convergence change in the convergence process of ABC.Firstly,the method of combination of number and shape is adopted,and the objective function diagram is combined to divide the convergence process of ABC into the global search stage and the optimal region search stage by using stage analysis.Then,the convergence process and changes of each stage are analyzed one by one based on transferring character that the artificial bees follow a certain degree of average distribution.Finally,the convergence results and change of ABC are obtained.This method can clearly show the convergence advantages and defects of the ABC algorithm,and reveal the changing process of the convergence probability of the algorithm.

CLC Number:

• TP301.6
 [1]KARABOGA D.An idea based on honey bee swarm fornumerical optimization[R].Erciyes University,2005.[2]KARABOGA D,BASTURK B.On the performance of artificial bee colony (ABC)algorithm[J].Applied Soft Computing,2008,8(1):687-697.[3]HORNG M H.Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation[J].Expert Systems with Applications,2011,38(11):13785-13791.[4]GAO W F,LIU S Y.A modified artificial bee colony algorithm[J].Computers & Operations Research,2012,39(3):687-697.[5]ALKIN Y,ERDAL E.A discrete artificial bee colony algorithm for single machine scheduling problems [J].International Journal of Production Research,2016,54(22):6860-6878.[6]YU W Y,HU D,TIAN N,et al.A novel search method based on artificial bee colony algorithm for block motion estimation[J].EURASIP Journal on Image & Video Processing,2017,2017(1):66.[7]ONDER B,FATIH T M.An artificial bee colony algorithm for the economic lot scheduling problem[J].International Journal of Production Research,2014,52(4):1150-1170.[8]KUANG F J,XU Y H,JIN Z.Artificial bee colony algorithm based on adaptive Tent chaotic search [J].Control Theory and Application,2014,31(11):1502-1509.(in Chinese) 匡芳君,徐蔚鸿,金忠.自适应Tent混沌搜索的人工蜂群算法[J].控制理论与应用,2014,31(11):1502-1509.[9]LUO J,LI Y.Swarm optimization algorithm with chaotic search strategy [J].Control and Decision,2010,25(12):1913-1916.(in Chinese) 罗钧,李研.具有混沌搜索策略的蜂群优化算法[J].控制与决策,2010,25(12):1913-1916.[10]ELKHATEEB N,BADR R.A Novel Variable Population Size Artificial Bee Colony Algorithm with Convergence Analysis for Optimal Parameter Tuning[J].International Journal of Computational Intelligence & Applications,2017,16(3):1-15.[11]ZAZAS I,DALEY S.Stability and convergence analysis for different harmonic control algorithm implementations[J].Journal of Vibration & Control,2017,23(8):1231-1247.[12]BONYADI,REZA M,ZBIGNIEW M.Analysis of Stability,Local Convergence,and Transformation Sensitivity of a Variant of the Particle Swarm Optimization Algorithm[J].IEEE Transactions on Evolutionary Computation,2016,20(3):370-385.[13]KIM S E,LEE J W,SONG W J.A noise-resilient affine projection algorithm and its convergence analysis[J].Signal Proces-sing,2016,121:94-101.[14]BONITO A,PASCIAK J E.Convergence analysis of variational and non-variational multigrid algorithms for the laplace-beltrami operator[J].Mathematics of Computation,2011,81(279):1263-1288.[15]REN Z H,WANG J,GAO Y L.The global convergence analysis of particle swarm optimization algorithm based on Markov China[J].Control Theory and Applications,2011,28(4):462-466.(in Chinese) 任子晖,王坚,高岳林.马尔科夫链的粒子群优化算法全局收敛性分析[J].控制理论与应用,2011,28(4):462-466.[16]CLEGHORN C W,ENGELBRECHT A P,et al.Particle swarm variants:standardized convergence analysis[J].Swarm Intelligence,2015,9(2／3):1935-3812.[17]DANTAS A F O D A,MAITELLI A L,et al.A Modified Matricial PSO Algorithm Applied to System Identification with Convergence Analysis[J].Journal of Control,Automation and Electrical Systems,2015,26(2):149-158.[18]NING A P,ZHANG X Y.Convergence analysis of artificial bee colony algorithm [J].Control and Decision,2013,28(10):1554-1558.(in Chinese) 宁爱平,张雪英.人工蜂群算法的收敛性分析[J].控制与决策,2013,28(10):1554-1558.[19]KONG X Y,LIU S Y,WANG Z.Almost sure convergence of artificial bee colony algorithm:martingale method[J].Computer Science,2015,42(9):246-248.(in Chinese) 孔翔宇,刘三阳,王贞.人工蜂群算法的几乎必然强收敛性:鞅方法[J].计算机科学,2015,42(9):246-248.[20]ZHU G,KWONG S.Gbest-guided artificial bee colony algo- rithm for numerical function optimization[J].Applied Mathematics and Conference on Computation,2010,217(2):3166-3177.[21]陈爱江,张文良.概率论与数理统计[M].北京:中国质检出版社,2011.
 [1] SHI Ke-xiang, BAO Li-yong, DING Hong-wei, GUAN Zheng, ZHAO Lei. Chaos Artificial Bee Colony Algorithm Based on Homogenizing Optimization of Generated Time Series [J]. Computer Science, 2021, 48(7): 270-280. [2] ZHANG Kai, LIU Jing-ju. Attack Path Analysis Method Based on Absorbing Markov Chain [J]. Computer Science, 2021, 48(5): 294-300. [3] WEI De-bin,YANG Peng,YANG Li,SHI Huai-feng. Virtual Network Function Fast Mapping Algorithm over Satellite Network [J]. Computer Science, 2020, 47(3): 248-254. [4] HUANG Guang-qiu,LU Qiu-qin. Protected Zone-based Population Migration Dynamics Optimization Algorithm [J]. Computer Science, 2020, 47(2): 186-194. [5] GUO Jia. Method of Predicting Performance of Storage System Based on Improved Artificial Neural Network [J]. Computer Science, 2019, 46(6A): 52-55. [6] ZHAO Xin-wei, LIU Wei. MANET Routing Discovery and Establishment Strategy Based on Node State [J]. Computer Science, 2019, 46(6): 112-117. [7] MU Xiao-fang, DENG Hong-xia, LI Xiao-bin, ZHAO Peng. Two-phase Image Steganalysis Algorithm Based on Artificial Bee Colony Algorithm [J]. Computer Science, 2019, 46(6): 174-179. [8] WANG Xue-jian, ZHAO Guo-lei, CHANG Chao-wen, WANG Rui-yun. Illegal Flow Analysis for Lattice Model of Information Flow [J]. Computer Science, 2019, 46(2): 139-144. [9] MA Wen-kai, LI Gui, LI Zheng-yu, HAN Zi-yang, CAO Ke-yan. Top-N Personalized Recommendation Algorithm Based on Tag [J]. Computer Science, 2019, 46(11A): 224-229. [10] YUAN Pei-yan, ZHANG Hao. Energy Efficient Routing Algorithm in Mobile Opportunistic Networks [J]. Computer Science, 2019, 46(11A): 387-392. [11] MAO Ying-chi and CHEN Yang. Uncertain Vehicle Intersection Trajectory Prediction [J]. Computer Science, 2018, 45(3): 235-240. [12] ZHANG Qi-man, ZHANG Ying. Study on Monte Carlo Location Algorithm in Wireless Sensor Networks [J]. Computer Science, 2018, 45(12): 77-80. [13] DING Dang, ZHANG Zhi-fei, MIAO Duo-qian and CHEN Yue-feng. Ordering Recommender Algorithm Based on Consumers’ Behavior [J]. Computer Science, 2017, 44(Z11): 46-50. [14] WANG Geng-sheng and ZHANG Min. Research of Improved CPF Algorithm for Intergrated Train Positioning [J]. Computer Science, 2017, 44(9): 296-299. [15] LIU Zhi-feng, CHEN Kai, LI Lei and ZHOU Cong-hua. Survivability Evaluation Model for Wireless Sensor Network under Multiple Attacks [J]. Computer Science, 2017, 44(8): 129-133.
Viewed
Full text

