An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.     

A variable iterated greedy algorithm with differential evolution for the no-idle permutation flowshop scheduling problem

This paper presents a variable iterated greedy algorithm (IG) with differential evolution (vIG_DE), designed to solve the no-idle permutation flowshop scheduling problem. In an IG algorithm, size d of jobs are removed from a sequence and re-inserted into all possible positions of the remaining sequences of jobs, which affects the performance of the algorithm. The basic concept behind the proposed vIG_DE algorithm is to employ differential evolution (DE) to determine two important parameters for the IG algorithm, which are the destruction size and the probability of applying the IG algorithm to an individual. While DE optimizes the destruction size and the probability on a continuous domain by using DE mutation and crossover operators, these two parameters are used to generate a trial individual by directly applying the IG algorithm to each target individual depending on the probability. Next, the trial individual is replaced with the corresponding target individual if it is better in terms of fitness. A unique multi-vector chromosome representation is presented in such a way that the first vector represents the destruction size and the probability, which is a DE vector, whereas the second vector simply consists of a job permutation assigned to each individual in the target population. Furthermore, the traditional IG and a variable IG from the literature are re-implemented as well. The proposed algorithms are applied to the no-idle permutation flowshop scheduling (NIPFS) problem with the makespan and total flowtime criteria. The performances of the proposed algorithms are tested on the Ruben Ruiz benchmark suite and compared to the best-known solutions available at http://soa.iti.es/rruiz as well as to those from a recent discrete differential evolution algorithm (HDDE) from the literature. The computational results show that all three IG variants represent state-of-art methods for the NIPFS problem.     

双目标流水线调度的动态双子群离散果蝇算法

提出了一种基于动态双子群的离散果蝇优化算法,求解以最大完工时间和机床空闲时间的最小化为目标的无等待流水线调度问题。与传统的果蝇算法不同,该算法采用基于工序的编码方式,并用改进的NEH方法进行初始化,提高初始解的质量;根据算法在进化过程中个体的进化水平,动态地将整个群体划分为先进子群和后进子群,简单但有效地插入方法在先进个体邻域内进化精细搜索,贪婪迭代进化机制用于优化后进个体,以此平衡算法的全局开发能力和局部搜索能力;为了提高算法效率,快速算法用于计算函数目标值和判断更新非支配解。仿真试验表明了所提果蝇算法的有效性和高效性。     

无等待流水车间调度问题的优化

文中研究了以生产周期为目标的无等待流水车间调度问题.首先,结合问题特征,提出了一种复杂度为O(n)的快速生产周期算法.其次,研究了两种插入邻域结构:基本插入邻域和多重插入邻域,并提出了快速基本插入邻域算法和最大多重插入移动算法.在此基础上,将离散粒子群算法与上述两种邻域搜索算法相结合,得到了离散粒子群优化调度算法.第三,根据问题生产周期的不规则性,给出了一种通过延长工序加工时间进一步改进调度方案的方法.最后,仿真实验表明了所得算法的可行性和有效性.     

An effective neighborhood search algorithm for scheduling a flow shop of batch processing machines

This paper considers scheduling problem of flow shop with many batch processing machines and objective of maximum lateness. An effective neighborhood search algorithm (NSA) is proposed for the problem, in which a job permutation and a batch permutation are used to indicate the solution of two sub-problems, respectively. Each job permutation consists of several family-permutations for the representation of jobs from the same family. Two swaps are applied to two permutations to produce new solutions. NSA is applied to a number of instances and compared with some methods, and computational results validate the good performance of NSA.     

A hybrid harmony search algorithm for the blocking permutation flow shop scheduling problem

This paper proposes a hybrid modified global-best harmony search (hmgHS) algorithm for solving the blocking permutation flow shop scheduling problem with the makespan criterion. First of all, the largest position value (LPV) rule is proposed to convert continuous harmony vectors into job permutations. Second, an efficient initialization scheme based on the Nawaz-Enscore-Ham (NEH) heuristic is presented to construct the initial harmony memory with a certain level of quality and diversity. Third, harmony search is employed to evolve harmony vectors in the harmony memory to perform exploration, whereas a local search algorithm based on the insert neighborhood is embedded to enhance the local exploitation ability. Moreover, a new pitch adjustment rule is developed to well inherit good structures from the global-best harmony vector. Computational simulations and comparisons demonstrated the superiority of the proposed hybrid harmony search algorithm in terms of solution quality.     

