An enhanced artificial bee colony algorithm with adaptive differential operators

Artificial bee colony algorithm (ABC) has been shown to be very effective to solve global optimization problems (GOPs). However, ABC performs well in exploration but relatively poorly in exploitation resulting in a slow convergence when it is used to handle complex GOPs. Differential evolution (DE) benefits from its differential operators, namely mutation operator and crossover operator, which could perturb multiple variables simultaneously and has shown a fast convergence speed. In order to improve ABC’s exploitation ability and accelerate its convergence, in this paper, we propose an enhanced ABC algorithm named ABCADE, which remedy the limitation of ABC by exploiting the advantage of differential operators. Particularly, in ABCADE, the employed bees employ differential operators to produce candidate solutions with an increasing probability, and the two important parameters (scale factor F and crossover rate CR) of differential operators are adaptively adjusted through Gaussian distribution. Moreover, to significantly differentiate the good solutions and bad solutions in a population, and put more effort in the exploitation around the good solutions, we design a new selection probability method for onlooker bees. To verify the performance of ABCADE, we compare ABCADE with other representative state-of-the-art ABC and DE algorithms, the comparison results on a set of 22 benchmark functions with various dimension sizes demonstrate that ABCADE obtains superior or comparable performance to other algorithms.     

基于最优高斯随机游走和个体筛选策略的差分进化算法

针对差分进化算法开发能力较差的问题, 提出一种具有快速收敛的新型差分进化算法. 首先, 利用最优高斯随机游走策略提高算法的开发能力; 然后, 采用基于个体优化性能的简化交叉变异策略实现种群的进化操作以加强其局部搜索能力; 最后, 通过个体筛选策略进一步提高算法的探索能力以避免陷入局部最优. 12 个标准测试函 数和两种带约束的工程优化问题的实验结果表明, 所提出的算法在收敛速度、算法可靠性及收敛精度方面均优于EPSDE、SaDE、JADE、BSA、CoBiDE、GSA和ABC等算法, 在加强算法探索能力的同时能够有效地提高算法的开发能力.

     

A modified artificial bee colony algorithm

Artificial bee colony algorithm (ABC) is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by differential evolution (DE), we propose an improved solution search equation, which is based on that the bee searches only around the best solution of the previous iteration to improve the exploitation. Then, in order to make full use of and balance the exploration of the solution search equation of ABC and the exploitation of the proposed solution search equation, we introduce a selective probability P and get the new search mechanism. In addition, to enhance the global convergence, when producing the initial population, both chaotic systems and opposition-based learning methods are employed. The new search mechanism together with the proposed initialization makes up the modified ABC (MABC for short), which excludes the probabilistic selection scheme and scout bee phase. Experiments are conducted on a set of 28 benchmark functions. The results demonstrate good performance of MABC in solving complex numerical optimization problems when compared with two ABC-based algorithms.     

A novel artificial bee colony algorithm with Powell's method

Artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. To address this concerning issue, we first propose a modified search equation which is applied to generate a candidate solution in the onlookers phase to improve the search ability of ABC. Further, we use the Powell's method as a local search tool to enhance the exploitation of the algorithm. The new algorithm is tested on 22 unconstrained benchmark functions and 13 constrained benchmark functions, and are compared with some other ABCs and several state-of-the-art algorithms. The comparisons show that the proposed algorithm offers the highest solution quality, fastest global convergence, and strongest robustness among all the contenders on almost all test functions.     

受粒子群和差分进化启发的人工蜂群算法

针对基本人工蜂群算法搜索策略探索能力强而开发能力弱的特点,受粒子群和差分进化思想的启发,提出了两种新的搜索策略：PSO-DE-PABC和PSO-DE-GABC。前者在随机个体附近产生新的候选位置以提高算法的多样性;后者在最优解附近产生新的候选位置以提高算法的收敛速度,并加入差分进化中的差异向量来增加种群的多样性。在此基础上,引入维度因子来控制算法的收敛速度,并且使用一种利用当前种群信息的侦查策略来增强算法的局部搜索能力。通过对10组标准测试函数的实验仿真并与基本ABC、GABC和ABC/best算法相比,结果表明PSO-DE-GABC和PSO-DE-PABC对数值优化具有更高的收敛速度和收敛精度。     

具有自适应全局最优引导快速搜索策略的人工蜂群算法

针对人工蜂群算法存在开发与探索能力不平衡的缺点,提出了具有自适应全局最优引导快速搜索策略的改进算法.在该策略中,首先采蜜蜂利用自适应搜索方程平衡了不同搜索方法的探索和开发能力;其次跟随蜂利用全局最优引导邻域搜索方程对蜜源进行精细化搜索,以提高其收敛精度和全局搜索能力.14个标准测试函数的仿真结果表明,相比其他算法,所提出的改进算法有效平衡了算法的开发与探索能力,并提高了其最优解的精度及收敛速度.     

