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.     

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.     

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.     

Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions

A Rosenbrock artificial bee colony algorithm (RABC) that combines Rosenbrock’s rotational direction method with an artificial bee colony algorithm (ABC) is proposed for accurate numerical optimization. There are two alternative phases of RABC: the exploration phase realized by ABC and the exploitation phase completed by the rotational direction method. The proposed algorithm was tested on a comprehensive set of complex benchmark problems, encompassing a wide range of dimensionality, and it was also compared with several algorithms. Numerical results show that the new algorithm is promising in terms of convergence speed, success rate, and accuracy. The proposed RABC is also capable of keeping up with the direction changes in the problems.     

改进的蜂群算法

针对蜂群算法收敛速度缓慢、容易出现早熟的问题,提出一种改进的蜂群算法(IABC)。IABC在跟随阶段食物源更新中根据邻域个体食物源质量调整信息共享程度,并且随着搜索进程减弱当前食物源的影响、增强邻域信息共享强度,使蜂群在搜索初期快速收敛到最优食物源所在区域、在搜索后期提高全局收敛性能。函数测试结果表明,IABC有效地提高了ABC的收敛速度和优化精度,特别适合复杂函数的优化问题。     

Elite-guided multi-objective artificial bee colony algorithm

Multi-objective optimization has been a difficult problem and a research focus in the field of science and engineering. This paper presents a novel multi-objective optimization algorithm called elite-guided multi-objective artificial bee colony (EMOABC) algorithm. In our proposal, the fast non-dominated sorting and population selection strategy are applied to measure the quality of the solution and select the better ones. The elite-guided solution generation strategy is designed to exploit the neighborhood of the existing solutions based on the guidance of the elite. Furthermore, a novel fitness calculation method is presented to calculate the selecting probability for onlookers. The proposed algorithm is validated on benchmark functions in terms of four indicators: GD, ER, SPR, and TI. The experimental results show that the proposed approach can find solutions with competitive convergence and diversity within a shorter period of time, compared with the traditional multi-objective algorithms. Consequently, it can be considered as a viable alternative to solve the multi-objective optimization problems.     

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.     

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。     

A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization

This paper suggests a dynamic multi-colony multi-objective artificial bee colony algorithm (DMCMOABC) by using the multi-deme model and a dynamic information exchange strategy. In the proposed algorithm, K colonies search independently most of the time and share information occasionally. In each colony, there are S bees containing equal number of employed bees and onlooker bees. For each food source, the employed or onlooker bee will explore a temporary position generated by using neighboring information, and the better one determined by a greedy selection strategy is kept for the next iterations. The external archive is employed to store non-dominated solutions found during the search process, and the diversity over the archived individuals is maintained by using crowding-distance strategy. If a randomly generated number is smaller than the migration rate R, then an elite, defined as the intermediate individual with the maximum crowding-distance value, is identified and used to replace the worst food source in a randomly selected colony. The proposed DMCMOABC is evaluated on a set of unconstrained/constrained test functions taken from the CEC2009 special session and competition in terms of four commonly used metrics EPSILON, HV, IGD and SPREAD, and it is compared with other state-of-the-art algorithms by applying Friedman test on the mean of IGD. The test results show that DMCMOABC is significantly better than or at least comparable to its competitors for both unconstrained and constrained problems.     

求解非线性方程的混合人工蜂群算法

结合牛顿法和人工蜂群算法的优点,提出了一种混合人工蜂群算法（HABC）,用于求解非线性方程,以克服牛顿法对初始值敏感和人工蜂群算法容易陷入局部极值、收敛速度慢的缺陷。实验仿真结果表明,混合人工蜂群算法能以满意的精度求出对未知数具有敏感性的非线性方程的解,具有较快的收敛速度和较高的搜索精度。     

基于局部最优解的改进人工蜂群算法

针对人工蜂群算法有时收敛速度较慢和探索能力较强而开发能力不足等问题,提出一种改进的人工蜂群（IABC）算法。该算法在跟随蜂阶段采用一种基于当前局部最优解（pbest）的搜索策略,能提高算法的局部搜索能力。为了加快算法的收敛速度,采用基于一般的反向学习的策略进行种群初始化,而且采蜜蜂和跟随蜂进行邻域搜索时,邻域搜索的维数根据循环代数动态调整。基于十个标准测试函数的仿真结果表明,该算法能有效加快收敛速度,局部优化能力有显著提高。     

Complex network oriented artificial bee colony algorithm for global bi-objective optimization in three-echelon supply chain

Finding the best flow patterns (i.e., choices of resources) for a family of products is a key part of supply chain management. It primarily focuses on reasonable selecting suppliers for every component, selecting plants for assembling every sub- or final assembly, and selecting the delivery options to bring products to customers. Different selecting operations form different cost and lead-time. Balancing a trade-off between cost and lead-time is a non-trivial problem in a three-echelon supply chain, which forms a complex network. We focus on finding the best flow patterns in which reasonable selections can be formed together to provide products or services. The objective is to minimize the bi-objective of cost and lead-time for any product. In this paper, we propose a complex network oriented artificial bee colony algorithm, which can be processed in parallel, to tackle the so-called combinatorial problem. Besides, we employ simulated annealing and gradient descent to find global Pareto optimal solutions in a supply chain network. Extensive experiments on the three-echelon supply chain network demonstrate the superiority of our proposals: (1) the proposed CN-ABC and CN-ABC-SAGD have the capability of discovering global POS in a complex three-echelon SCN; (2) the speed of searching global POS is accelerated to satisfy the requirement of its complexity of a SCN.     

