Minimizing makespan in a two-machine no-wait flow shop with batch processing machines

Given a set of jobs and two batch processing machines (BPMs) arranged in a flow shop environment, the objective is to batch the jobs and sequence the batches such that the makespan is minimized. The job sizes, ready times, and processing times on the two BPMs are known. The batch processing machines can process a batch of jobs as long as the total size of all the jobs assigned to a batch does not exceed its capacity. Once the jobs are batched, the processing time of the batch on the first machine is equal to the longest processing job in the batch; processing time of the batch on the second machine is equal to the sum of processing times of all the jobs in the batch. The batches cannot wait between two machines (i.e., no-wait). The problem under study is NP-hard. We propose a mathematical formulation and present a particle swarm optimization (PSO) algorithm. The solution quality and run time of PSO is compared with a commercial solver used to solve the mathematical formulation. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using PSO to solve large-scale problems.     

Particle swarm optimization for scheduling batch processing machines in a permutation flowshop

Batch processing machines are capable of processing several jobs in a batch simultaneously. These machines are used in many real-life applications. This paper presents solution approaches to schedule batch processing machines arranged in a permutation flowshop in order to minimize its makespan (or completion time of the last batch). The processing time of each job on all the machines and their sizes are given. Each machine can process a batch of jobs as long as its capacity is not violated. The batch processing time is equal to the longest processing job in the batch. Since the problem under study is NP-hard, commercial mixed-integer solvers may require prohibitively long run time to solve even modest sized problems. Consequently, a particle swarm optimization (PSO) algorithm is proposed. Three heuristics to update the particle’s positions are also proposed. The effectiveness of the proposed PSO algorithm is compared with a commercial solver (which was used to solve a mathematical model) and several heuristics from the literature. The experimental study conducted indicates that the proposed PSO algorithm outperforms both the commercial solver and the heuristics in terms of solution quality. The commercial solver requires longer run times compared to PSO.     

Minimizing makespan during environmental stress screening using a genetic algorithm and an ant colony optimization

The environmental stress screening (ESS) chamber employed in a typical electronics manufacturing service (EMS) provider’s facility is used for screening products, attempting to expose defects that cannot be detected by visual inspection or electrical testing. The ESS chambers are bottleneck work centers in most of the EMS facilities. This research uses a genetic algorithm (GA) and an ant colony optimization (ACO) to solve the job-scheduling problem at the ESS chamber where the makespan of the process is minimized. The performances of the two approaches were compared against some of the first-fit (FF) techniques from the literature. Both the GA and ACO techniques produced satisfactory results up to a job size of 40. Furthermore, ACO generally requires a longer computational time, while offering more consistent solution quality.     

Genetic algorithms for minimizing makespan in a flow shop with two capacitated batch processing machines

This paper considers a flow shop with two batch processing machines. The processing times of the job and their sizes are given. The batch processing machines can process multiple jobs simultaneously in a batch as long as the total size of all the jobs in a batch does not exceed its capacity. When the jobs are grouped into batches, the processing time of the batch is defined by the longest processing job in the batch. Batch processing machines are expensive and a bottleneck. Consequently, the objective is to minimize the makespan (or maximize the machine utilization). The scheduling problem under study is NP-hard, hence, a genetic algorithm (GA) is proposed. The effectiveness (in terms of solution quality and run time) of the GA approach is compared with a simulated annealing approach, a heuristic, and a commercial solver which was used to solve a mixed-integer formulation of the problem. Experimental study indicates that the GA approach outperforms the other approaches by reporting better solution.     

A joint GA+DP approach for single burn-in oven scheduling problems with makespan criterion

This research is motivated by the scheduling problem found in the burn-in operation of semiconductor final testing, where jobs are associated with release times, processing times, and sizes. The burn-in ovens are modeled as batch-processing machines which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity, and the processing time of a batch is equal to the longest time among all the jobs in the batch. Moreover, this paper attempts to schedule jobs on a single batch-processing machine to minimize makespan. A joint GA+DP algorithm is proposed involving two stages: (1) the formation of job sequence by genetic algorithm operators, and (2) the formation of batches by a dynamic programming algorithm. Computational experiments are given to examine the performance of the proposed algorithm. The experimental results indicate that the joint GA+DP approach has well improved on all instances with respect to solution quality and runtime.     

A hybrid genetic algorithm to minimize makespan for the single batch machine dynamic scheduling problem

This paper considers a single batch machine dynamic scheduling problem, which is readily found in the burn-in operation of semiconductor manufacturing. The batch machine can process several jobs as a batch simultaneously, within the capacity limit of the machine, and the processing time is represented by the longest processing time among all jobs in a batch. For a single batch machine problem with arbitrary job release time, we proposed an improved algorithm (merge-split procedure) to refine the solution obtained by the LPT-BFF heuristic, and two versions of a hybrid genetic algorithm (GA) are introduced in this paper. Each version of the hybrid GA diversifies job sequences using the GA operators in stage 1, forms batches in stage 2, and finally sequence the batches in stage 3. The difference is that merge-split procedures are involved in the second version of the hybrid GA. Computational experiments showed that the hybrid GA would obtain satisfactory average solution quality and the merge-split procedures would be good at reinforcing the solution consistency of the hybrid GA.     

