离散人工蜂群算法求解资源时变的项目调度问题

针对资源量随时间变动的项目调度问题提出了一种新的离散人工蜂群求解算法。算法食物源的位置采用基于任务排列的编码方法,并提出一种可以保持解的离散性和可行性的候选食物源生成方法。仿真结果表明,该算法能有效地求解资源时变的受限项目调度问题,研究发现在保持资源总量不变甚至减少的情况下,通过调整资源配置能够显著缩短项目工期,可见资源配置优化在项目管理中的重要作用。     

A modified ABC algorithm for the stage shop scheduling problem

Stage shop problem is an extension of the mixed shop as well as job shop and open shop. The problem is also a special case of the general shop. In a stage shop, each job has a number of stages; each of which includes one or more operations. As a subset of operations of a job, the operations of a stage can be done without any precedence consideration of each other, whereas the stages themselves should be processed according to a preset sequence. Due to the NP-hardness of the problem, a modified artificial bee colony (ABC) algorithm is suggested. In order to improve the exploitation feature of ABC, an effective neighborhood of the stage shop problem and PSO are used in employed and onlooker bee phases, respectively. In addition, the idea of tabu search is substituted for the greedy selection property of the artificial bee colony algorithm. The proposed algorithm is compared with the traditional ABC and the state-of-the-art CMA-ES. The computational results show that the modified ABC outperforms CMA-ES and completely dominates the traditional ABC. In addition, the proposed algorithm found high quality solutions within short times. For instance, two new optimal solutions and many new upper bounds are discovered for the unsolved benchmarks.     

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。     

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 discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops

Obtaining an optimal solution for a permutation flowshop scheduling problem with the total flowtime criterion in a reasonable computational timeframe using traditional approaches and optimization tools has been a challenge. This paper presents a discrete artificial bee colony algorithm hybridized with a variant of iterated greedy algorithms to find the permutation that gives the smallest total flowtime. Iterated greedy algorithms are comprised of local search procedures based on insertion and swap neighborhood structures. In the same context, we also consider a discrete differential evolution algorithm from our previous work. The performance of the proposed algorithms is tested on the well-known benchmark suite of Taillard. The highly effective performance of the discrete artificial bee colony and hybrid differential evolution algorithms is compared against the best performing algorithms from the existing literature in terms of both solution quality and CPU times. Ultimately, 44 out of the 90 best known solutions provided very recently by the best performing estimation of distribution and genetic local search algorithms are further improved by the proposed algorithms with short-term searches. The solutions known to be the best to date are reported for the benchmark suite of Taillard with long-term searches, as well.     

基于信息素调整的蚁群算法求解JSP问题

为更好的求解作业车间调度问题,针对基本蚁群算法求解作业车间调度问题容易进入局部最优问题的情况,提出了一种基于信息素调整的蚁群算法.该算法通过判断信息素矩阵中最大值与最小值之间的比值,当该比值达到算法设定的阀值时,根据相应策略时信息素矩阵进行调整,有效地缩小了信息素之间的差距,有利于跳出局部最优状态;给出了该算法实施的具体步骤.用该算法求解作业车间调度问题,仿真实验结果表明,该算法与基本蚁群算法相比在收敛速度和计算最优解方面都有了改进.     

Improved artificial bee colony algorithm for global optimization

The artificial bee colony algorithm is a relatively new optimization technique. This paper presents an improved artificial bee colony (IABC) algorithm for global optimization. Inspired by differential evolution (DE) and introducing a parameter M, we propose two improved solution search equations, namely “ABC/best/1” and “ABC/rand/1”. Then, in order to take advantage of them and avoid the shortages of them, we use a selective probability p to control the frequency of introducing “ABC/rand/1” and “ABC/best/1” and get a new search mechanism. In addition, to enhance the global convergence speed, when producing the initial population, both the chaotic systems and the opposition-based learning method are employed. Experiments are conducted on a suite of unimodal/multimodal benchmark functions. The results demonstrate the good performance of the IABC algorithm in solving complex numerical optimization problems when compared with thirteen recent 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.     

A modified genetic algorithm for the flow shop sequencing problem to minimize mean flow time

A modified genetic algorithm (MGA) is developed for solving the flow shop sequencing problem with the objective of minimizing mean flow time. To improve the general genetic algorithm (GA) procedure, two additional operations are introduced into the algorithm. One replaces the worst solutions in each generation with the best solutions found in previous generations. The other improves the most promising solution, through local search, whenever the best solution has not been updated for a certain number of generations. Computational experiments on randomly generated problems are carried out to compare the MGA with the general GA and special-purpose heuristics. The results show that the MGA is superior to general GA in solution quality with similar computation times. The MGA solutions are also better than those given by special-purpose heuristics though MGA takes longer computation time.     

