Job Shop 调度的序列拉格朗日松驰法

拉格朗日松驰法为求解复杂调度问题次最优解的一种重要方法，陆宝森等人把这种方法推广到Ｊｏｂ Ｓｈｏｐ调度问题，但他们的方法存在解振荡问题。本文提出一种序列拉格朗日松驰法，它能避免解振荡。     

Group shops scheduling with makespan criterion subject to random release dates and processing times

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.     

基于Hopfield神经网络的作业车间生产调度方法

该文提出了基于Hopfield神经网络的作业车间生产调度的新方法.文中给出了作业车 间生产调度问题(JSP)的约束条件及其换位矩阵表示,提出了新的包括所有约束条件的计算能 量函数表达式,得到相应的作业车间调度问题的Hopfield神经网络结构与权值解析表达式,并 提出相应的Hopfield神经网络作业车间调度方法.为了避免Hopfield神经网络容易收敛到局部 极小,从而产生非法调度解的缺点,将模拟退火算法应用于Hopfield神经网络求解,使Hopfield 神经网络收敛到计算能量函数的最小值0,从而保证神经网络输出是一个可行调度方案.该文 改进了已有文献中提出的作业调度问题的Hopfield神经网络方法,与已有算法相比,能够保证 神经网络稳态输出为可行的作业车间调度方案.     

A linear programming-based method for job shop scheduling

We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach.     

Scheduling of manufacturing systems using the Lagrangian relaxationtechnique

The practical solutions for three manufacturing scheduling problems are examined. As each problem is formulated, constraints are added or modified to reflect increasing real world complexity. The first problem considers scheduling single-operation jobs on identical machines. The second problem is concerned with scheduling multiple-operation jobs with simple fork/join precedence constraints on identical machines. The third problem is the job shop problem in which multiple-operation jobs with general precedence constraints are scheduled on multiple machine types Langrangian relaxation is used to decompose each of the scheduling problems into job- or operation-level subproblems. The subproblems are easier to solve than the original problem and have intuitive appeal. This technique results in algorithms which generate near-optimal schedules efficiently, while giving a lower bound on the optimal cost. In resolving the scheduling problem from one time instant to the next, the Lagrange multipliers from the last schedule can be used to initialize the multipliers, further reducing the computation time     

Branch‐and‐bound approach for optima localization in scheduling multiprocessor jobs

We consider multiprocessor task scheduling problems with dedicated processors. We determine the tight optima localization intervals for different subproblems of the basic problem. Based on the ideas of a computer‐aided technique developed by Sevastianov and Tchernykh for shop scheduling problems, we elaborate a similar method for the multiprocessor task scheduling problem. Our method allows us to find an upper bound for the length of the optimal schedule in terms of natural lower bound. As a byproduct of our results, a family of linear‐time approximation algorithms with a constant ratio performance guarantee is designed for the NP‐hard subproblems of the basic problem, and new polynomially solvable classes of problems are found.     

Production capacity planning and scheduling in a no-wait environment with controllable processing times: An integrated modeling approach

This paper develops an integrated model between a production capacity planning and an operational scheduling decision making process in which a no-wait job shop (NWJS) scheduling problem is considered incorporating with controllable processing times. The duration of any operations are assumed to be controllable variables based on the amount of capacity allocated to them, whereas in classical NWJS it is assumed that the machine capacity and hence processing times are fixed and known in advance. The suggested problem which is entitled no-wait job shop crashing (NWJSC) problem is decomposed into the crashing, sequencing and timetabling subproblems. To tackle the addressed NWJSC problem, an improved hybrid timetabling procedure is suggested by employing the concept of both non-delay and enhanced algorithms which provides better solution than each one separately. Furthermore, an effective two-phase genetic algorithm approach is devised integrating with hybrid timetabling to deal with the crashing and sequencing components. The results obtained from experimental evaluations support the outstanding performance of the proposed approach.     

