﻿ 基于模糊控制的权重决策灰狼优化算法
 计算机系统应用  2018, Vol. 27 Issue (10): 202-208 PDF

1. 中国科学院 声学研究所, 北京 100190;
2. 中国科学院 声学研究所 中国科学院水下航行器信息技术重点实验室, 北京 100190;
3. 中国科学院大学, 北京 100049

Hybrid Grey Wolf Optimizer Algorithm with Fuzzy Weight Strategy
XING Yan-Zhen1,2,3, WANG Dong-Hui2,3
1. Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;
2. CAS Key laboratory of Technology for Autonomous Underwater Vehicles, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;
3. University of Chinese Academy of Sciences, Beijing 100049, China
Foundation item: National Natural Science Foundation of China (61274025); Youth Telant Project of Institute of Acoustics, Chinese Academy of Sciences (QNYC201622)
Abstract: To solve the problem of slow convergence speed before reaching the global optimum and low precision of optimization in Grey Wolf Optimizor (GWO), a hybrid GWO algorithm based on fuzzy weight strategy is proposed. By replacing the linear convergence factor in original algorithm with a new non-linear convergence factor, global search ability is improved. Furthermore, the algorithm employs a fuzzy weight strategy to offer discrepant weight to agents who are responsible for the decision, which will enhance the optimizing ability therefore. Numberical experiments are conducted in 23 standard test functions. Experimental results show that the proposed FWGWO algorithm has better performance compared with other algorithms.
Key words: Grey Wolf Optimizor (GWO)     fuzzy control     heuristic algorithm     weight factor     population optimization algorithm

1 GWO算法 1.1 灰狼群体的社会层级制度

1.2 GWO算法描述

GWO算法是模拟灰狼群体捕食过程的寻优算法. 寻找最优解的过程可看做狼群捕食的过程, 目标猎物的位置即为对应函数的最优解. 将靠近目标最优解的个体看作狼群中起领导决策作用的狼, 领导个体通过不断更新与目标之间的距离判断移动的方向, 最后带领群体靠近目标.

 图 1 灰狼群体社会等级示意图

 $D=|C \cdot {X_p}(t) - X(t)|$ (1)
 $C=2 \cdot {r_1}$ (2)

 $X(t + 1)={X_p}(t) - A \cdot D$ (3)
 $A=2a \cdot {r_2} - a$ (4)
 $a=2 - \frac{2}{{Max\_iter}}t$ (5)

 ${D_\alpha }=|{C_1} \cdot {X_\alpha } - {{X}}|$ (6)
 ${D_\beta }=|{C_2} \cdot {X_\beta } - {{X}}|$ (7)
 ${D_\delta }=|{C_3} \cdot {X_\delta } - {{X}}|$ (8)
 ${X_1}{\rm{ = }}{X_\alpha } - A \cdot {D_\alpha }$ (9)
 ${X_2}{\rm{ = }}{X_\beta } - A \cdot {D_\beta }$ (10)
 ${X_3}{\rm{ = }}{X_\delta } - A \cdot {D_\delta }$ (11)
 $X(t + 1)=\frac{{{X_1} + {X_2} + {X_3}}}{3}$ (12)
2 FWGWO算法 2.1 改进的收敛因子

 图 2 变量A与种群搜索的关系

 $a=2\sqrt {1 - {{\left( {\frac{t}{{Max\_iter}}} \right)}^2}}$ (13)
2.2 基于权重决策的位置更新策略

 \begin{aligned} X(t + 1)= & \frac{{f{w_\alpha }}}{{f{w_\alpha } + f{w_\beta } + f{w_\delta }}}{X_1} + \frac{{f{w_\beta }}}{{f{w_\alpha } + f{w_\beta } + f{w_\delta }}}{X_2} \\ & + \frac{{f{w_\delta }}}{{f{w_\alpha } + f{w_\beta } + f{w_\delta }}}{X_3} \\ \end{aligned} (14)

 图 3 基本模糊控制器

 图 4 模糊控制器输入—迭代次数的隶属度函数

 图 5 模糊控制器输出—fwα/fwβ/fwδ的隶属度函数

2.3 FWGWO算法描述

1) 初始化种群规模N, 随机产生初始种群, 初始化t=0, 初始化 $a$ , AC等参数;

2) 计算种群中每个个体的适应度值, 将适应度排名前三的个体分别记为Xα, XβXδ;

3) 由式(6)–(8)计算种群中其他个体与Xα, XβXδ的距离, 并根据式(9)–(11)更新个体位置.