求解作业排序问题的一种改进修复约束满足算法

修复约束满足算法(修复法)是在完整初始解的基础上不断对变量进行修复,最终得到可行解.对此,提出一种求解flow shop排序问题的改进修复法(IRCS_WT),通过采用新的变量表达方式,设计了一种以启发式优化规则为指导的变量选择算法(LWT),并采用一种变量互换算法(LTEE)保证算法的全局搜索性能.将新算法应用于31个标准算例,与传统算法及遗传算法的优化结果进行比较,结果表明在相同运算时问下改进算法具有明显的优越性.     

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.     

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。     

Ant colony optimization combined with taboo search for the job shop scheduling problem

In this paper, we present a hybrid algorithm combining ant colony optimization algorithm with the taboo search algorithm for the classical job shop scheduling problem. Instead of using the conventional construction approach to construct feasible schedules, the proposed ant colony optimization algorithm employs a novel decomposition method inspired by the shifting bottleneck procedure, and a mechanism of occasional reoptimizations of partial schedules. Besides, a taboo search algorithm is embedded to improve the solution quality. We run the proposed algorithm on 101 benchmark instances and obtain competitive results and a new best upper bound for one open benchmark instance is found.     

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。     

A polynomial-time approximation scheme for the two-machine flow shop scheduling problem with an availability constraint

We study the problem of scheduling n preemptable jobs in a two-machine flow shop where the first machine is not available for processing during a given time interval. The objective is to minimize the makespan. We propose a polynomial-time approximation scheme for this problem. The approach is extended to solve the problem in which the second machine is not continuously available.     

Solving reliability redundancy allocation problems using an artificial bee colony algorithm

This paper proposed a penalty guided artificial bee colony algorithm (ABC) to solve the reliability redundancy allocation problem (RAP). The redundancy allocation problem involves setting reliability objectives for components or subsystems in order to meet the resource consumption constraint, e.g. the total cost. RAP has been an active area of research for the past four decades. The difficulty that one is confronted with the RAP is the maintenance of feasibility with respect to three nonlinear constraints, namely, cost, weight and volume related constraints. In this paper nonlinearly mixed-integer reliability design problems are investigated where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of the system. The reliability design problems have been studied in the literature for decades, usually using mathematical programming or heuristic optimization approaches. To the best of our knowledge the ABC algorithm can search over promising feasible and infeasible regions to find the feasible optimal/near-optimal solution effectively and efficiently; numerical examples indicate that the proposed approach performs well with the reliability redundant allocation design problems considered in this paper and computational results compare favorably with previously-developed algorithms in the literature.     

A heuristic for job shop scheduling to minimize total weighted tardiness

This paper considers the job shop scheduling problem to minimize the total weighted tardiness with job-specific due dates and delay penalties, and a heuristic algorithm based on the tree search procedure is developed for solving the problem. A certain job shop scheduling to minimize the maximum tardiness subject to fixed sub-schedules is solved at each node of the search tree, and the successor nodes are generated, where the sub-schedules of the operations are fixed. Thus, a schedule is obtained at each node, and the sub-optimum solution is determined among the obtained schedules. Computational results on some 10 jobs and 10 machines problems and 15 jobs and 15 machines problems show that the proposed algorithm can find the sub-optimum solutions with a little computation time.     

A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem

To minimize the makespan in permutation flowshop scheduling problems, a hybrid discrete artificial bee colony (HDABC) algorithm is presented. In the HDABC, each solution to the problem is called a food source and represented by a discrete job permutation. First, the initial population with certain quality and diversity is generated from Greedy Randomized Adaptive Search Procedure (GRASP) based on Nawaz–Enscore–Ham (NEH) heuristics. Second, the discrete operators and algorithm, such as insert, swap, path relinking and GRASP are applied to generate new solution for the employed bees, onlookers and scouts. Moreover, local search is applied to the best one. The presented algorithm is tested on scheduling problem benchmarks. Experimental results show its efficiency.     

基于分布估计的二进制人工蜂群算法

为了充分利用种群的全局统计信息,将分布估计算法引入二进制人工蜂群算法,提出一种基于分布估计的二进制人工蜂群算法。该算法利用分布估计算法获得的全局统计信息引导候选解的产生,提高了全局探索能力;采用直接针对离散域的多维邻域更新策略,加快了收敛速度,降低了计算复杂度。仿真结果表明,与传统二进制人工蜂群算法相比,改进算法在优化精度、收敛速度和鲁棒性方面均有明显改善。