A heuristic for minimizing the makespan in no-idle permutation flow shops

The paper deals with the problem of finding a job sequence that minimizes the makespan in m-machine flow shops under the no-idle condition. This condition requires that each machine must process jobs without any interruption from the start of processing the first job to the completion of processing the last job. Since the problem is NP-hard, we propose a constructive heuristic for solving it that significantly outperforms heuristics known so far.     

A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.     

Exact resolution of the one-machine sequencing problem with no machine idle time

This paper investigates the one-machine sequencing problem in a workshop where the machine has to satisfy the no-idle constraint, that is, the machine must process jobs without interruption. The objective is to minimize the makespan. Each job has a release date for which it is available for processing on the machine and a delivery time during which it must remain in the system after being processed by the machine. This problem has been studied without adding the no-idle constraint. It is solved in polynomial time, when the preemption of jobs is allowed, applying Jackson’s rule. But, when the preemption of jobs is not allowed, it becomes strongly NP-hard. Although, it can be solved in a very short time using Carlier’s branch and bound algorithm. Below, we propose to adapt Carlier’s branch and bound method in order to calculate an optimal nonpreemptive schedule for the problem when adding the no-idle constraint.     

Tabu search methods for a single machine scheduling problem

In this paper we discuss the use of three local search strategies within a tabu search (TS) method for the approximate solution of a single machine scheduling problem. The problem consists of minimizing the sum of the set-up costs and linear delay penalties whenN jobs, arriving at time zero, are to be scheduled for sequential processing on a continuously available machine. Following a review of a previous study of this problem, we first consider a TS method that uses the common approach of making a succession of pairwise job exchanges, or swaps, to move from one trial solution to another. Next, we consider the use of insert moves to define the local neighborhood of each trial solution. These moves consist of transferring a single job from one position to another in the schedule. Finally, we construct a TS method (TS-hybrid) that employs both swap and insert moves. Experiments with benchmark problems of up to 60 jobs illustrate that there is an advantage in using more than one strategy to move from one trial solution to another within a TS method.This work was begun during the author's summer internship at the Advanced Knowledge Systems Group of US West Advanced Technologies.     

Flowshop scheduling of deteriorating jobs on dominating machines

In this paper we consider the general, no-wait and no-idle permutation flowshop scheduling problem with deteriorating jobs, i.e., jobs whose processing times are increasing functions of their starting times. We assume a linear deterioration function with identical increasing rates for all the jobs and there are some dominating relationships between the machines. We show that the problems to minimize the makespan and the total completion time remain polynomially solvable when deterioration is considered, although these problems are more complicated than their classical counterparts without deterioration.     

超启发式遗传算法求解模糊柔性作业车间调度

本文提出一种混合超启发式遗传算法(HHGA),用于求解一类采用三角模糊数表示工件加工时间的模糊柔性作业车间调度问题(FFJSP),优化目标为最小化最大模糊完工时间(即makespan).首先,详细分析现有三角模糊数排序准则性质,并充分考虑取大操作的近似误差和模糊度,设计一种更为准确的三角模糊数排序准则,可合理计算FFJSP和其他各类调度问题解的目标函数值.其次,为实现对FFJSP解空间不同区域的有效搜索,HHGA将求解过程分为两层,高层利用带自适应变异算子的遗传算法对6种特定操作(即6种有效邻域操作)的排列进行优化;低层将高层所得的每种排列作为一种启发式算法,用于对低层相应个体进行操作来执行紧凑的变邻域局部搜索并生成新个体,同时加入模拟退火机制来避免搜索陷入局部极小.最后,仿真实验和算法比较验证了所提排序准则和HHGA的有效性.     