改进搜索策略的人工蜂群算法

针对人工蜂群(ABC)算法存在收敛速度慢、收敛精度低的问题,给出一种改进的人工蜂群算法用于数值函数优化问题。在ABC的邻域搜索公式中利用目标函数自适应调整步长,并根据迭代次数非线性减小侦查蜂的搜索范围。改进ABC算法提高了ABC算法的局部搜索能力,能够有效避免早熟收敛。基于6个标准测试函数的仿真实验表明,改进ABC算法的寻优能力有较大提高,对于多个高维多模态函数该算法可取得理论全局最优解。与对比算法相比,该算法具有更高的收敛精度,并且收敛速度更快。     

基于搜索能力均衡的人工蜂群算法

鉴于标准人工蜂群算法（ABC）局部开发能力不足,提出一种改进搜索策略的人工蜂群算法（IABC）。为提高ABC的局部开发能力,在其雇佣蜂阶段引入了一个新的具有最好个体引导的解搜索方程,为均衡ABC的搜索能力,在ABC跟随蜂阶段的搜索策略中引入了新的随机因素以增强ABC的全局探索能力,为了进一步平衡全局探索和局部开发能力,改进了ABC的侦察蜂搜索机制。为验证IABC的收敛效果,通过在12个复杂基准测试函数上的仿真实验并与其他算法相比较,发现IABC的收敛性能有显著提高。     

An efficient and robust artificial bee colony algorithm for numerical optimization

Artificial bee colony (ABC) algorithm has already shown more effective than other population-based algorithms. However, ABC is good at exploration but poor at exploitation, which results in an issue on convergence performance in some cases. To improve the convergence performance of ABC, an efficient and robust artificial bee colony (ERABC) algorithm is proposed. In ERABC, a combinatorial solution search equation is introduced to accelerate the search process. And in order to avoid being trapped in local minima, chaotic search technique is employed on scout bee phase. Meanwhile, to reach a kind of sustainable evolutionary ability, reverse selection based on roulette wheel is applied to keep the population diversity. In addition, to enhance the global convergence, chaotic initialization is used to produce initial population. Finally, experimental results tested on 23 benchmark functions show that ERABC has a very good performance when compared with two ABC-based algorithms.     

基于反向学习的自适应差分进化算法

为解决差分进化（DE）算法过早收敛与搜索能力低的问题,讨论对控制参数的动态调整,提出一种基于反向学习的自适应差分进化算法。该算法通过反向精英学习机制来增强种群的局部搜索能力,获取精确度更高的最优个体;同时,采用高斯分布随机性提高单个个体的开发能力,通过扩充种群的多样性,避免算法过早收敛,整体上平衡全局搜索与局部寻优的能力。采用CEC 2014中的6个测试函数进行仿真实验,并与其他差分进化算法进行对比,实验结果表明所提算法在收敛速度、收敛精度及可靠性上表现更优。     

基于向量整体扰动的快速收敛人工蜂群算法

针对标准人工蜂群算法收敛速度慢和易陷入早熟收敛等问题,提出一种快速收敛人工蜂群算法。首先借助反向学习理论初始化种群来提高初始解的分布质量,并在雇佣蜂和跟随蜂阶段引入向量整体扰动搜索方程加快局部搜索;然后为了跳出局部最优,采用一种随机更新搜索策略来增加蜂群多样性以平衡全局探索和局部利用能力;最后通过八个标准测试函数的仿真实验,发现所提出的算法与几个改进的人工蜂群算法相比,具有更快的收敛速度且获得了更高的求解精度,验证了算法的优越性。     

