一种改进的求解柔性作业车间调度问题的灰狼算法

柔性作业车间调度问题是智能制造领域的一类典型调度问题,它是制造流程规划和管理中最关键的环节之一,有效的求解方法对提高生产效率具有重要的现实意义。本文基于经典灰狼算法进行改进,以优化最大完工时间为目标,提出一种改进的灰狼算法来求解柔性作业车间调度问题。算法首先采用基于权值的编码形式,实现对经典狼群算法中连续性编码的离散化;其次在迭代优化过程中加入随机游走策略,以增强局部搜索能力;然后在种群更新过程中加入尾部淘汰策略,在避免局部优化的同时增加种群多样性,合理扩大算法的广度搜索范围。在标准算例上的仿真实验结果表明,改进的灰狼算法在求解FJSP时比经典灰狼算法在寻优能力方面具有明显的优势,相比其它智能优化算法,本文所提算法在每种算例上均具有更好的优化性能。     

基于遗传算法的某航空发动机装配车间优化调度

航空发动机装配车间装配生产线的调度问题,是一类比较典型的混合Flowshop问题,同时还带有工件可重人等特点,这就区别于一般的Flowshop和Jobshop调度问题,因此,将可重入混合车间调度问题划为第三类调度问题。关于重入式混合车间生产调度的优化问题通常来说都是属于NP难问题。文中通过某航空发动机装配车间生产线的研究,以最小化最大完工时间为目标函数,借助随机矩阵的编码方式和改进的交叉方法与变异方法,提出了基于遗传算法的调度优化方法。最后实验结果表明,文中提出的改进算法能够有效地实现装配车间调度的优化。     

Ant colony optimization for multi-objective flow shop scheduling problem

Flow shop scheduling problem consists of scheduling given jobs with same order at all machines. The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, multi-objective approach for scheduling to reduce the total scheduling cost is important. Hence, in this study, we consider the flow shop scheduling problem with multi-objectives of makespan, total flow time and total machine idle time. Ant colony optimization (ACO) algorithm is proposed to solve this problem which is known as NP-hard type. The proposed algorithm is compared with solution performance obtained by the existing multi-objective heuristics. As a result, computational results show that proposed algorithm is more effective and better than other methods compared.     

A genetic algorithm and the Monte Carlo method for stochastic job-shop scheduling

This paper proposes a method for solving stochastic job‐shop scheduling problems using a hybrid of a genetic algorithm in uncertain environments and the Monte Carlo method. First, the genetic algorithm in uncertain environments is applied to stochastic job‐shop scheduling problems where the processing times are treated as stochastic variables. The Roulette strategy is adopted for selecting the optimum solution having the minimum expected value for makespan. Applying crossover based on Giffler and Thompson's algorithm results in two offspring inheriting the ancestor's characteristics as the operation completion times averaged up to the parent's generation. Individuals having very high frequency through all generations are selected as the good solutions. Second, the Monte Carlo method is effectively used for finding out the approximately optimum solution among these good solutions.     

Integrating simulation and genetic algorithm to schedule a dynamic flexible job shop

Much of the research on operations scheduling problems has ignored dynamic events in real-world environments where there are complex constraints and a variety of unexpected disruptions. Besides, while most scheduling problems which have been discussed in the literature assume that machines are incessantly available, in most real life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to a scheduled preventive maintenance where the periods of unavailability are determined in advance (deterministic unavailability). This paper describes how we can integrate simulation into genetic algorithm to the dynamic scheduling of a flexible job shop with machines that suffer stochastic breakdowns. The objectives are the minimization of two criteria, expected makespan and expected mean tardiness. An overview of the flexible job shops and scheduling under the stochastic unavailability of machines are presented. Subsequently, the details of integrating simulation into genetic algorithm are described and implemented. Consequently, problems of various sizes are used to test the performance of the proposed algorithm. The results obtained reveal that the relative performance of the algorithm for both abovementioned objectives can be affected by changing the levels of the breakdown parameters.     

