Artificial Bee Colony Algorithm Based on Adaptive Search Equation and Extended Memory

From the perspective of psychology, a modified artificial bee colony algorithm (ABC, for short) based on adaptive search equation and extended memory (ABCEM, for short) for global optimization is proposed in this paper. In the proposed ABCEM algorithm, an extended memory factor is introduced into store employed bees’ and onlooker bees’ historical information comprising recent food sources, personal best food sources, and global best food sources, and the solution search equation for the employed bees is equipped with adaptive ability. Moreover, a parameter is employed to describe the importance of the extended memory. Furthermore, the extended memory is added to two solution search equations for the employed bees and the onlookers to improve the quality of food source. To evaluate the proposed algorithm, experiments are conducted on a set of numerical benchmark functions. The results show that the proposed algorithm can balance the exploration and exploitation, and can improve the accuracy of optima solutions and convergence speed compared with other current improved ABCs for global optimization in most of the tested functions.     

基于分段搜索策略的改进蜂群算法

针对基本人工蜂群算法在解决优化问题时收敛速度不够快、易陷入局部最优的缺陷,提出一种改进蜂群算法.该算法采用“分段搜索”方式对食物源进行贪婪更新,以提高食物源更新的成功率;同时,招募所有观察蜂选择当前最优食物源,以实现对最优食物源的充分优化.对经典测试函数反复实验的结果表明,改进算法计算结果稳定,与基本蜂群算法相比,加速收敛效果非常明显,全局搜索能力显著提高,运行时间大大缩短.     

基于当前最优解的分段搜索策略的人工蜂群算法

为了克服人工蜂群算法在求解函数优化问题中所存在的局部搜索能力差、收敛精度低的缺点,提出了一种基于当前最优解的分段搜索策略的人工蜂群算法。该算法中跟随蜂利用由全局当前最优解和个体当前最优解引导的局部搜索策略逐维进行变异,并采用基于“分段思想”的局部搜索策略对蜜源进行贪婪更新,以提高蜜源的更新效率,从而提高了人工蜂群算法的局部搜索能力。6个标准测试函数的仿真实验结果表明,与基本人工蜂群算法相比,改进后的人工蜂群算法在寻优精度和收敛速度上均有明显提高。     

基于动态评价选择策略的改进人工蜂群算法

针对标准人工蜂群(ABC)算法易陷入局部极值的问题,对标准ABC算法的轮盘赌选择机制进行了修改,提出了一种基于动态评价选择策略的改进人工蜂群(DSABC)算法。首先,根据到当前为止一定迭代次数内蜜源位置的连续更新或停滞次数,对每个蜜源位置进行动态评价;然后,利用所得的评价函数值为蜜源招募跟随蜂。在6个经典测试函数上的实验结果表明:与标准ABC算法相比,动态评价选择策略改进了标准ABC算法的选择机制,使得DSABC算法的求解精度有较大幅度提高,特别是对于两种不同维数的Rosenbrock函数,所得最优值的绝对误差分别由0.0017和0.0013减小到0.000049和0.000057;而且,DSABC算法克服了进化后期因群体位置多样性丢失较快而产生的早熟收敛现象,提高了整个种群的收敛精度及解的稳定性,从而为函数优化问题提供了一种高效可靠的求解方法。     

Gaussian bare-bones artificial bee colony algorithm

As a relatively new global optimization technique, artificial bee colony (ABC) algorithm becomes popular in recent years for its simplicity and effectiveness. However, there is still an inefficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. To overcome this drawback, a Gaussian bare-bones ABC is proposed, where a new search equation is designed based on utilizing the global best solution. Furthermore, we employ the generalized opposition-based learning strategy to generate new food sources for scout bees, which is beneficial to discover more useful information for guiding search. A comprehensive set of experiments is conducted on 23 benchmark functions and a real-world optimization problem to verify the effectiveness of the proposed approach. Some well-known ABC variants and state-of-the-art evolutionary algorithms are used for comparison. The experimental results show that the proposed approach offers higher solution quality and faster convergence speed.     

