A genetic algorithm and particle swarm optimization for no-wait flow shop problem with separable setup times and makespan criterion

This paper considers the problem of no-wait flow shop scheduling, in which a number of jobs are available for processing on a number of machines in a flow shop context with the added constraint that there should be no waiting time between consecutive operations of a job. Each operation has a separable setup time, meaning that the setup time of an operation is independent on the previous operations; and the machine can be prepared for a specific operation and remain idle before the operation actually starts. The considered objective function in this paper is the makespan. The problem is proven to be NP-hard. In this paper, two frameworks based on genetic algorithm and particle swarm optimization are developed to deal with the problem. For the case of no-wait flow shop problem without setup times, the developed algorithms are applied to a large number of benchmark problems from the literature. Computational results confirm that the proposed algorithms outperform other methods by improving many of the best-known solutions for the test problems. For the problems with setup time, the algorithms are compared against the famous 2-Opt algorithm. Such comparison reveals the efficiency of the proposed method in solving the problem when separable setup times are considered.     

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.     

A branch-and-bound and heuristic algorithm for the single-machine time-dependent scheduling problem

The time-dependent scheduling problems have received considerable attention recently. However, machine availability, an important and practical consideration, is usually neglected. Motivated by this observation, we introduce a single-machine scheduling problem where deteriorating jobs and an availability constraint are considered. Our objective is to minimize the total completion time. In this paper, we derived optimal and near-optimal solutions for the problem, and we also gave a simulation study to show that our algorithm successfully yields the optimal solution for instances with less than 20 jobs in less than a minute. Our computational experiment also showed that the mean error percentage of the proposed heuristic algorithm for all test instances is less than 1.3% and drops to zero as the number of jobs increases.     

A conflict-based priority dispatching rule and operation-based approaches to job shops

Job shop scheduling (JSS) problems consist of a set of machines and a collection of jobs to be scheduled. Each job consists of several operations with a specified processing order. In this paper, a job shop model problem is scheduled with the help of the Giffler and Thompson algorithm using a priority dispatching rule (PDR). A conflict based PDR is used to schedule the job shop model by using Genetic Algorithms (GAs). An iterative method is applied to the job model to find the optimal conflict-based PDR order and the operation sequence. The same job shop model is also scheduled based on an operation using simulated annealing (SA) and hybrid simulated annealing (HSA). A makespan of the job model is used as an objective. These four methods are considered as different solutions for each problem. A two-way analysis of variance (ANOVA) is applied to test its significance.     

A general flow shop scheduling problem with consideration of position-based learning effect and multiple availability constraints

In this paper, a more general version of the flow shop scheduling problem with the objective of minimizing the total flow time is investigated. In order to get closer to the actual conditions of the problem, some realistic assumptions including non-permutation scheduling, learning effect, multiple availability constraints, and release times are considered. It is assumed that the real processing time of each job on a machine depends on the position of that job in the sequence, and after processing a specified number of jobs at each machine, an unavailability period is occurring because of maintenance activities. Moreover, it is supposed that each job may not be ready for processing at time zero and may have a release time. According to these assumptions, a new mixed integer linear programming (MILP) model is proposed to formulate the problem. Due to the high complexity of the problem, a heuristic method and a simulated annealing algorithm are presented to find the nearly optimal solutions for medium- and large-sized problems. To obtain better and more robust solutions, the Taguchi method is used in order to calibrate the simulated annealing algorithm parameters. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution methods.     

Flexible job shop scheduling with tabu search algorithms

This paper presents a tabu search algorithm that solves the flexible job shop scheduling problem to minimize the makespan time. As a context for solving sequencing and scheduling problems, the flexible job shop model is highly complicated. Alternative operation sequences and sequence-dependent setups are two important factors that frequently appear in various manufacturing environments and in project scheduling. In this paper, we present a model for a flexible job shop scheduling problem while considering those factors simultaneously. The purpose of this paper is to minimize the makespan time and to find the best sequence of operations and the best choice of machine alternatives, simultaneously. The proposed tabu search algorithm is composed of two parts: a procedure that searches for the best sequence of job operations, and a procedure that finds the best choice of machine alternatives. Randomly generated test problems are used to evaluate the performance of the proposed algorithm. Results of the algorithm are compared with the optimal solution using a mathematical model solved by the traditional optimization technique (the branch and bound method). After modeling the scheduling problem, the model is verified and validated. Then the computational results are presented. Computational results indicate that the proposed algorithm can produce optimal solutions in a short computational time for small and medium sized problems. Moreover, it can be applied easily in real factory conditions and for large size problems. The proposed algorithm should thus be useful to both practitioners and researchers.     