4) 由模糊控制器获得决策层Xα, XβXδ的权重系数, 由式(14)完成目标定位.

5) 更新算法中 $a$ , AC等参数

6) 判定算法是否满足收敛条件. 如果满足, 则算法结束; 否则, 令t=t+1, 返回第3)步.

3 实验及分析

4 结论与展望

 图 6 算法针对不同函数的收敛曲线示意图

 [1] Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Boston: Addison-Wesley Professional, 1989: 2104–2116. [2] Kennedy J, Eberhart R. Particle swarm optimization. Proceedings of ICNN’95-International Conference on Neural Networks. Perth, WA, Australia. 2002. 1942–1948. [3] Dorigo M, Birattari M, Stutzle T. Ant colony optimization. IEEE Computational Intelligence Magazine, 2006, 1(4): 28-39. DOI:10.1109/MCI.2006.329691 [4] Bertsimas D, Tsitsiklis J. Simulated Annealing. Statistical Science, 1993, 8(1): 10-15. DOI:10.1214/ss/1177011077 [5] Yang XS. A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, et al, eds. Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). Berlin: Springer, 2010. 65–74. [6] Yang XS. Firefly algorithms for multimodal optimization. In: Watanabe O, Zeugmann T, eds. Stochastic Algorithms: Foundations and Applications. Berlin: Springer. 2010. 169–178. [7] Yang XS, Deb S. Cuckoo search via levy flights. World 2009 Congress on Nature & Biologically Inspired Computing. Coimbatore, India. 2010. 210–214. [8] Mirjalili S, Mirjalili SM, Lewis A. Grey wolf optimizer. Advances in Engineering Software, 2014, 69: 46-61. DOI:10.1016/j.advengsoft.2013.12.007 [9] Komaki GM, Kayvanfar V. Grey wolf optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time. Journal of Computational Science, 2015, 8: 109-120. DOI:10.1016/j.jocs.2015.03.011 [10] Daniel E, Anitha J, Kamaleshwaran KK, et al. Optimum spectrum mask based medical image fusion using gray wolf optimization. Biomedical Signal Processing and Control, 2017, 34: 36-43. DOI:10.1016/j.bspc.2017.01.003 [11] Shayeghi H, Asefi S, Younesi A. Tuning and comparing different power system stabilizers using different performance indices applying GWO algorithm. International Comprehensive Competition Conference on Engineering Sciences. Anzali, Iran. 2016. [12] Mirjalili S. How effective is the grey wolf optimizer in training multi-layer perceptrons. Applied Intelligent, 2015, 43(1): 150-161. DOI:10.1007/s10489-014-0645-7 [13] Faris H, Aljarah I, Al-Betar MA, et al. Grey wolf optimizer: A review of recent variants and applications. Neural Computing and Applications, 2018, 30(2): 413-435. DOI:10.1007/s00521-017-3272-5 [14] Kohli M, Arora S. Chaotic grey wolf optimization algorithm for constrained optimization problems. Journal of Computational Design and Engineering, 2017. DOI:10.1016/j.jcde.2017.02.005 [15] Natesan G, Chokkalingam A. Opposition learning-based grey wolf optimizer algorithm for parallel machine scheduling in cloud environment. International Journal of Intelligent Engineering and Systems, 2017, 10(1): 186-195. DOI:10.22266/ijies2017.0228.20 [16] 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. 控制与决策, 2016, 31(11): 1991-1997. [17] Mittal N, Singh U, Sohi BS. Modified grey wolf optimizer for global engineering optimization. Applied Computational Intelligence and Soft Computing, 2016, 2016(8). DOI:10.1155/2016/7950348 [18] Singh N, Singh SB. Hybrid algorithm of particle swarm optimization and grey wolf optimizer for improving convergence performance. Journal of Applied Mathematics, 2017, 2017: 2030489. DOI:10.1155/2017/2030489 [19] Tawhid MA, Ali AF. A hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function. Memetic Computing, 2017, 9(4): 347-359. DOI:10.1007/s12293-017-0234-5 [20] 龙文, 伍铁斌. 协调探索和开发能力的改进灰狼优化算法. 控制与决策, 2017, 32(10): 1749-1757. [21] Muro C, Escobedo R, Spector L, et al. Wolf-pack (Canis Iupus) hunting strategies emerge from simple rules in computational simulations. Behavioural Processes, 2011, 88(3): 192-197. DOI:10.1016/j.beproc.2011.09.006 [22] 石绍应, 王小谟, 曹晨, 等. 规则数确定的自适应模糊分类器. 西安电子科技大学学报(自然科学版), 2017, 44(2): 81-87.