Abstract

Cited

Shared
Discussed
 [1] . [J]. Computer Science, 2018, 1(1): 1 . [2] LEI Li-hui and WANG Jing. Parallelization of LTL Model Checking Based on Possibility Measure[J]. Computer Science, 2018, 45(4): 71 -75 . [3] SUN Qi, JIN Yan, HE Kun and XU Ling-xuan. Hybrid Evolutionary Algorithm for Solving Mixed Capacitated General Routing Problem[J]. Computer Science, 2018, 45(4): 76 -82 . [4] ZHANG Jia-nan and XIAO Ming-yu. Approximation Algorithm for Weighted Mixed Domination Problem[J]. Computer Science, 2018, 45(4): 83 -88 . [5] WU Jian-hui, HUANG Zhong-xiang, LI Wu, WU Jian-hui, PENG Xin and ZHANG Sheng. Robustness Optimization of Sequence Decision in Urban Road Construction[J]. Computer Science, 2018, 45(4): 89 -93 . [6] SHI Wen-jun, WU Ji-gang and LUO Yu-chun. Fast and Efficient Scheduling Algorithms for Mobile Cloud Offloading[J]. Computer Science, 2018, 45(4): 94 -99 . [7] ZHOU Yan-ping and YE Qiao-lin. L1-norm Distance Based Least Squares Twin Support Vector Machine[J]. Computer Science, 2018, 45(4): 100 -105 . [8] LIU Bo-yi, TANG Xiang-yan and CHENG Jie-ren. Recognition Method for Corn Borer Based on Templates Matching in Muliple Growth Periods[J]. Computer Science, 2018, 45(4): 106 -111 . [9] GENG Hai-jun, SHI Xin-gang, WANG Zhi-liang, YIN Xia and YIN Shao-ping. Energy-efficient Intra-domain Routing Algorithm Based on Directed Acyclic Graph[J]. Computer Science, 2018, 45(4): 112 -116 . [10] CUI Qiong, LI Jian-hua, WANG Hong and NAN Ming-li. Resilience Analysis Model of Networked Command Information System Based on Node Repairability[J]. Computer Science, 2018, 45(4): 117 -121 .