Flow shop scheduling with two batch processing machines and nonidentical job sizes

A batch processing machine can process several jobs simultaneously. In this research, we consider the problem of a two-stage flow shop with two batch processing machines to minimize the makespan. We assume that the processing time of a batch is the longest processing time among all the jobs in that batch and the sizes of the jobs are nonidentical. There is a limitation on batch sizes and the sum of job sizes in a batch must be less than or equal to the machine capacity. Since this problem is strongly nondeterministic polynomial time hard, we propose two heuristic algorithms. The first one is knowledge-based and the other is based on the batch first fit heuristic proposed previously. To further enhance the solution quality, two different simulated annealing (SA) algorithms based on the two constructive heuristics is also developed. Since heuristic methods for this problem has not been proposed previously, a lower bound is developed for evaluating the performance of the proposed methods. Several test problems have been solved by SAs and lower bound method and the results are compared. Computational studies show that both algorithms provide good results but the first SA (ARSA) algorithm considerably outperforms the second one (FLSA). In addition, the results of ARSA algorithm, optimal solutions, and lower bounds are compared for several small problems. The comparisons show that except for one instance, the ARSA could find the optimal solutions and the proposed lower bound provides small gaps comparing with the optimal solutions.     

Scheduling jobs under constant period-by-period resource availability to maximize project profit at a due date

In this paper, we propose a lump-sum payment model for the resource-constrained project scheduling problem, which is a generalization of the job shop scheduling problem. The model assumes that the contractor will receive the profit of each job at a predetermined project due date, while taking into account the time value of money. The contractor will then schedule the jobs with the objective of maximizing his total future net profit value at the due date. This proposed problem is nondeterministic polynomial-time (NP)-hard and mathematically formulated in this paper. Several variable neighborhood search (VNS) algorithms are developed by using insertion move and two-swap to generate various neighborhood structures, and making use of the well-known backward–forward scheduling, a proposed future profit priority rule, or a short-term VNS as the local refinement scheme (D-VNS). Forty-eight 20-job instances were generated using ProGen and optimally solved with ILOG CPLEX. The performances of these algorithms are evaluated based on the optimal schedules of the 48 test instances. Our experimental results indicate that the proposed VNS algorithms frequently obtain optimal solutions in a short computational time. For larger size problems, our experimental results also indicate that the D-VNS with forward direction movement outperforms the other VNS algorithms, as well as a genetic algorithm and a tabu search algorithm.     

Group shop scheduling with uncertain data and a general cost objective

In this paper, a stochastic group shop scheduling problem with a due date-related objective is studied. The group shop scheduling problem provides a general formulation including two other shop scheduling problems, the job shop and the open shop. Both job release dates and processing times are assumed to be random variables with known distributions. Moreover, earliness and tardiness of jobs are penalized at different rates. The objective is to minimize the expected maximum completion cost among all jobs. A lower bound on the objective function is proposed, and then, a hybrid approach following a simulation optimization procedure is developed to deal with the problem. An ant colony optimization algorithm is employed to construct good feasible solutions, while a discrete-event simulation model is used to estimate the performance of each constructed solution that, taking into account its lower bound, may improve the best solution found so far. The proposed approach is then evaluated through computational experiments.     

Application of chance-constrained programming for stochastic group shop scheduling problem

In this paper, we study a group shop scheduling (GSS) problem subject to uncertain release dates and processing times. The GSS problem is a general formulation including the other shop scheduling problems such as the flow shop, the job shop, and the open shop scheduling problems. The objective is to find a job schedule which minimizes the total weighted completion time. We solve this problem based on the chance-constrained programming. First, the problem is formulated in a form of stochastic programming and then prepared in a form of deterministic mixed binary integer linear programming such that it can be solved by a linear programming solver. To solve the problem efficiently, we develop an efficient hybrid method. Exploiting a heuristic algorithm in order to satisfy the constraints, an ant colony optimization algorithm is applied to construct high-quality solutions to the problem. The proposed approach is tested on instances where the random variables are normally, uniformly, or exponentially distributed.     