A Pareto archive particle swarm optimization for multi-objective job shop scheduling

In this paper, we present a particle swarm optimization for multi-objective job shop scheduling problem. The objective is to simultaneously minimize makespan and total tardiness of jobs. By constructing the corresponding relation between real vector and the chromosome obtained by using priority rule-based representation method, job shop scheduling is converted into a continuous optimization problem. We then design a Pareto archive particle swarm optimization, in which the global best position selection is combined with the crowding measure-based archive maintenance. The proposed algorithm is evaluated on a set of benchmark problems and the computational results show that the proposed particle swarm optimization is capable of producing a number of high-quality Pareto optimal scheduling plans.     

Two-machine flow shop scheduling integrated with preventive maintenance planning

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.     

Flexible flow shop scheduling with stochastic processing times: A decomposition-based approach

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. Although some methods have been developed to address such problems, they remain inherently difficult to solve by any single approach. This paper presents a novel decomposition-based approach (DBA), which combines both the shortest processing time (SPT) and the genetic algorithm (GA), to minimizing the makespan of a flexible flow shop (FFS) with stochastic processing times. In the proposed DBA, a neighbouring K-means clustering algorithm is developed to firstly group the machines of an FFS into an appropriate number of machine clusters, based on their stochastic nature. Two optimal back propagation networks (BPN), corresponding to the scenarios of simultaneous and non-simultaneous job arrivals, are then selectively adopted to assign either SPT or GA to each machine cluster for sub-schedule generation. Finally, an overall schedule is generated by integrating the sub-schedules of machine clusters. Computation results show that the DBA outperforms SPT and GA alone for FFS scheduling with stochastic processing times.     

A multi objective optimization approach for flexible job shop scheduling problem under random machine breakdown by evolutionary algorithms

This paper addresses the stable scheduling of multi-objective problem in flexible job shop scheduling with random machine breakdown. Recently, numerous studies are conducted about robust scheduling; however, implementing a scheme which prevents a tremendous change between scheduling and after machine breakdown (preschedule and realized schedule, respectively) can be critical for utilizing available resources. The stability of the schedule can be detected by a slight deviation of start and completion time of each job between preschedule and realized schedule under the uncertain conditions. In this paper, two evolutionary algorithms, NSGA-II and NRGA, are applied to combine the improvement of makespan and stability simultaneously. A simulation approach is used to evaluate the state and condition of the machine breakdowns. After the introduction of the evaluation criteria, the proposed algorithms are tested on a variety of benchmark problems. Finally, through performing statistical tests, the algorithm with higher performance in each criterion is identified.     

求解置换流水线调度问题的改进萤火虫优化算法

针对最小化最大完成时间的置换流水线调度问题,提出了一种改进的离散萤火虫优化算法。在传统萤火虫优化算法的基础上,采用基于升序排序的随机键编码方式对萤火虫种群进行离散化处理,使用NEH算法对萤火虫种群进行初始化处理,结合遗传算法的交叉变异思想改进位置更新策略,采用个体变异方式解决孤立个体问题,提高算法的寻优能力。最后通过典型算例对改进算法进行仿真测试,实验结果表明该算法求解置换流水线调度问题时具备很强的寻优能力和鲁棒性,明显优于传统萤火虫优化算法和遗传算法,是解决置换流水线调度问题的一种有效算法。     

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.     

A GEP-based reactive scheduling policies constructing approach for dynamic flexible job shop scheduling problem with job release dates

Flexible job shop scheduling problem (FJSSP) is generalization of job shop scheduling problem (JSSP), in which an operation may be processed on more than one machine each of which has the same function. Most previous researches on FJSSP assumed that all jobs to be processed are available at the beginning of scheduling horizon. The assumption, however, is always violated in practical industries because jobs usually arrive over time and can not be predicted before their arrivals. In the paper, dynamic flexible job shop scheduling problem (DFJSSP) with job release dates is studied. A heuristic is proposed to implement reactive scheduling for the dynamic scheduling problem. An approach based on gene expression programming (GEP) is also proposed which automatically constructs reactive scheduling policies for the dynamic scheduling. In order to evaluate the performance of the reactive scheduling policies constructed by the proposed GEP-based approach under a variety of processing conditions three factors, such as the shop utilization, due date tightness, problem flexibility, are considered in the simulation experiments. The scheduling performance measure considered in the simulation is the minimization of makespan, mean flowtime and mean tardiness, respectively. The results show that GEP-based approach can construct more efficient reactive scheduling policies for DFJSSP with job release dates under a big range of processing conditions and performance measures in the comparison with previous approaches.     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

