基于深度强化学习的非置换流水车间调度问题

针对传统调度算法不能有效利用历史数据进行学习,实时性较差而难以应对复杂多变的实际生产调度环境等问题,首次提出一种基于时序差分法的深度强化学习算法.该方法综合神经网络和强化学习实时性、灵活性的优势,直接依据输入的加工状态进行行为策略选取,更贴近实际订单响应式生产制造系统的调度决策过程.通过将调度问题转化为多阶段决策问题,...     

Single-machine scheduling with a position-based learning effect and fuzzy processing times

In scheduling problems with learning effects, most researches assume that processing times are deterministic. This paper considers a single-machine scheduling problem with a position-based learning effect and fuzzy processing times, simultaneously. The position-based learning effect of a job is assumed to be a function of its position. The processing times are considered to be triangular fuzzy numbers. A polynomial time algorithm is proposed for the problem where the objective is to minimize the total completion time. The solution procedure is based on applying the shortest processing time rule to triangular fuzzy processing times. Computational results show that our model gives better results than the model ignoring the uncertainty.     

求解同顺序加工调度问题的一种启发式方法

为了更加有效地求解同顺序加工调度问题,分析了现有启发式求解方法,发现影响解的质量的主要因素是调整近似解的方法和初始解,其中调整近似解的方法对解的质量影响较大。对此,提出了一种新的启发式方法。新方法中的调整方法考虑了调整对最短总加工时间的影响,调整任意给定的近似解不会降低解的质量,经过迭代运算,可以逐步改善近似解;新方法采用了多起点策略,利用调整方法调整不同初始解,选取最好的近似解作为问题的解,从而减小了初始解对问题解的质量的影响。实验结果表明,这种方法是有效的。     

流水车间作业提前/拖期调度问题研究

在非正规性能指标提前／拖期调度问题中,工件的加工顺序和每个加工活动的开始时刻都属于需要优化的变量,增加了求解的难度。针对这一问题,提出了采用分层调度模式求解流水车间提前／拖期调度问题的联合算法。首先,采用遗传算法对加工顺序进行寻优;其次,在给定调度序列的情况下采用启发式算法对加工开始时刻进行优化,制定插入机器空闲时段的策略,确定何时插入空闲时段和空闲时段的大小,即在给定顺序下确定工件加工活动的开始时刻,以满足在加工完所有工件后,使提前惩罚费用与拖期惩罚费用之和最小。数值计算结果证明了该联合算法的有效性。     

A note on single-machine scheduling with learning effect and an availability constraint

Recent empirical studies in several industries have verified that unit costs decline as firms produce more of a product and gain knowledge or experience. This phenomenon is known as the “learning effect.” However, most of the papers assume that the machine is available at all times. In reality, the machine might become unavailable due to machine breakdowns or preventive maintenance during the scheduling period. Motivated by this, single-machine scheduling problems with considerations of the learning effect and machine availability are considered in this paper. It is shown that the shortest processing time rule provides the optimal schedules for the makespan and the total completion time minimization problems when jobs are assumed to be resumable. Moreover, mixed integer programming techniques are used to solve the problems when jobs are non-resumable.     

求解流水车间调度问题的瓶颈指向启发式算法

针对最小化时间表长的流水车间调度问题,提出一种根据工件加工时间特征构建工件调度的瓶颈指向启发式算法。首先,为构建初始工件排序,充分利用各机器负荷一般不相等的特点,瓶颈阶段前加工时间较短而之后加工时间相对较长的工件优先开始加工;其次,当有工件等待加工时,根据工件在瓶颈机器前或后加工时间的特征调整工件加工顺序;最后,采用邻近工件成对交换和插入的方式改进初始调度。当瓶颈机器趋于中间阶段,或瓶颈机器上工件的加工时间趋于增加时,求解效果较好。数据实验表明算法是有效的。     

同顺序加工调度问题的一种精确求解方法

同顺序加工调度问题是NP问题,分析了这类问题的特点及求解的难点,结合广度优先搜索方法的特点,提出了启发式双侧广度优先搜索方法,混合使用动态规划方法、下界算法和近似求解方法求解同顺序加工调度问题.实验结果表明,启发式双侧广度优先搜索方法求解同顺序加工调度问题时,可以大大减少搜索次数,适合于求解工序较少的同顺序加工调度问题;如果下界算法较好,还能快速求解工序较多的同顺序加工调度问题.     

