﻿ 混沌搜索策略的改进人工蜂群算法
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1. 辽宁工程技术大学基础教学部, 辽宁葫芦岛 125105;
2. 辽宁工程技术大学电气与控制工程学院, 辽宁葫芦岛 125105

Improved artificial bee colony algorithm based on chaos searching strategy
PENG Xiaohua1, LIU Liqiang2
1. Ministry of basic education, Liaoning University of engineering and Technology, Huludao 125105, China;
2. College of electrical and control engineering, Liaoning University of engineering and Technology, Huludao 125105, China
Abstract: The current artificial bee colony algorithm results in the swarm lacking diversity, and the global and local search abilities and convergence speed are slow. We propose an improved artificial bee colony algorithm based on a chaotic search strategy. We map the algorithm with the carrier using a chaos decision variable transformation, generating new neighborhood points, and recruiting bees within a broader search space and from better source locations, while enhancing swarm diversity. In addition, the investigation of a local honey bee search better solved the algorithm problem of the local minimum and improved the convergence property of the artificial bee colony algorithm. The most recent six simulation validations of the standard test functions using the proposed artificial bee colony algorithm, based on the chaotic search strategy, are significantly better than the performance results of the current artificial bee colony algorithm.
Key words: artificial bee colony algorithm     chaotic search strategy     carrier mapping     local search nectar     the swarm diversity     chaos-decision variable     convergence performance     simulation experiment

1 人工蜂群算法

 图 1 人工蜂群算法的基本原理 Fig. 1 The basic principle of artificial swarm algorithm

1)初始化参数。设置蜂群规模NP，采蜜蜂Ne，观察蜂Nu，蜜源个数NP/2，蜜源维数D，邻域搜索空间S，迭代次数K，蜜蜂停留阈值Limit，采蜜蜂种群记为X=[X1 X2XNe]，其中XiS(i≤Ne)Ne个个体，X(0)代表初始采蜜蜂种群，X(n)代表第n代采蜜蜂种群。

2)对于n=0时刻，随机生成Ns个可行解(X1,X2，…,XNe)，具体随机产生的可行解Xi

3) 设置初始迭代次数iter=0，对于第n步的采蜜蜂Xi(n)，在当前位置向量附近邻域进行搜索新的位置，搜索公式为

4)根据最优适应度选择原则，既要保留最优位置蜜源，又要使蜂群搜索方向向着蜜源含量高升的方向迭代。故当采蜜蜂在蜂巢邻域范围第2次找到新蜜源时，记此时位置向量为new_Xi，而上一次所找到的蜜源位置向量为Xi，则记2次蜜源搜索中，适应度值较大的位置蜜源为Ts，其概率分布为

5)当许多个采蜜蜂将所采蜜源信息带到舞蹈区共享给观察蜂时，观察蜂将会做出2个动作行为：首先，观察蜂根据概率式(4)选择符合自身条件的采蜜蜂，转化为采蜜蜂；其次，通过式(4)中适应度值公式在蜂群邻域进行初次蜜源的搜索。不同观察蜂被招募为对应采蜜蜂的概率为

6)对比多次搜索到的新蜜源位置，生成最优蜜源位置向量集(x1,x2,…,xd)，d为现有采蜜蜂个数，同时得出，到目前为止更新的最优适应度Best_Fitness。

7)在蜜源搜索中，不断地用标志向量trail(i)记录着同一采蜜蜂对同一蜜源位置的搜索次数，当trail(i)>Limit且不满足式(3)时，即说明该邻域范围位置蜜源含蜜量整体偏低，若再在此地搜索蜜源，会严重影响蜜源质量及搜索速度，故须将此类采蜜蜂重新规定初始蜜源位置。即

8)如果满足停止准则，则停止计算并输出最优适应度值Best_Fitness，迭代次数iter=iter+1，相应的参数(x1,x2,…,xD)，否则转向第3)步。

2 基于混沌搜索策略的改进人工蜂群算法

1)按照操作1)进行，记最大混沌迭代次数为Cmax

2)利用混沌序列初始蜂群生成数值都在(0,1)的NP个互异D维向量y0，通过式(7)的载波方式将y0映射到原解空间邻域范围内，产生决策变量。

3)将混沌变量y′n,dyn,d线性组合得到新的决策变量y″n,d[19]