基于分段搜索策略的自适应差分进化人工蜂群算法

针对人工蜂群算法在求解函数优化问题时存在的探索能力强,而开发能力不足和收敛性能差的问题,本文提出一种基于分段搜索策略的自适应差分进化人工蜂群算法。该算法将改进后的差分进化算法中的变异操作引入到观察蜂的局部搜索策略中,让观察蜂在雇佣蜂逐维变异后的当前最优解周围进行局部搜索,并采用分段搜索的方式更新蜜源,以提高其局部搜索能力。仿真实验结果表明,与基本人工蜂群算法相比,改进后的算法有效地平衡了算法的探索能力和开发能力,并提高了算法的寻优精度和收敛速度。     

云变异人工蜂群算法

针对传统人工蜂群算法存在收敛速度慢和易陷入局部最优的问题,提出一种基于云模型的改进人工蜂群算法。通过正态云算子计算候选位置,自适应调整算法的局部搜索范围,以提高算法的收敛速度和勘探能力。为保持种群多样性,引入一个新的概率选择策略,使较差的个体具有较大的选择概率,并且利用历史最优解探索新的位置。标准复合函数测试表明,改进算法的收敛速度和求解精度得到提升,优于一些新近提出的改进人工蜂群算法。     

量子位Bloch坐标的量子人工蜂群优化算法

为了改善人工蜂群(ABC)算法在解决多变量优化问题时存在的收敛速度较慢、容易陷入局部最优的不足,结合量子理论和人工蜂群算法提出一种新的量子优化算法。算法首先采用量子位Bloch坐标对蜂群算法中食物源进行编码,扩展了全局最优解的数量,提高了蜂群算法获得全局最优解的概率;然后用量子旋转门实现搜索过程中的食物源更新。对于量子旋转门的转角关系的确定,提出了一种新的方法。从理论上证明了蜂群算法在Bloch球面每次以等面积搜索时,量子旋转门的两个旋转相位大小近似于反比例关系,避免了固定相位旋转的不均等性,使得搜索呈现规律性。在典型函数优化问题的实验中,所提算法在搜索能力和优化效率两个方面优于普通量子人工蜂群(QABC)算法和单一人工蜂群算法。     

A recombination-based hybridization of particle swarm optimization and artificial bee colony algorithm for continuous optimization problems

This paper presents a hybridization of particle swarm optimization (PSO) and artificial bee colony (ABC) approaches, based on recombination procedure. The PSO and ABC are population-based iterative methods. While the PSO directly uses the global best solution of the population to determine new positions for the particles at the each iteration, agents (employed, onlooker and scout bees) of the ABC do not directly use this information but the global best solution in the ABC is stored at the each iteration. The global best solutions obtained by the PSO and ABC are used for recombination, and the solution obtained from this recombination is given to the populations of the PSO and ABC as the global best and neighbor food source for onlooker bees, respectively. Information flow between particle swarm and bee colony helps increase global and local search abilities of the hybrid approach which is referred to as Hybrid approach based on Particle swarm optimization and Artificial bee colony algorithm, HPA for short. In order to test the performance of the HPA algorithm, this study utilizes twelve basic numerical benchmark functions in addition to CEC2005 composite functions and an energy demand estimation problem. The experimental results obtained by the HPA are compared with those of the PSO and ABC. The performance of the HPA is also compared with that of other hybrid methods based on the PSO and ABC. The experimental results show that the HPA algorithm is an alternative and competitive optimizer for continuous optimization problems.     

求解工程约束优化问题的PSO-ABC混合算法*

针对包含约束条件的工程优化问题,提出了基于人工蜂群的粒子群优化PSO-ABC算法。将PSO中较优的粒子作为ABC算法的蜜源,并使用禁忌表存储其局部极值,克服粒子群优化算法易陷入局部最优的缺陷。采用可行性规则进行约束处理,将粒子种群分为可行子群和不可行子群,并在ABC算法产生蜜源的过程中保留部分较优的可行解和不可行解的信息,弥补了可行性规则处理最优点位于约束边界附近的问题时存在的不足。四个典型工程优化设计的实验结果表明,该算法能够寻得更优的约束最优化解,且稳健性更强。     

An Artificial Bee Colony algorithm with guide of global & local optima and asynchronous scaling factors for numerical optimization

Artificial Bee Colony (ABC) algorithm is a wildly used optimization algorithm. However, ABC is excellent in exploration but poor in exploitation. To improve the convergence performance of ABC and establish a better searching mechanism for the global optimum, an improved ABC algorithm is proposed in this paper. Firstly, the proposed algorithm integrates the information of previous best solution into the search equation for employed bees and global best solution into the update equation for onlooker bees to improve the exploitation. Secondly, for a better balance between the exploration and exploitation of search, an S-type adaptive scaling factors are introduced in employed bees’ search equation. Furthermore, the searching policy of scout bees is modified. The scout bees need update food source in each cycle in order to increase diversity and stochasticity of the bees and mitigate stagnation problem. Finally, the improved algorithms is compared with other two improved ABCs and three recent algorithms on a set of classical benchmark functions. The experimental results show that the our proposed algorithm is effective and robust and outperform than other algorithms.     