基于基因表达式的克隆选择算法求解JSP问题

针对作业车间调度问题的特征,提出一种基于基因表达式的克隆选择算法。在这个方法中,采用基因表达式编程算法中的编码方式来表示调度方案,同时为了提出的方法具有更强的全局搜索能力,运用克隆选择算法作为搜索引擎。最后,验证提出的方法的有效性,对7组Benchmark实例进行测试。实验结果表明,基于基因表达式的克隆选择算法在求解作业车间调度问题中是非常有效的。     

作业车间调度转换瓶颈算法的不可行解问题

文章讨论了作业车间调度问题转换瓶颈算法的一个缺陷。转换瓶颈算法是解决作业车间调度最小makespan(完工时间)问题的很有效的启发式算法。它是基于反复的解决某些单机调度问题。然而在转换瓶颈算法中用Carlier算法解单机调度问题并不总能得到可行解,文中给出了一个反例证明了有产生不可行解的情况。另外,文章还以简洁的方法证明了转换瓶颈算法若用Schrage算法替代Carlier算法解单机调度问题不会产生不可行解。     

A global constraint for total weighted completion time for unary resources

We introduce a novel global constraint for the total weighted completion time of activities on a single unary capacity resource. For propagating the constraint, we propose an O(n ⁴) algorithm which makes use of the preemptive mean busy time relaxation of the scheduling problem. The solution to this problem is used to test if an activity can start at each start time in its domain in solutions that respect the upper bound on the cost of the schedule. Empirical results show that the proposed global constraint significantly improves the performance of constraint-based approaches to single-machine scheduling for minimizing the total weighted completion time. We then apply the constraint to the multi-machine job shop scheduling problem with total weighted completion time. Our experiments show an order of magnitude reduction in search effort over the standard weighted-sum constraint and demonstrate that the way in which the job weights are associated with activities is important for performance.     

An efficient search method for multi-objective flexible job shop scheduling problems

Flexible job shop scheduling is very important in both fields of production management and combinatorial optimization. Owing to the high computational complexity, it is quite difficult to achieve an optimal solution to this problem with traditional optimization approaches. Motivated by some empirical knowledge, we propose an efficient search method for the multi-objective flexible job shop scheduling problems in this paper. Through the work presented in this work, we hope to move a step closer to the ultimate vision of an automated system for generating optimal or near-optimal production schedules. The final experimental results have shown that the proposed algorithm is a feasible and effective approach for the multi-objective flexible job shop scheduling problems.     

Generating subproblems in branch and bound algorithms for parallel machines scheduling problem

A branch and bound algorithm (B&B) has been widely used in various discrete and combinatorial optimization fields. To obtain optimal solutions as soon as possible for scheduling problems, three tools, which are branching, bounding and dominance rules, have been developed in the B&B algorithm. One of these tools, a branching is a method for generating subproblems and directly determines size of solution to be searched in the B&B algorithm. Therefore, it is very important to devise effective branching scheme for the problem.In this note, a survey of branching schemes is performed for parallel machines scheduling (PMS) problems with n independent jobs and m machines and new branching schemes that can be used for identical and unrelated PMS problems, respectively, are suggested. The suggested branching methods show that numbers of generated subproblems are much smaller than that of other methods developed earlier and therefore, it is expected that they help to reduce a lot of CPU time required to obtain optimal solutions in the B&B algorithm.     

基于遗传算法的作业车间调度优化求解方法

针对 job shop调度问题 ,提出了一种遗传算法编码方法和解码方法。该方法根据问题的特点 ,采用一种按工序用不同编号进行的染色体编码方案 ,并采用矩阵解码方法。此编码与调度方案一一对应 ,并且该编码方案有多种交叉操作算子可用 ,无须专门设计算子。算例计算结果表明 ,该算法是有效的 ,适用于解决 job shop调度问题 ,通过比较 ,该遗传算法优化 job shop调度操作简单并且收敛速度快。     

Heuristics for the two‐machine scheduling problem with a single server

In this paper, the NP‐hard two‐machine scheduling problem with a single server is addressed. The problem consists of a given set of jobs to be scheduled on two identical parallel machines, where each job must be processed on one of the machines, and prior to processing, the job is set up on its machine using one server; the latter is shared between the two machines. An ant colony optimization (ACO) algorithm is introduced for the problem and its performance was assessed by comparing with an exact solution (branch and bound [B&B]), a genetic algorithm (GA), and simulated annealing (SA). The computational results reflected the superiority of “ACO” in large problems, with a performance similar to SA and GA in smaller problems, while solving the tested problems within a reasonable computational time.     