A novel hybrid DE–random search approach for unit commitment problem

Differential evolution (DE) is a population-based stochastic search algorithm, whose simple yet powerful and straightforward features make it very attractive for numerical optimization. DE uses a rather greedy and less stochastic approach to problem-solving than other evolutionary algorithms. DE combines simple arithmetic operators with the classical operators of recombination, mutation and selection to evolve from a randomly generated starting population to a final solution. Although global exploration ability of DE algorithm is adequate, its local exploitation ability is feeble and convergence velocity is too low and it suffers from the problem of untime convergence for multimodal objective function, in which search process may be trapped in local optima and it loses its diversity. Also, it suffers from the stagnation problem, where the search process may infrequently stop proceeding toward the global optimum even though the population has not converged to a local optimum or any other point. To improve the exploitation ability and global performance of DE algorithm, a novel and hybrid version of DE algorithm is presented in the proposed research. This research paper presents a hybrid version of DE algorithm combined with random search for the solution of single-area unit commitment problem. The hybrid DE–random search algorithm is tested with IEEE benchmark systems consisting of 4, 10, 20 and 40 generating units. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and meta-heuristics search algorithms, and by experimental analysis, it has been found that proposed algorithm yields global results for the solution of unit commitment problem.

     

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.     

自扰动人工蜂群算法

人工蜂群(Artificial Bee Colony,ABC)算法是一种模仿蜂群寻找蜜源的新型算法,因具有参数简单、灵活性强等优点而被广泛用于解决工程问题。但该算法在早熟、收敛速度慢和个体越界等缺点。为此,提出一种自扰动人工蜂群算法(Novel Artificial Bee Algorithm with Adaptive Disturbance,IGABC)。该算法采用轴对称策略处理蜂群中的越界个体,提高了算法的搜索效率。通过改进全局搜索方程的结构,同时加入带阈值的线性递增策略,提出一种全新的自适应搜索方程。自适应搜索方程提高了算法的收敛精度并加快了速度。为了获得更好的全局最优解,提出一种自扰动方法对全局最优解进行扰动。选取18个基准测试函数以及近4年提出的6个改进ABC算法进行对比实验,结果表明,该算法在收敛速度和精度上均有较大的优势,尤其在处理Rosenbrock等很难寻优的复杂函数时,收敛精度提高了16个数量级。     

基于改进量子差分进化的含分布式电源的配电网无功优化

差分进化算法（DE）已被证明为解决无功优化问题的有效方法.随着越来越多的分布式电源并网,对配电网潮流、电压均有一定改变,同时也影响了DE的鲁棒性和性能.本文在研究DE基础上,针对其收敛过早、局部搜索能力较差的缺陷,分析了量子计算思想和人工蜂群算法的优势,提出改进量子差分进化混合算法（IQDE）.通过量子编码思想提高了种群个体的多样性,人工蜂群算法的观察蜂加速进化操作和侦查蜂随机搜索操作分别提高了算法的局部搜索和全局搜索性能.建立以有功网损最小为目标的数学模型,将IQDE算法和DE算法分别用于14节点和30节点标准数据集进行大量仿真实验.实验结果表明,IQDE算法用更少的收敛时间、更小的种群规模便可以获得与DE算法相同甚至更佳的优化效果,并且可以很好的应用于解决难分布式电源的配电网无功优化问题.     

基于双变异模式协同的自适应微分进化算法

针对微分进化算法(DE)易陷入局部最优解、进化后期收敛速度慢、求解精度低等缺点,结合DE/rand/1和DE/best/1两种变异模式分别具有全局探索能力和局部开发能力的优点,引入精英存档策略和控制参数自适应策略,提出一种双变异模式协同自适应微分进化(DMCSaDE)算法.15个典型benchmark测试函数的实验结果表明,DMCSaDE能够有效提高算法的全局探索能力和局部开发能力,避免早熟收敛,大大提高算法的收敛性能和鲁棒性,同时,精英种群的大小对DMCSaDE的优化性能具有明显的影响.     

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.     

保存基因的2-Opt一般反向差分演化算法

为了进一步提高差分演化算法的性能,提出一种采用保存基因的2-Opt一般反向差分演化算法,并把它应用于函数优化问题中.新算法具有以下特征:(1)采用保存被选择个体基因的方式组成参加演化的新个体.保存基因的方法可以很好的保持种群多样性;(2)采用一般反向学习(GOBL)机制进行初始化,提高了初始化效率;(3)采用2-Opt算法加速差分演化算法的收敛速度,提高搜索效率.通过测试函数的实验,并与其他差分演化算法进行比较.实验结果证实了新算法的高效性,通用性和稳健性.     

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。     

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。