Makespan minimization in a job shop with a BPM using simulated annealing

A scheduling problem commonly observed in the metal working industry has been studied in this research effort. A job shop equipped with one batch processing machine (BPM) and several unit-capacity machines has been considered. Given a set of jobs, their process routes, processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized. The BPM can process a batch of jobs as long as its capacity is not exceeded. The batch processing time is equal to the longest processing job in the batch. If no batches were to be formed, the scheduling problem under study reduces to the classical job shop problem with makespan objective, which is known to be nondeterministic polynomial time-hard. A network representation of the problem using disjunctive and conjunctive arcs, and a simulated annealing (SA) algorithm are proposed to solve the problem. The solution quality and run time of SA are compared with CPLEX, a commercial solver used to solve the mathematical formulation and with four dispatching rules. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using SA to solve large-scale problems.     

Heuristics to minimize makespan of parallel batch processing machines

Batch-processing machines can process several jobs simultaneously. These machines are commonly used to test Printed Circuit Boards (PCBs). The processing time and the dimensions of the PCB are given. Each batch is formed such that the total size of all the PCBs in the batch does not exceed the machine capacity. The batch processing time is equal to the longest processing time of all the PCBs in the batch. These batch processing machines are expensive and a bottleneck. Scheduling PCBs on these parallel batch processing machines to minimize their makespan is NP-hard. Consequently, we propose several heuristics. The performance of the proposed heuristics is compared to a simulated annealing approach and a commercial solver.     

Determination of number of kanban in a cellular manufacturing system with considering rework process

The main element of just-in-time production system is kanban and the number of kanban influences the product inventory level. This research studies the cellular manufacturing system controlled by kanban mechanism which defective items are produced in any production run of each product and rework is carried out to transform them into serviceable items. In each cycle after the normal production of each product, the machine is setup for the rework process. In this paper, a mixed-integer nonlinear programming (MINLP) model in order to minimize total cost was developed to determine number of kanban, batch size, and number of batches. To avoid the large computational time in optimal solution, a particle swarm optimization (PSO) and simulated annealing (SA) algorithms as metaheuristic methods are used for solving a large MINLP. Some problems are solved by PSO and SA and performance of the PSO and the SA is evaluated by comparing their results with the optimal solution. It is shown that both PSO and SA result in a near-optimal solution but the PSO algorithm gives a better performance than the SA method.     

GRASP to minimize makespan for a capacitated batch-processing machine

This paper presents a Greedy Randomized Adaptive Search Procedure (GRASP) to minimize the makespan of a capacitated batch-processing machine. Given a set of jobs and their processing times and sizes, the objective is to group these jobs into batches and schedule the batches on a single batch-processing machine such that the time taken to complete the last batch of jobs (or makespan) is minimized. The batch-processing machine can process a batch of jobs simultaneously as long as the total size of all the jobs in that batch does not exceed the machine capacity. The batch-processing time is equal to the longest processing time for a job in the batch. It has been shown that the problem under study is non-deterministic polynomial-time hard. Consequently, a GRASP approach was developed. The solution quality of GRASP was compared to other solution approaches such as simulated annealing, genetic algorithm, and a commercial solver through an experimental study. The study helps to conclude that GRASP outperforms other solution approaches, especially on larger problem instances.     

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.     

Minimizing total weighted tardiness on a batch-processing machine with non-agreeable release times and due dates

This study considers the scheduling problem observed in the burn-in operation of semiconductor final testing, where jobs are associated with release times, due dates, processing times, sizes, and non-agreeable release times and due dates. The burn-in oven is modeled as a batch-processing machine which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity and the processing time of a batch is equal to the longest time among all the jobs in the batch. Due to the importance of on-time delivery in semiconductor manufacturing, the objective measure of this problem is to minimize total weighted tardiness. We have formulated the scheduling problem into an integer linear programming model and empirically show its computational intractability. Due to the computational intractability, we propose a few simple greedy heuristic algorithms and meta-heuristic algorithm, simulated annealing (SA). A series of computational experiments are conducted to evaluate the performance of the proposed heuristic algorithms in comparison with exact solution on various small-size problem instances and in comparison with estimated optimal solution on various real-life large size problem instances. The computational results show that the SA algorithm, with initial solution obtained using our own proposed greedy heuristic algorithm, consistently finds a robust solution in a reasonable amount of computation time.     