4)按照操作2)~6)进行。

5)通过计算适应度函数值Fitness(y′n,d)，取适应度值大的前NP/2个向量作为蜜源位置，对应NP/2个采蜜蜂。通过式(2) 更新蜂群位置，NP/2个采蜜蜂在邻域附近按照式(7)寻找新解y″n,d，再次计算适应度值Best_Fitness(y′n,d)，若Best_Fitness(y″n,d)Fitness(y′n,d)，y′n,d=y″n,d，trail(i)=0；否则y′n,d不变，trail(i)=trail(i)+1，并计算观察蜂转化为采蜜蜂的个数。

6)若trail(i)>Limit时，进行7)，然后第i个采蜜蜂舍弃蜜源转变为侦查蜂，侦查蜂在混沌区域范围内搜索邻域蜜源y″n,d

7)记录到目前为止的所有蜜蜂寻找的最优蜜源，更新iter=iter+1，判断是否达到最大混沌迭代次数，如果是，结束混沌搜索，找到最优解，否则，返回到 2)。CSABC算法的基本流程图[14]图 2

 图 2 CSABC算法流程图 Fig. 2 CSABC algorithm flow chart
3 CSABC算法仿真 3.1 标准测试函数

 函数 测试函数表达式 搜索范围 最优值 f 1 [－100,100] f 1(0,0,…,0)=0 f 2 [－30,30] f 2(1,1,…,1)=0 f 3 [－5.12,5.12] f 3(0,0,…,0)=0 f 4 [－600,600] f 4(0,0,…,0)=0 f 5 [－32,32] f 5(0,0,…,0)=0 f 6 [－500,500] f 6(420.9687,…)=418.9829
3.2 实验仿真分析

 图 3 Sphere函数寻优对比曲线 Fig. 3 Sphere of function optimization curve
 图 4 Rosenbrock函数寻优对比曲线 Fig. 4 Rosenbrock of function optimization curve
 图 5 Rastrigin函数寻优对比曲线 Fig. 5 Rastrigin of function optimization curve
 图 6 Griewank函数寻优对比曲线 Fig. 6 Griewank of function optimization curve
 图 7 Ackley函数寻优对比曲线 Fig. 7 Ackley of function optimization curve
 图 8 Schwefel函数寻优对比曲线 Fig. 8 Schwefe of function optimization curve

 函数 算法 均值 标准差 最优值 Sphere ABC 5.34516×10 -11 3.55671×10 -12 4.85461×10 -12 CSABC 1.23503×10 -16 6.12312×10 -17 1.92924×10 -16 Rosenbrock ABC 25.697894 13.10012 23.28459 CSABC 0.541187 0.556073 0.330645 Rastrigrin ABC 9.05027×10 -9 1.59532×10 -8 6.25471×10 -7 CSABC 6.20541×10 -13 1.07481×10 -12 0 Griewank ABC 3.71686×10 -6 4.70565×10 -6 9.04417×10 -7 CSABC 2.22828×10 -10 3.82682×10 -10 6.64705×10 -10 Ackley ABC 1.5099×10 -8 0.78904×10 -8 1.80593×10 -8 CSABC 1.74675×10 -14 4.10232×10 -15 2.22045×10 -14 Schwefel ABC -19.6952 0.958708 -16.1453 CSABC -34.8402 0.671552 -34.4944

 函数 算法 均值 标准差 平均时间 Rosen-brock IABC 4.95867×10 -1 7.66847×10 -1 25.1755 SFABC 6.471200 3.852700 26.6514 LRABC 1.35918×10 -1 8.74717×10 -2 24.1843 CSABC 5.2657×10 -2 6.38326×10 -3 17.5548 Grie-wank IABC 0 0 31.0128 SFABC 2.5457×10 -15 7.78426×10 -16 22.8748 LRABC 0 0 27.8934 CSABC 0 0 18.2354

5 结束语

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DOI: 10.11992/tis.201507032

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#### 文章信息

PENG Xiaohua, LIU Liqiang

Improved artificial bee colony algorithm based on chaos searching strategy

CAAI Transactions on Intelligent Systems, 2015, 10(6): 927-933.
DOI: 10.11992/tis.201507032