求解多目标作业车间调度问题的混合变异杂草优化算法

针对多目标作业车间调度问题,提出一种混合变异杂草优化算法。该算法采用基于各子目标熵值权重的欧氏贴近度作为适应度值计算方法,引导种群向Pareto前端进化。在进化过程中,运用快速非支配排序策略构建Pareto档案,并利用进化种群中最优个体实时更新Pareto最优解集,提升算法的优化性能;同时通过引入变异算子增加种群多样性,避免算法陷入局部最优。最后,基于Benchmark算例的仿真实验,验证了该算法求解多目标作业车间调度问题的有效性。     

A computer simulation model for job shop scheduling problems minimizing makespan

One of the basic and significant problems, that a shop or a factory manager is encountered, is a suitable scheduling and sequencing of jobs on machines. One type of scheduling problem is job shop scheduling. There are different machines in a shop of which a job may require some or all these machines in some specific sequence. For solving this problem, the objective may be to minimize the makespan. After optimizing the makespan, the jobs sequencing must be carried out for each machine. The above problem can be solved by a number of different methods such as branch and bound, cutting plane, heuristic methods, etc. In recent years, researches have used genetic algorithms, simulated annealing, and machine learning methods for solving such problems. In this paper, a simulation model is presented to work out job shop scheduling problems with the objective of minimizing makespan. The model has been coded by Visual SLAM which is a special simulation language. The structure of this language is based on the network modeling. After modeling the scheduling problem, the model is verified and validated. Then the computational results are presented and compared with other results reported in the literature. Finally, the model output is analyzed.     

The Machine Duplication Problem in a Job Shop with Two Jobs

This paper addresses a problem related to the classical job shop scheduling problem with two jobs. The problem consists in concurrently determining the best subset of machines to be duplicated and the optimal scheduling of the operations in order to minimize completion time. Such a problem arises in the tool management for a class of flexible manufacturing cells. The job shop with two jobs is first reviewed, the application of the classical search algorithm A* to this problem is discussed and its performance compared with a previous approach. The complexity of the machine duplication problem is then analysed. The problem is proved to be in general NP-hard in the strong sense, but in a class of special cases, relevant from the applications viewpoint, it can be solved in polynomial time by a dynamic programming algorithm. A heuristic based on such an algorithm and on A* is proposed for the general problem; the results are satisfactory in terms of both efficiency and quality of the solution.     

A neighborhood for complex job shop scheduling problems with regular objectives

Due to the limited applicability in practice of the classical job shop scheduling problem, many researchers have addressed more complex versions of this problem by including additional process features, such as time lags, setup times, and buffer limitations, and have pursued objectives that are more practically relevant than the makespan, such as total flow time and total weighted tardiness. However, most proposed solution approaches are tailored to the specific scheduling problem studied and are not applicable to more general settings. This article proposes a neighborhood that can be applied for a large class of job shop scheduling problems with regular objectives. Feasible neighbor solutions are generated by extracting a job from a given solution and reinserting it into a neighbor position. This neighbor generation in a sense extends the simple swapping of critical arcs, a mechanism that is widely used in the classical job shop but that is not applicable in more complex job shop problems. The neighborhood is embedded in a tabu search, and its performance is evaluated with an extensive experimental study using three standard job shop scheduling problems: the (classical) job shop, the job shop with sequence-dependent setup times, and the blocking job shop, combined with the following five regular objectives: makespan, total flow time, total squared flow time, total tardiness, and total weighted tardiness. The obtained results support the validity of the approach.     

相关工件车间调度问题的拓扑算法

针对加工装配型离散制造企业实际生产的特点,提出了一类用于表示工序之间偏序关系的相关工件车间调度问题。为了利用已有的求解表示工序之间的线序关系的传统车间调度算法求解相关工件车间调度问题,设计了一种拓扑算法,该算法能够将工序之间的偏序关系转化为线序关系,将相关工件车间调度问题转化为传统的车间调度问题,通过实证研究,结果表明了拓扑算法是可行和高效的。     

Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems

A linguistic-based meta-heuristic modeling and solution approach for solving the flexible job shop scheduling problem (FJSSP) is presented in this study. FJSSP is an extension of the classical job-shop scheduling problem. The problem definition is to assign each operation to a machine out of a set of capable machines (the routing problem) and to order the operations on the machines (the sequencing problem), such that predefined performance measures are optimized. In this research, the scope of the problem is widened by taking into account the alternative process plans for each part (process plan selection problem). Probabilistic selection of alternative process plans and machines are also considered. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls (Baykasolu, 2002). Using these controls and Giffler and Thompson's (1960) priority rule-based heuristic along with the multiple objective tabu search algorithm of Baykasolu et al. (1999) FJSSP is solved. This novel approach simplifies the modeling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its fast solution. Instead of scheduling job shops with inflexible algorithms that cannot take into account the flexibility which is available in the job shop, the present algorithm is developed which can take into account the flexibility during scheduling. Such an approach will considerably increase the responsiveness of the job shops.