增强开发能力的改进人工蜂群算法

为解决人工蜂群（ABC）算法收敛速度慢、精度不高和易于陷入局部最优等问题，提出一种增强开发能力的改进人工蜂群算法。一方面，将得出的最优解以两种方式直接引入雇佣蜂搜索公式中，通过最优解指导雇佣蜂的邻域搜索行为，以增强算法的开发或局部搜索能力；另一方面，在旁观蜂搜索公式中结合当前解及其随机邻域进行搜索，以改善算法的全局优化能力。对多个常用基准测试函数的仿真实验结果表明，在收敛速度、精度和全局优化能力等方面，所提算法总体上优于其他类似的ABC算法（例如ABC/best）和集成多种搜索策略的ABC算法（例如ABCVSS（ABC algorithm with Variable Search Strategy）和ABCMSSCE（ABC algorithm with Multi-Search Strategy Cooperative Evolutionary））。     

基于中心解的改进人工蜂群算法

为了解决人工蜂群(ABC)算法在用于函数优化时所具有的局部探索能力不强、收敛精度不高的问题,提出一种基于中心解的人工蜂群算法。该算法结合中心解和当前最优候选解的优点,并将中心解引入到跟随蜂的局部变异策略中。跟随蜂采用轮盘赌的形式,选择某些适应度值较好的蜜源,在雇佣蜂中心解的基础上深度局部寻优,并在每次迭代中逐维更新蜜源每一维度的值。为了验证该算法的有效性,选择六个基准测试函数对三种算法进行仿真对比实验。与标准ABC算法和Best-so-far ABC算法相比,改进的ABC算法的求解精度有较大幅度提高,特别是对于Rastrigin函数,两种不同维数下均达到了理论最优值。实验结果表明:所提算法在收敛速度和寻优精度上都有明显改善。     

Networked correlation-aware manufacturing service supply chain optimization using an extended artificial bee colony algorithm

Manufacturing service supply chain (MSSC) optimization has been intensively studied to find an optimal service composition solution with the best quality of service (QoS) value. However, traditional MSSC optimization methods usually assume that candidate services are independent of one another. Therefore, potentially better MSSC solutions may have been neglected by not considering the positive influence of correlations between services on the QoS value. This study proposes a novel networked correlation-aware manufacturing service composition (NCMSC) mathematical model to characterize the influence of vertical and horizontal correlations between services on the QoS value of MSSC solution. To solve the NCMSC model, an extended artificial bee colony (ABC) algorithm is proposed to find a near-optimal solution with the best QoS value. The specific improvements to the original ABC algorithm include the following: (1) a new matrix-based encoding scheme is proposed to describe the MSSC solution in which each column contains a vertical composite structure and collaborative services for each subtask; (2) the migration operator of a biogeography-based optimization algorithm is combined with the original ABC algorithm to address the discrete MSSC optimization problem and improve the performance of the original ABC algorithm. The results of the experiments illustrate the importance of networked correlations between services, better practicality, effectiveness, and efficiency of the extended ABC algorithm in solving the optimization problem of MSSC.     

基于混沌局部搜索算子的人工蜂群算法

在求解函数优化问题时,为了提升人工蜂群算法局部搜索能力,提出了一种新颖的混沌蜂群算法。新算法设计了一种混沌局部搜索算子,并将其嵌入蜂群算法框架中;该算子不仅能够实现在最优食物源周围局部搜索,还能够随着进化代数增加使搜索范围不断缩小。仿真实验结果表明,与人工蜂群算法相比,新算法在Rosenbrock函数上,求解精度和收敛速度明显占优;此外新算法在多模函数Griewank和Rastrigin上,收敛速度明显占优。     

An adaptive artificial bee colony algorithm based on objective function value information

