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1. 管理科学系 深圳大学，广东 深圳 518060;
2. 宁波诺丁汉大学 计算机科学系，浙江 宁波 315100;
3. 西交利物浦大学 电气电子工程系，江苏 苏州 215123

Artificial bee colony algorithm: a survey
QIN Quande1, CHENG Shi2, LI Li1, SHI Yuhui3
1. Department of Management Science, Shenzhen University, Shenzhen 518060, China ;
2. Division of Computer Science, The University of Nottingham Ningbo, Ningbo 315100, China ;
3. Department of Electrical and Electronics Engineering, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China
Abstract: As a new swarm intelligence optimization algorithm, the artificial bee colony (ABC) algorithm has received wide attention in academic circles since its inception. Currently, the ABC algorithm is being used successfully in several real-world fields. Firstly, this article introduces the biological background and principles of the ABC algorithm. On the basis of analyzing the drawbacks of the basic ABC algorithm, we summarized the current studies on improvements of the basic ABC algorithm with regards to three aspects: parameter adjustment, hybrid algorithms, and design of new learning strategies. In view of the realistic complex environment, this article introduces the research progress on constrained optimization and multi-objective optimization using the ABC algorithm. Finally, the applications of the ABC algorithm are described and several further research directions are proposed.
Key words: swarm intelligence     artificial bee colony algorithm     constrained optimization     multi-objective optimization     optimization algorithm

1 人工蜂群算法 1.1 人工蜂群算法的生物背景

1.2 人工蜂群算法的基本原理

ABC算法在求解优化问题时，蜜源的位置被抽象成解空间中的点，代表问题的潜在解，蜜源i(i=1, 2, …, NP)的质量对应于解的适应度值fiti，NP为蜜源的数量。ABC算法将蜂群分为引领蜂、跟随蜂和侦察蜂3种类型，其中引领蜂和跟随蜂各占蜂群的一半，数量等于蜜源的数量，且每个蜜源同一时间内只有一只引领蜂采蜜[2, 4]

 (1)

 (2)

 (3)

 (4)

 (5)

1.3 人工蜂群算法的步骤

ABC的主要步骤如下[2, 5]

1)初始化各蜜源Xi；设定参数NP、limit以及最大迭代次数；t=1；

2)为蜜源Xi分配一只引领蜂，按式(2)进行搜索，产生新蜜源Vi

3)依据式(5)评价Vi的适应度，根据贪婪选择的方法确定保留的蜜源；

4)由式(3)计算引领蜂找到的蜜源被跟随的概率；

5)跟随峰采用与引领蜂相同的方式进行搜索，根据贪婪选择的方法确定保留的蜜源；

6)判断蜜源Xi是否满足被放弃的条件。如满足，对应的引领蜂角色变为侦察蜂，否则直接转到8)；

7)侦察蜂根据式(4)随机产生新蜜源；

8)t=t+1；判断算法是否满足终止条件，若满足则终止，输出最优解，否则转到2)。

2 人工蜂群算法的改进

2.1 算法的参数调整

Akay和Karaboga[11]通过多组实验系统研究了参数设置对ABC算法性能的影响，实验结果表明：1) ABC算法对问题维数不太敏感，适合于求解高维问题；2)群体规模(colony size，CZ)对ABC算法的性能影响不明显，即使较小的群体规模仍可获得满意解；3) limit值对算法的性能有较大的影响，太小的limit不利于蜂群协作搜索，太大的limit降低了算法的探索能力，对于较复杂的函数，limit设置为(CZD)是较好的初始选择。为了使初始解具有多样性，较均匀地分布在搜索空间，暴励等[12]采用反向学习(opposition-based learning)的方法产生初始解。罗钧等[13]利用混沌序列初始化的方法，提高了解的多样性和遍历性。Akay和Karaboga[6]在基本ABC算法的基础上增加了修改率(modification rate, MR)的参数，其用于控制搜索的扰动维数，给出了基于Rechenberg 1/5变异规则的自适应调整扰动幅度的方法。在基本ABC算法中，跟随蜂按照式(3)计算选择蜜源的概率，这种方法容易导致较大的选择压力(selection pressure)，群体多样性难以维护。Bao等[14]对ABC算法的选择机制进行系统分析和比较，并提出了3种新的选择机制：裂变选择(disruptive selection)、排序选择(rank selection)和竞标赛选择(tournament selection), 实验结果表明了新的选择机制的有效性。Konrady等[15]研究了基于跟随蜂与引领蜂之间距离的选择方法，当跟随蜂与引领蜂的距离越小时，跟随蜂选择该引领蜂发现蜜源的概率越大，反之选择概率越小。Lee等[16]在ABC算法中引入群体多样性的机制，根据群体多样性的门槛值选择采用不同的搜索公式。Rajasekhar等[17]利用Levy分布具有正态分布与柯西分布的特点，给出了基于Levy分布变异的改进ABC算法。Alam等[18]提出了一种基于指数分布的自适应变异步长机制的ABC算法，动态控制搜索过程中的探索和开发能力。Alatas[19]在基本ABC算法中运用混沌映射机制实现参数的适应变化，提高了算法收敛速度和全局搜索能力。