Scheduling in aerospace composite manufacturing systems: a two-stage hybrid flow shop problem

This research investigates a real-world complex two-stage hybrid flow shop scheduling problem which is faced during the manufacturing of composite aerospace components. There are a number of new constraints to be taken into account in this special hybrid flow shop, in particular limited physical capacity of the intermediate buffer, limited waiting time between processing stages, and limited tools/molds used in both stages in each production cycle. We propose a discrete-time mixed integer linear programming model with an underlying branch and bound algorithm, to solve small- and medium-size problems (up to 100 jobs). To solve the large instances of the problem (up to 300 jobs), a genetic algorithm with a novel crossover operator is developed. A new heuristic method is introduced to generate the initial population of the genetic algorithm. The results show the high level of computational efficiency and accuracy of the proposed genetic algorithm when compared to the optimal solutions obtained from the mathematical model. The results also show that the proposed genetic algorithm outperforms the conventional dispatching rules (i.e., shortest processing time, earliest dues date and longest processing time) when applied to large-size problems. A real case study undertaken at one of the leading aerospace companies in Canada is used to formulate the model, collect data for the parameters of the model, and analyze the results.     

A two-stage genetic algorithm for large size job shop scheduling problems

The majority of large size job shop scheduling problems are non-polynomial-hard (NP-hard). In the past few decades, genetic algorithms (GAs) have demonstrated considerable success in providing efficient solutions to many NP-hard optimization problems. But there is no literature available considering the optimal parameters when designing GAs. Unsuitable parameters may generate an inadequate solution for a specific scheduling problem. In this paper, we proposed a two-stage GA which attempts to firstly find the fittest control parameters, namely, number of population, probability of crossover, and probability of mutation, for a given job shop problem with a fraction of time using the optimal computing budget allocation method, and then the fittest parameters are used in the GA for a further searching operation to find the optimal solution. For large size problems, the two-stage GA can obtain optimal solutions effectively and efficiently. The method was validated based on some hard benchmark problems of job shop scheduling.     

A modified shifting bottleneck heuristic for the reentrant job shop scheduling problem with makespan minimization

This paper proposes a modified shifting bottleneck heuristic (MSBH) for the reentrant job shop scheduling problem (RJSSP) with makespan minimization objective. Recently, the reentrant job shop has come into prominence as a new type of manufacturing shop. The principle characteristic of a reentrant job shop is that a job may visit certain machines more than once during the process flow, whereas in the classic job shop, each job visits a machine only once. The shifting bottleneck heuristic (SBH) is one of the most successful heuristic approaches for the classical job shop scheduling problem, which decomposes the problem into a number of single-machine subproblems. This paper adapts the SBH for the RJSSP and proposes a new sequencing heuristic for the single-machine maximum lateness subproblem considering the reentrant jobs in order to handle large-size RJSSPs. It also uses a subproblem criticality measure that further shortens the implementation time. The proposed MSBH is tested by using instances up to 20 machines and 100 jobs, and it is illustrated that good quality solutions can be obtained in reasonable computational times. A real-life application of the MSBH is also given as a case study to evaluate its performance.     

A hybrid genetic algorithm for integrated process planning and scheduling problem with precedence constraints

Process planning and scheduling are two important functions in a modern manufacturing system. Although integrating decisions related to these functions gives rise to a hard combinatorial problem, due to the impressive improvement in system performance which is resulted through this integration, developing effective methods to solve this problem is of great theoretical and practical importance. In this research, after formulating the integrated process planning and scheduling problem as a mathematical program, we propose a hybrid genetic algorithm (GA) for the problem. In the proposed algorithm, problem-specific genetic operators are designed to enhance the global search power of GA. Also, a local search procedure has been incorporated into the GA to improve the performance of the algorithm. The model considers precedence relations among job operations, based on which feasible process plans for each job can be represented implicitly. A novel neighborhood function, considering the constraints of a flexible job shop environment and nonlinear precedence relations among operations, is presented to speed up the local search process. In experimental study, the performance of the proposed algorithm has been evaluated based on a number of problems adopted from the literature. The experimental results demonstrate the efficiency of the proposed algorithm to find optimal or near-optimal solutions.     