Artificial bee colony (ABC) algorithm is a novel biological-inspired optimization algorithm, which has many advantages compared with other optimization algorithm, such as less control parameters, great global optimization ability and easy to carry out. It has proven to be more effective than some evolutionary algorithms (EAs), particle swarm optimization (PSO) and differential evolution (DE) when testing on both benchmark functions and real issues. ABC, however, its solution search equation is poor at exploitation. For overcoming this insufficiency, two new solution search equations are proposed in this paper. They apply random solutions to take the place of the current solution as base vector in order to get more useful information. Exploitation is further improved on the basis of enhancing exploration by utilizing the information of the current best solution. In addition, the information of objective function value is introduced, which makes it possible to adjust the step-size adaptively. Owing to their respective characteristics, the new solution search equations are combined to construct an adaptive algorithm called MTABC. The methods our proposed balance the exploration and exploitation of ABC without forcing severe extra overhead in respect of function evaluations. The performance of the MTABC algorithm is extensively judged on a set of 20 basic functions and a set of 10 shifted or rotated functions, and is compared favorably with other improved ABCs and several state-of-the-art algorithms. The experimental results show that the proposed algorithm has a higher convergence speed and better search ability for almost all functions.     

改进的人工蜂群算法在函数优化问题中的应用

人工蜂群算法是近年来新提出的一种优化算法。针对标准人工蜂群算法的局部搜索能力差,精度低的缺点,提出了一个改进的人工蜂群算法,利用全局最优解和个体极值的信息来改进人工蜂群算法中的搜索模式,并引入异步变化学习因子,保持全局搜索和局部搜索的平衡。将改进的人工蜂群算法在函数优化问题上进行测试,结果表明改进的人工蜂群算法优于原算法。     

引入跟踪搜索和免疫选择的人工蜂群算法

针对人工蜂群算法中食物源更新和观察蜂选择食物源机制存在的缺点,提出一种具有跟踪搜索和免疫选择的人工蜂群算法。在原搜索方法基础上,引入跟踪全局最优解和随机选择解的搜索方法,选择搜索到的最优解作为候选解,以加快种群的收敛速度,提高算法的收敛性;在观察蜂选择食物源时,引入免疫系统的抗体浓度调节机制,以维持种群的多样性,提高算法的全局搜索能力。对6个经典测试函数的仿真计算结果表明,与ABC、GABC、RABC和TABC算法相比,改进算法在寻优精度、收敛性能方面具有较明显的优势。     

人工蜂群算法求解资源受限项目调度问题

针对资源受限项目调度问题,提出了一种基于人工蜂群算法的优化方法。人工蜂群算法中每个食物源的位置代表一种项目任务的优先权序列,每个食物源的位置通过扩展串行调度机制转换成可行的调度方案,迭代中由三种人工蜂执行不同的操作来实现全局最优解的更新。实验结果表明,人工蜂群算法是求解资源受限项目调度问题的有效方法,同时扩展调度机制的引入可以加速迭代收敛的进程。     

Multi-circle detection on images using artificial bee colony (ABC) optimization

Hough transform has been the most common method for circle detection, exhibiting robustness, but adversely demanding considerable computational effort and large memory requirements. Alternative approaches include heuristic methods that employ iterative optimization procedures for detecting multiple circles. Since only one circle can be marked at each optimization cycle, multiple executions ought to be enforced in order to achieve multi-detection. This paper presents an algorithm for automatic detection of multiple circular shapes that considers the overall process as a multi-modal optimization problem. The approach is based on the artificial bee colony (ABC) algorithm, a swarm optimization algorithm inspired by the intelligent foraging behavior of honeybees. Unlike the original ABC algorithm, the proposed approach presents the addition of a memory for discarded solutions. Such memory allows holding important information regarding other local optima, which might have emerged during the optimization process. The detector uses a combination of three non-collinear edge points as parameters to determine circle candidates. A matching function (nectar-amount) determines if such circle candidates (bee-food sources) are actually present in the image. Guided by the values of such matching functions, the set of encoded candidate circles are evolved through the ABC algorithm so that the best candidate (global optimum) can be fitted into an actual circle within the edge-only image. Then, an analysis of the incorporated memory is executed in order to identify potential local optima, i.e., other circles. The proposed method is able to detect single or multiple circles from a digital image through only one optimization pass. Simulation results over several synthetic and natural images, with a varying range of complexity, validate the efficiency of the proposed technique regarding its accuracy, speed, and robustness.