A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints

In this paper, a hybrid discrete firefly algorithm is presented to solve the multi-objective flexible job shop scheduling problem with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow a process sequence and each operation must be processed on an assigned machine. These constraints are used to balance between the resource limitation and machine flexibility. Three minimisation objectives—the maximum completion time, the workload of the critical machine and the total workload of all machines—are considered simultaneously. In this study, discrete firefly algorithm is adopted to solve the problem, in which the machine assignment and operation sequence are processed by constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. Meanwhile, local search method with neighbourhood structures is hybridised to enhance the exploitation capability. Benchmark problems are used to evaluate and study the performance of the proposed algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

A mathematical model and extension algorithm for assembly flexible flow shop scheduling problem

In this paper, a scheduling problem for a two-stage production system including machining operations and assembly operations is studied. In this system, a number of products of different kinds are produced. Each product is assembled with a set of several parts. The first stage is a hybrid flow shop to produce parts. All machines can process all kinds of parts in this stage, but each machine can process only one part at a time. The second stage is a single assembly machine or a single assembly team of workers. The considered objective is to minimize the completion time of all products (makespan). A mathematical modeling is presented, and since this problem has been proved strongly nondeterministic polynomial-time hard, a series of heuristic algorithms based on the basic idea of Johnson algorithm is proposed. Also, two lower bounds is introduced and improved to evaluate the final solution obtained from heuristic algorithms. The numerical experiments are used to evaluate the performance of the proposed algorithms.     

Flow shop scheduling with multiple objective of minimizing makespan and total flow time

This paper deals with the multicriterion approach to flow shop scheduling [FSS] problems by considering makespan time and total flow time. The primary concern of flow shop scheduling is to obtain the best sequence, which minimizes the makespan, flow time, idle time, tardiness, etc. In this work, makespan and total flow time of the jobs are considered for minimization. Three heuristic algorithms namely HAMC1, HAMC2 and HAMC3 have been proposed in this paper. The effectiveness of the heuristics has been analyzed using the problems generated by Taillard [16]. The results of the problems are compared with the solution procedures proposed by Rajendran [15]. The new hybrid algorithms are developed by taking the seed sequences yielded by a method proposed by Rajendran [14] in his work to minimize flow time and improving it using search algorithm. The hybrid algorithm gives better results.     

Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm

Flow shop scheduling problems have gained wide attention both in practical and academic fields. In this paper, we consider a multi-objective no-wait flow shop scheduling problem by minimizing the weighted mean completion time and weighted mean tardiness simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, an effective immune algorithm (IA) is proposed for searching locally the Pareto-optimal frontier for the given problem. To validate the performance of the proposed algorithm in terms of solution quality and diversity level, various test problems are carried out and the efficiency of the proposed algorithm, based on some comparison metrics, is compared with a prominent multi-objective genetic algorithm, i.e., strength Pareto evolutionary algorithm II (SPEA-II). The computational results show that the proposed IA outperforms the above genetic algorithm, especially for large problems.     

Effective heuristics for the no-wait flow shop scheduling problem with total flow time minimization

The no-wait flow shop scheduling problem with total flow time criterion has important applications in industrial systems. Heuristics that explore specific characteristics of the problem are essential to find good solutions in limited computational time for many practical applications. This paper first presents two constructive heuristics, namely improved standard deviation heuristic (ISDH) and improved Bertolissi heuristic (IBH), by combining the standard deviation heuristic (Gao et al., Int J Adv Manf Technol 56:683–692, 2011) and Bertolliso heuristic (Bertolissi, J Mater Process Technol 107:459–465, 2000) with the procedure of the constructive heuristic of Laha (Int J Adv Manf Technol 41:97–109, 2009). Then, four composite heuristics, i.e., ISDH with local search, IBH with local search, ISDH with iteration, and IBH with iteration, are separately proposed using the insertion-based local search method and iteration operator to improve the solutions of the ISDH and IBH. Extensive computational experiments are carried out based on a set of well-known flow shop benchmark instances that are considered as no-wait flow shop instances. Computational results and comparisons show that the proposed composite heuristics perform significantly better than the existing ones, and the proposed composite heuristics further improve the presented constructive heuristics for the no-wait flow shop scheduling problem with total flow time criterion.     