[工艺规划与装配线平衡]两阶段混合算法求解集成工艺规划与调度问题

提出了求解集成式工艺规划与车间调度问题的两阶段混合算法。在工艺规划阶段,使用遗传算法为每个工件生成可选的近优工艺路线集,动态地为车间调度阶段输入已确定的工艺路线;在车间调度阶段,使用蜜蜂交配优化算法快速寻优,设计了蜂王婚飞的流程以保证算法的全局搜索能力,构建了基于不同邻域结构的工蜂培育幼蜂局部搜索策略。使用基准测试集对提出的方法进行验证,并与现有算法进行对比,计算结果证明了提出方法的有效性。     

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.     

一类带有deadline约束的作业车间提前/拖期调度问题研究

针对带有零件deadline时间约束的一类作业车间提前/拖期调度问题,设计了一种改进型遗传算法(EGA)。EGA算法采用拖期优先的调度策略,将原有的非正规性能指标的E/T调度问题转化为拖期子问题、修复子问题和提前子问题,以此来降低E/T调度问题的求解复杂度。采用基于工序的编码方法,在染色体解码过程中,分别采用了主动解码、染色体修复和逆向重调度三阶段的解码操作,以期实现在满足零件deadline约束的前提下尽可能降低提前/拖期惩罚总成本。180个调度测试用例仿真结果表明,EGA算法在解决问题数、寻优能力、调度结果的均衡性等方面具有一定的优势。     

Production planning in virtual cell of reconfiguration manufacturing system using genetic algorithm

This paper focuses on the scheduling problem of the reconfiguration manufacturing system (RMS) for execution level, where the final objective is to output a production plan. The practical situation in Chinese factory is analyzed, and the characteristics are summarized into the contradiction between flow and job shop production. In order to handle this problem, a new production planning algorithm in virtual cells is proposed for RMS using an improved genetic algorithm. The advantages of this algorithm have three parts: (1) the virtual cell reconfiguration is formed to assist making production plans through providing relationship among task families and machines from cell formation; (2) The operation buffer algorithm is developed for flow style production in cells, which can realize the nonstop processing for flow style jobs; and (3) The multicell sharing method is proposed to schedule job shop jobs in order to fully utilize manufacturing capability among machines in multicells. Based on the above advantages, an improved genetic algorithm is developed to output scheduling plan. At last, the algorithm is tested in different instances with LINGO and the other genetic algorithm, and then the scheduling solution comparison shows the proposed algorithm can get a better optimum result with the same time using the comparison algorithm.     

一种求解Job Shop问题的合作型协同进化算法

针对Job Shop调度问题，提出了一种改进的合作型协同进化算法。根据机器数量“自然”分割种群，每个种群对应一台机器，个体以机器前工件的优先列表为编码；将静态繁殖理论引入遗传算子，并通过三种共生伙伴选择方式，利用改进的基于优先列表的G＆T算法解码来评价个体；最后采用一种更新技术和动态群体更新策略来加快算法收敛。通过对Job Shop基准问题的优化，该算法获得了比传统的遗传算法更好的结果。     

Combined column generation and constructive heuristic for a proportionate flexible flow shop scheduling

In a proportionate flow shop problem, jobs have to be processed through a fixed sequence of machines, and processing time for each job is equal on all machines. Such a problem has seldom been tackled. Proportionate flexible flow shop (PFFS) scheduling problems combine the properties of proportionate flow shop scheduling problems and parallel machine scheduling problems. This study presents a combined approach based on column generation (CG) for a PFFS problem with the criterion to minimize the objective of the total weighted completion time (TWCT). Minimizing TWCT in a PFFS problem significantly differs from the parallel-identical-machine scheduling problem, an optimal schedule in which jobs on each machine are in the weighted shortest processing time (WSPT) order. This combined approach adopts a CG approach to effectively handle job assignments to machines, and a constructive heuristic to obtain an optimal sequence for a single machine. Experimental results show the effectiveness of the combined approach in obtaining excellent quality solutions in a reasonable time, especially for large-scale problems.