Flow shop scheduling problems with decreasing linear deterioration under dominant machines

This paper considers the general, no-wait and no-idle flow shop scheduling problems with deteriorating jobs, respectively. By a deteriorating job, we mean that the processing time is a decreasing function of its execution starting time. The normal processing time proportional to its decreasing rate is assumed and some dominant relationships between machines can be satisfied. It is shown that for the problems to minimize the makespan or the weighted sum of completion time, polynomial algorithms still exist, although these problems are more complicated than the classical ones. When the objective is to minimize the maximum lateness, the solutions of a classical version may not hold.     

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.     

Memetic algorithm with node and edge histogram for no-idle flow shop scheduling problem to minimize the makespan criterion

This paper presents a memetic algorithm with hybrid node and edge histogram (MANEH) to solve no-idle permutation flow shop scheduling problem (NIPFSP) with the criterion to minimize the maximum completion time (the makespan criterion). The MANEH mainly composes of two components: population-based global search and local refinements for individuals. At the initialization stage, a modified speed-up NEH method and the random initialization are utilized to generate more promising solutions with a reasonable running time. At the population-based global search stage, a random sample crossover is first proposed to construct a hybrid node and edge histogram matrix (NEHM) with superior solutions in the population, and then a new sequence is generated by sampling the NEHM or selecting jobs from a template sequence. At the local refinements stage, an improved general variable neighborhood search with the simulated annealing acceptance (GVNS-SA) is developed to improve the current best individual. The GVNS-SA adopts a random referenced local search in the inner loop and the probability of SA to decide whether accept the incumbent solution for the next iteration. Moreover, the influence of key parameters in the MANEH is investigated based on the approach of a design of experiments (DOE). Finally, numerical simulation based on the benchmark of Ruiz and thorough statistical analysis are provided. The comparisons between MANEH and some existing algorithms as well as MA-based algorithms demonstrate the effectiveness and superiority of the proposed MANEH in solving the NIPFSP. Furthermore, the MANEH improves 89 out of the 250 current best solutions reported in the literature.     

解决零空闲流水线调度问题的离散粒子群算法

研究了以最大完工时间为目标的零空闲流水线调度问题.提出一种复杂度为O(nm)的最大完工时间算法和一种快速插入邻域搜索算法;提出了解决该问题的离散粒子群调度算法,并结合简化邻域搜索算法给出了提高调度算法性能的措施.仿真实验表明了所得算法的有效性.     

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.     

A neural network to enhance local search in the permutation flowshop

This paper considers the n-job, m-machine permutation flowshop with the objective of minimizing the mean flowtime. Initial sequences that are structured to enhance the performance of local search techniques are constructed from job rankings delivered by a trained neural network. The network's training is done by using data collected from optimal sequences obtained from solved examples of flowshop problems. Once trained, the neural network provides rankable measures that can be used to construct a sequence in which jobs are located as close as possible to the positions they would occupy in an optimal sequence. The contribution of these ‘neural’ sequences in improving the performance of some common local search techniques, such as adjacent pairwise interchange and tabu search, is examined. Tests using initial sequences generated by different heuristics show that the sequences suggested by the neural networks are more effective in directing neighborhood search methods to lower local optima.     

Minimizing total weighted completion time with uncertain data: A stability approach

A single-machine scheduling problem is investigated provided that the input data are uncertain: The processing time of a job can take any real value from the given segment. The criterion is to minimize the total weighted completion time for the n jobs. As a solution concept to such a scheduling problem with an uncertain input data, it is reasonable to consider a minimal dominant set of job permutations containing an optimal permutation for each possible realization of the job processing times. To find an optimal or approximate permutation to be realized, we look for a permutation with the largest stability box being a subset of the stability region. We develop a branch-and-bound algorithm to construct a permutation with the largest volume of a stability box. If several permutations have the same volume of a stability box, we select one of them due to one of two simple heuristics. The efficiency of the constructed permutations (how close they are to a factually optimal permutation) and the efficiency of the developed software (average CPU-time used for an instance) are demonstrated on a wide set of randomly generated instances with 5 ≤ n ≤ 100.