The continuous artificial bee colony algorithm for binary optimization

Artificial bee colony (ABC) algorithm, one of the swarm intelligence algorithms, has been proposed for continuous optimization, inspired intelligent behaviors of real honey bee colony. For the optimization problems having binary structured solution space, the basic ABC algorithm should be modified because its basic version is proposed for solving continuous optimization problems. In this study, an adapted version of ABC, ABC_bin for short, is proposed for binary optimization. In the proposed model for solving binary optimization problems, despite the fact that artificial agents in the algorithm works on the continuous solution space, the food source position obtained by the artificial agents is converted to binary values, before the objective function specific for the problem is evaluated. The accuracy and performance of the proposed approach have been examined on well-known 15 benchmark instances of uncapacitated facility location problem, and the results obtained by ABC_bin are compared with the results of continuous particle swarm optimization (CPSO), binary particle swarm optimization (BPSO), improved binary particle swarm optimization (IBPSO), binary artificial bee colony algorithm (binABC) and discrete artificial bee colony algorithm (DisABC). The performance of ABC_bin is also analyzed under the change of control parameter values. The experimental results and comparisons show that proposed ABC_bin is an alternative and simple binary optimization tool in terms of solution quality and robustness.     

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.     

人工蜂群算法的改进

为改善人工蜂群算法(ABC)的深度搜索能力,提出一种改进的人工蜂群算法(SABC)。借鉴混合蛙跳算法(SFLA)的进化机制,将蜂群划分为多个模因组,使每个新个体与自身所在模因组的最坏个体进行优劣比较,能够更加容易保存群体中的"新生"个体,改善群体的整体质量,增加算法的深度搜索能力。通过7个测试函数进行实验,统计结果表明了SABC算法在求解函数优化问题时具有较好的算法性能。     

基于动态搜索策略的人工蜂群算法

为避免人工蜂群算法陷入早熟,提出一种基于动态搜索策略的人工蜂群算法,新算法改进了人工蜂群算法的搜索策略,将两种不同的搜索策略组合成新的搜索策略,以便动态利用两种不同搜索策略的优点,平衡了算法的局部搜索能力和全局搜索能力。基准函数的仿真实验表明,新算法收敛速度快、求解精度高、鲁棒性较强,适合求解高维复杂的全局优化问题。     

A grey artificial bee colony algorithm

Artificial bee colony (ABC) algorithm is a very popular population-based algorithm. Unfortunately, there exists a shortcoming of slow convergence rate, which partly results from random choices of neighbor individuals regarding its solution search equation. A novel scheme for the choice of neighbors is introduced based on grey relational degrees between a current individual and its neighbors to overcome the insufficiency. Then, the chosen neighbor is used to guide the search process. Additionally, inspired by differential evolution, a solution search equation called ABC/rand/2 is employed to balance the previous exploitation and a new perturbation scheme is also employed. What is more, solution search equations using information of the best individual, an opposition-based learning method and a chaotic initialization technique are also integrated into the proposed algorithm called grey artificial bee colony algorithm (GABC for short). Subsequently, the effectiveness and efficiency of GABC are validated on a test suite composed of fifty-seven benchmark functions. Furthermore, it is also compared with a few state-of-the-art algorithms. The related experimental results show the effectiveness and superiority of GABC.     

Enhanced artificial bee colony algorithm through differential evolution

Artificial bee colony algorithm (ABC) is a relatively new optimization algorithm. However, ABC does well in exploration but badly in exploitation. One possible way to improve the exploitation ability of the algorithm is to combine ABC with other operations. Differential evolution (DE) can be considered as a good choice for this purpose. Based on this consideration, we propose a new algorithm, i.e. DGABC, which combines DE with gbest-guided ABC (GABC) by an evaluation strategy with an attempt to utilize more prior information of the previous search experience to speed up the convergence. In addition, to improve the global convergence, when producing the initial population, a chaotic opposition-based population initialization method is employed. The comparison results on a set of 27 benchmark functions demonstrate that the proposed method has better performance than the other algorithms.     

基于信息熵的改进人工蜂群算法

为了克服人工蜂群算法在处理复杂性问题时收敛速度慢、收敛精度不高、易早熟等缺陷,在原始人工蜂群算法的基础上引入信息熵。信息熵本身是不确定性的一种度量,由信息熵的值来度量人工蜂群算法中跟随蜂选择的不确定性,通过控制信息熵的值达到控制算法中跟随蜂选择过程的目的,实现算法的自适应调节。通过对测试函数和不同规模TSP问题的模拟仿真,对人工蜂群算法、蚁群算法和其他改进方法进行了对比,验证了所提出改进方法的可行性和有效性。     

Development and investigation of efficient artificial bee colony algorithm for numerical function optimization

Artificial bee colony algorithm (ABC), which is inspired by the foraging behavior of honey bee swarm, is a biological-inspired optimization. It shows more effective than genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO). However, ABC is good at exploration but poor at exploitation, and its convergence speed is also an issue in some cases. For these insufficiencies, we propose an improved ABC algorithm called I-ABC. In I-ABC, the best-so-far solution, inertia weight and acceleration coefficients are introduced to modify the search process. Inertia weight and acceleration coefficients are defined as functions of the fitness. In addition, to further balance search processes, the modification forms of the employed bees and the onlooker ones are different in the second acceleration coefficient. Experiments show that, for most functions, the I-ABC has a faster convergence speed and better performances than each of ABC and the gbest-guided ABC (GABC). But I-ABC could not still substantially achieve the best solution for all optimization problems. In a few cases, it could not find better results than ABC or GABC. In order to inherit the bright sides of ABC, GABC and I-ABC, a high-efficiency hybrid ABC algorithm, which is called PS-ABC, is proposed. PS-ABC owns the abilities of prediction and selection. Results show that PS-ABC has a faster convergence speed like I-ABC and better search ability than other relevant methods for almost all functions.