2.2 混合算法

2.3 设计新的学习策略

Banharnsakun等[10]在跟随蜂的搜索公式上添加了迄今为止最佳个体(Best-so-far)的适应度值来提高开发能力，且搜索半径随着迭代次数增加呈线性递减，标准测试函数的实验结果和在图像压缩上的应用表明该算法能快速搜索到高质量的解。Li等[8]在基本ABC算法的蜜源搜索公式上添加了惯性权重和加速系数、惯性权重和加速系数根据适应度值确定。在DE算法的启发下，Gao和Liu[34]提出了2种改进的蜜源搜索公式：“ABC/best/1”和“ABC/rand/1”。类似于PSO算法，Zhu等在蜜源搜索公式上增加了全局最优位置的引导，并对增加的参数进行了实验分析，结果表明改进算法能较好地平衡探索和开发能力。Tsai等[35]将引领蜂与跟随蜂之间的关系利用万有引力定律进行描述，提出了一种交互作用的ABC算法。Liu等[36]分析了基本ABC算法在搜索时没有考虑配对个体之间的适应度好坏，可能误导搜索方式，从而提出了一种基于相互学习(mutual learning)的改进ABC算法。为提高搜索能力，Gao等[37]提出一种改进的蜜源搜索公式，将解的每一维看成是一次抽样，通过正交学习策略可以产生更具前景的解，提出了基于改进的搜索公式和正交学习的ABC算法。

3 人工蜂群算法的约束优化

Deb规则是处理约束优化问题的一种常见方法，在ABC算法中得到较多应用。Deb规则采用了竞标赛选择的方法区别对待不可行解和可行解[38]，简单描述为：1)可行解总是优于不可行解；2)在可行解中，按适应度值的大小排序；3)在2个不可行解中，违背约束量较小的不可行解优先选择。Karaboga和Basturk[39]最早提出了基于Deb规则求解约束优化问题的ABC算法。比较有代表性的工作是Karaboga和Akay在2011年发表的文章[40]，其不但运用Deb规则处理约束，而且根据可行解的适应度值和不可行解违背约束的程度计算随蜂选择蜜源的概率。Tuba等[41]采用同文献[40]的方法处理约束，区别在于侦察蜂不是在搜索空间随机寻找蜜源，而是在最优蜜源和另一个蜜源的共同引导下搜寻。Li等[42]提出了一种自适应的ABC算法求解约束优化问题，引领蜂搜索阶段采用了Deb规则，跟随蜂搜索阶段将约束优化问题转化为多目标问题，给出了MR的自适应机制。采用Deb规则处理优化问题简单易行，但其存在一定的缺陷[43]：1)难于维持群体的多样性；2)当最优解位于或靠近边界的时候，Deb规则的效果不佳。

4 人工蜂群算法的多目标优化

5 人工蜂群算法的应用研究

ABC算法是为求解函数优化问题而提出来的，较多的研究集中于此。ABC算法求解函数优化问题具有天然的优势，也是目前应用最为成功的领域。经过学者们的研究，将ABC算法的应用领域不断推广，目前已经成功应用于神经网络训练、组合优化、电脑系统优化、系统和工程设计等多个领域。

5.1 神经网络训练

Karaboga等[53]最早应用ABC算法于训练前馈神经网络。Ozurk等[54]提出了ABC算法和Levenberg-Marquardt的混合方法用于训练神经网络。Zhang等[55]基于适应度缩放和混沌理论提出一种改进的ABC算法，并应用于前馈神经网络的训练。Kurban等[56]采用ABC算法训练RBF神经网络，并与GA、卡尔曼滤波和梯度下降算法进行了比较，结果表明ABC算法是一种高效训练RBF的算法。Yeh等[57]于2011年提出了应用ABC算法和蒙特卡洛模拟训练递归神经网络，并成功应用于预测网络的可靠性。Garro等[58]采用ABC算法同时优化神经网络的结构、连接权重和转换函数。

5.2 组合优化

5.3 电力系统优化

Cobanli等[73]运用ABC算法求解电力系统中有功率损耗最小化的问题。Özyön等[74]通过目标加权的方式将环境经济调度问题转变为一个单目标问题，利用ABC算法进行求解。Rezaei Adaryani等[75]在考虑燃料成本、有功功率损耗和电压稳定性等因素的情况下，构建了非线性非凸的多目标的最优潮流模型，运用ABC算法对模型进行求解。Hemamalini等[76]采用ABC算法求解成本函数为非光滑的负荷经济批量调度问题。Ayan和Kilic[77]应用了ABC算法求解最优无功潮流(optimal reactive power flow)的优化问题，对IEEE 30-bus和IEEE 118-bus的求解结果表明了ABC算法的有效性。Govardhan[78]等采用了ABC算法求解机组最优启停(optimal unit commitment)问题，并将求解结果与PSO算法、DE算法进行了比较。

5.4 系统与工程设计

6 结论与展望

ABC算法以其良好的搜索性能和简单易操作的性能，受到了学术界的广泛关注。综观ABC算法的研究现状，总体来说，其相关的研究仍处于初级阶段，有很多问题值得进一步的研究，简单归纳如下：

1)ABC算法的理论研究。

2)ABC算法参数的自适应策略。

3)多目标ABC算法的研究。

4)设计更加符合真实自然的ABC算法。

ABC算法受蜜蜂觅食行为的启发而提出，模拟了蜜蜂觅食的部分行为。真实自然环境中蜜蜂的觅食行为更为复杂，例如：蜂群采蜜时进行了合理分工，但在某些特殊情况下，蜜蜂的职能可以发生转化，如他们的年龄变化、性激素、由遗传决定的个体的倾向等。综合考虑这些因素，将蜜蜂觅食的一些特性通过抽象设计合适的算子嵌入到ABC算法中，将进一步推动ABC算法的发展。

5)ABC算法的动态优化研究。

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DOI: 10.3969/j.issn.1673-4785.201309064

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#### 文章信息

QIN Quande, CHENG Shi, LI Li, SHI Yuhui

Artificial bee colony algorithm: a survey

CAAI Transactions on Intelligent Systems, 2014, 9(2): 127-135
http://dx.doi.org/10.3969/j.issn.1673-4785.201309064