A hybrid Jaya algorithm for solving flexible job shop scheduling problem considering multiple critical paths

As an extension of the classical job shop scheduling problem, flexible job shop scheduling problem (FJSP) is considered as a challenge in manufacturing systems for its complexity and flexibility. Meta-heuristic algorithms are shown effective in solving FJSP. However, the multiple critical paths issue, which has not been formally discussed in the existing literature, is discovered to be a primary obstacle for further optimization by meta-heuristics. In this paper, a hybrid Jaya algorithm integrated with Tabu search is proposed to solve FJSP for makespan minimization. Two Jaya operators are designed to improve solutions under a two-vector encoding scheme. During the local search phase, three approaches are proposed to deal with multiple critical paths and have been evaluated by experimental study and qualitative analyses. An incremental parameter setting strategy and a makespan estimation method are employed to speed up the searching process. The proposed algorithm is compared with several state-of-the-art algorithms on three well-known FJSP benchmark sets. Extensive experimental results suggest its superiority in both optimality and stability. Additionally, a real world scheduling problem, including six instances with different scales, is applied to further prove its ability in handling large-scale scheduling problems.     

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 hybrid differential evolution algorithm for job shop scheduling problems with expected total tardiness criterion

In real-world manufacturing systems, the processing of jobs is frequently affected by various unpredictable events. However, compared with the extensive research for the deterministic model, study on the random factors in job shop scheduling has not received sufficient attention. In this paper, we propose a hybrid differential evolution (DE) algorithm for the job shop scheduling problem with random processing times under the objective of minimizing the expected total tardiness (a measure for service quality). First, we propose a performance estimate for roughly comparing the quality of candidate solutions. Then, a parameter perturbation algorithm is applied as a local search module for accelerating the convergence of DE. Finally, the K-armed bandit model is utilized for reducing the computational burden in the exact evaluation of solutions based on simulation. The computational results on different-scale test problems validate the effectiveness and efficiency of the proposed approach.     

Process plan and part routing optimization in a dynamic flexible job shop scheduling environment: an optimization via simulation approach

This paper presents an optimization via simulation approach to solve dynamic flexible job shop scheduling problems. In most real-life problems, certain operation of a part can be processed on more than one machine, which makes the considered system (i.e., job shops) flexible. On one hand, flexibility provides alternative part routings which most of the time relaxes shop floor operations. On the other hand, increased flexibility makes operation machine pairing decisions (i.e., the most suitable part routing) much more complex. This study deals with both determining the best process plan for each part and then finding the best machine for each operation in a dynamic flexible job shop scheduling environment. In this respect, a genetic algorithm approach is adapted to determine best part processing plan for each part and then select appropriate machines for each operation of each part according to the determined part processing plan. Genetic algorithm solves the optimization phase of solution methodology. Then, these machine-operation pairings are utilized by discrete-event system simulation model to estimate their performances. These two phases of the study follow each other iteratively. The goal of methodology is to find the solution that minimizes total of average flowtimes for all parts. The results reveal that optimization via simulation approach is a good way to cope with dynamic flexible job shop scheduling problems, which usually takes NP-Hard form.     

求解柔性作业调度问题的协同进化粒子群算法

柔性作业车间调度问题是典型的NP难题。柔性作业车间调度问题涉及到设备分配和作业分配两个问题,并且两问题之间具有较强的耦合性,提出了基于协同进化的粒子群算法。该算法将设备选择和工件调度分别作为两个寻优变量,利用PSO算法分别进行寻优,根据两个变量的内容进行互相评价。实验表明该算法对FJSP问题的有效性。     

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.     

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。