基于候鸟优化算法的阻塞流水车间调度问题

针对以最小化总流程时间为目标的阻塞流水车间调度问题,提出一种有效的候鸟优化算法。采用最小最大算法产生初始鸟群中的领飞鸟,并以领飞鸟的邻域解作为初始鸟群中的其他个体,保证了初始鸟群的质量和多样性。通过最优插入+最优交换操作产生鸟群的邻域解,使算法能更快地搜索到高质量的解。基于迭代贪婪算法的毁坏和构造操作的局部搜索策略进一步增强了算法的局部寻优能力,使算法在集中搜索和分散搜索之间达到更合理的平衡。通过求解经典的Taillard基准算例验证了所提算法的高效性和鲁棒性。     

A mathematical model for integrating lot-sizing and scheduling problem in capacitated flow shop environments

In this paper, a multiproduct multiperiod capacitated production system that has been organized as a flow shop is considered. The main novelty of the paper is proposing a more efficient mathematical model for the problem of integrating lot sizing and scheduling with sequence-dependent setups. In comparison to the former model, because of fewer continuous and binary decision variables and constraints in the proposed model, this model is very easier to solve. Comparison between two models proves the superiority of the proposed model. Two mixed integer programming-based approaches with rolling horizon framework have been used to solve this model. To evaluate the performance of the proposed model and solution method, problems of different scales have been studied. The used algorithms search the solution space for both lot-sizing and scheduling problems and find a combination of production planning and scheduling that is feasible and close to optimum.     

An effective constructive heuristic for permutation flow shop scheduling problem with total flow time criterion

This article addresses the permutation flow-shop scheduling problem with total flow time minimization criterion. The problem is proved to be NP-hard; thus, the development of heuristic methods that provide high-quality solutions with computational efficiency are the motivating aspects for the development of this research. In this article, a new simple constructive heuristic method has been proposed to solve the problem. Initially, an extensive literature review with key methods was performed for analysis, comparison, and evaluation. Then, a new simple heuristic method has been proposed and evaluated by means of extensive computational experiments. The results showed that the proposed method provides high-quality solutions with computational efficiency, significantly outperforming the best simple heuristics found in the literature.     

A two-machine flowshop maximum tardiness scheduling problem with a learning effect

The primary objective of this paper is to study a two-machine flowshop scheduling problem with a learning effect where the goal is to find a sequence that minimizes the maximum tardiness. We employ a branch-and-bound method and a simulated annealing (SA) method to search for the optimal solution and a near-optimal solution, respectively. Computational results, using Fisher’s (Math Program 11:229–251 1971) framework, show that the mean and maximum number of nodes for the branch-and-bound algorithm decrease when the learning effect is stronger, the value of the tardiness factor is smaller, or the value of the due date range is larger. In addition, comparisons between the SA method and the earliest due date first (EDD) rule are provided for large-job sizes. Results indicate that the percentage of time that the SA solution outperforms the EDD solution decreases as the job size increases and the learning effect becomes greater. Additionally, the SA solution is never worse than the EDD solution.     

A hybrid particle swarm optimization algorithm for a no-wait flow shop scheduling problem with the total flow time

This paper proposes a particle swarm optimization (PSO) algorithm based on memetic algorithm (MA) that hybridizes with a local search method for solving a no-wait flow shop scheduling problem. The main objective is to minimize the total flow time. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as global search. In addition, a self-organized random immigrant's scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in search space. The experimental study over the moving peaks benchmark problem shows that the proposed PSO-based MA is robust. Finally, the analysis of the computational results and conclusion are given.     

基于模糊时间并具有成组约束的车间排序算法

针对模具制造过程工件到达时间和加工时间难以精确的特点,以最小化最大完成时间为调度目标,研究了前阶段带有成组约束的两阶段柔性同序加工车间的排序问题.借助模糊数学理论,将工件的加工时间和到达时间作模糊数处理,采用均匀分布的Lee-Li法将模糊数转化为精确值,通过遗传算法优化排序,应用企业实际算例仿真说明该算法的有效性和可行性.     

A hybridisation of metaheuristics for flow shop scheduling

The present paper deals with the formation of an optimal sequence of flow shop scheduling (FSS) for efficient operation. The primary concern of FSS is to obtain the optimal sequence, which minimises the idle time, tardiness, makespan, etc. Among these, the criteria of minimising the makespan plays a vital part. Thus, in this paper, the sequencing of the FSS for minimising the makespan is addressed. An effective hybrid has been formed with the metaheuristics, namely an ant system and a genetic algorithm (GA). A number of illustrative examples with different combinations of machines and jobs have been solved using the proposed hybrid method.