基于免疫算法的并行机间歇过程模糊生产调度

研究了一类具有顺序无关模糊产品切换时间和成本以及模糊单位加工时间和成本的并行机间歇过程调度问题,目的是确定每种产品在每个设备上处理的批次数目、批量以及批次顺序,优化目标为最小化总完成时间和最小化总生产成本。根据任意设备上同种产品的所有批次均顺序处理的性质,建立了问题的模糊运输模型。利用加权和方法将多目标函数转化为单目标函数,并使用基于积分值的方法对模糊数进行排序。提出了基于排列边集编码的免疫算法,通过求解不同规模的问题实例证明,免疫算法不仅能获得比遗传算法和免疫遗传算法更好的解,而且比免疫遗传算法更高效,同时具有良好的动态性能。     

2个加工时间不同工序组批的嵌套批综合调度算法

针对已有的批加工工序数为2的批综合调度算法,没有考虑组批工序不同和后续工序中存在组批工序的情况,不能适用于更复杂的批综合调度问题,提出求解2个加工时间不同工序组批的嵌套批综合调度算法。该算法根据批处理工序加工时间不同的特点,定义串行衔接时间和并行衔接时间;提出判断组批的余差比较策略;当可与等待工序一同批处理的工序不唯一时,采用组批前移最大化策略确定组批处理工序;当准备组批处理工序的后续工序中存在组批工序时,在余差比较策略中加入嵌套优化策略确定该工序是否组批;由于组批工序的后续工序较多且对调度结果影响较大,采用前续工序优先策略使组批工序尽早加工。理论分析和实例表明,提出的算法可解决2个加工时间不同工序组批的嵌套批综合调度问题。     

Sequencing two-stage flowshop with nonidentical job sizes

This study addresses the two-machine flowshop in which a batch processor is followed by a discrete processor. The batch machine processes a batch of jobs simultaneously and the discrete machine processes one job at a time. Each job has a certain size or capacity requirements. The capacity of the batch processor is limited. The objective is to minimize the makespan. This problem is shown to be nondeterministic polynomial time hard. A heuristic algorithm and a branch-and-bound algorithm are presented. Computational results show that the proposed heuristic algorithm works effectively compared to the optimal solution, with an overall average quality of 99.42%.     

间歇过程PSO SQP混合优化算法研究*

针对SQP算法在求解具有复杂约束的间歇过程优化时容易陷入局部极值点的问题,本文提出一种PSO-SQP混合优化算法。该算法首先采用外点罚函数法将间歇过程有约束的优化问题转换为无约束的优化问题,利用PSO强大的全局搜索能力对其进行求解,并把搜索结果作为SQP搜索初始点,以此弥补SQP全局搜索弱的缺点,再利用SQP良好的局部收敛性和较强的非线性收敛速度对原优化问题进行精细搜索,弥补了PSO局部搜索弱的缺点,通过不断的迭代最终获得优化问题的全局最优解。该算法充分利用了SQP和PSO的优缺点,增强了其对复杂约束优化问题的求解能力。将本文提出的算法用于连续搅拌化学反应系统温度控制中,仿真结果表明产物浓度能够充分逼近期望值,且反应器的温度轨迹收敛,从而验证了该算法的有效性和实用价值。     

A swarm optimization approach for flexible flow shop scheduling with multiprocessor tasks

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (C_max). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.     

考虑批量装配的柔性作业车间调度问题研究

柔性作业车间调度是生产调度领域中的一个重要组合优化问题,由于取消了工序与加工设备的唯一性对应关系,因而相较于作业车间调度问题,具有更高的复杂度。针对该问题在批量装配方面的不足,考虑将批量因素与装配环节同时集成到柔性作业车间调度问题当中。以成品件的完工时间为优化目标,对该批量装配柔性作业车间调度问题进行了数学建模。针对该模型,提出一种多层编码结构的粒子群算法,并对该算法的各个模块进行了设计。最后,以实例验证了该数学模型的正确性及算法的有效性。     

基于改进PSO算法的电液位置伺服系统MRAC跟踪控制

针对电液位置伺服系统控制性能不佳的问题,提出一种基于改进PSO算法优化的模型参考自适应(Model Reference Adaptive Control,MRAC)跟踪控制方法。首先,建立电液位置伺服系统数学模型,设计出模型参考自适应控制器;其次,分析PSO算法、APSO算法在参数寻优过程中的不足,提出一种改进的PSO算法;最后,将改进的PSO算法用于模型参考自适应控制器以改善其控制性能。结果表明,改进PSO算法优化的模型参考自适应控制具有响应速度快、跟踪精度高的优点。     

基于粒子群优化的开放式车间调度

开放式车间调度(OSP)是重要的调度问题,它在制造领域中的应用非常广泛。优化调度算法是调度理论的重要研究内容。基于人工智能的元启发式算法是解决该问题的常用方法。分析了一种新的元启发式算法——粒子群优化(PSO)在信息共享机制上的缺陷,提出新的基于群体智能的信息共享机制。在该信息共享机制的基础上, 设计新的基于PSO的元启发式调度算法——PSO-OSP。该算法利用问题的邻域知识指导局部搜索,可克服元启发式算法随机性引起的盲目搜索。该算法应用于开放式车间调度问题的标准测试实例。仿真结果显示,PSO-OSP算法在加快收敛速度的同时提高了开放式车间调度解的质量。