Research on job-shop scheduling optimization method with limited resources

Job-shop scheduling is an important subject in the fields of production management and combinatorial optimization. It is also an urgent problem to be solved in actual production. It is usually difficult to achieve the optimal solution with classical methods, due to a high computational complexity (NP-Hard). According to the nature of job-shop scheduling, a solution based on a particle swarm optimiser (PSO) is presented in this paper. In addition to establishing a job-shop scheduling model based on PSO, we have researched the coding and optimized operation of PSO. We have also considered more suitable methods of coding and operation for job-shop scheduling as well as the target function and calculation of the proper figure. The software system of job-shop scheduling is developed according to the PSO algorithm. Test simulations illustrate that the PSO algorithm is a suitable and effective approach for solving the job-shop scheduling problem.     

多生产线作业协调调度的PSOGA混合优化算法

为了求解多目标多生产线调度问题,采用协同进化思想,提出了多种群PSOGA混合优化算法(MC-HPSOGA)。以最小化最大完工时间、最大化生产线利用率和最大化客户满意度为目标函数,建立了多生产线作业协调调度问题的多目标批量调度数学模型,并且设计最小批量动态分批策略,将MC-HPSOGA算法应用于BSPT公司角磨机装配线的多目标多生产线调度问题实例中,通过与粒子群(PSO)和遗传算法(GA)的比较,验证了MC-HPSOGA算法和模型的有效性。     

Integrated scheduling of flexible manufacturing system using evolutionary algorithms

Effective sequencing and scheduling of the material handling system (MHS) have an impact on the productivity of the flexible manufacturing system (FMS). The MHS cannot be neglected while scheduling the production tasks. It is necessary to take into account the interaction between machines and MHS. This paper highlights the importance of integration between production schedule and MHS schedule in FMS. The Giffler and Thompson algorithm with different priority dispatching rules is developed to minimize the makespan in the FMS production schedule. Its output is used for MHS scheduling where the distance traveled and the number of backtrackings of the automated-guided vehicles are minimized using an evolutionary algorithms such as an ant colony optimization algorithm and particle swarm optimization (PSO) algorithm. The proposed evolutionary algorithms are validated with benchmark problems. The results available for the existing algorithms are compared with results obtained by the proposed evolutionary algorithms. The analysis reveals that PSO algorithm provides better solution with reasonable computational time.     

An ant colony algorithm for scheduling in flowshops with sequence-dependent setup times of jobs

The problem of scheduling in flowshops with sequence-dependent setup times of jobs is considered and solved by making use of ant colony optimization (ACO) algorithms. ACO is an algorithmic approach, inspired by the foraging behavior of real ants, that can be applied to the solution of combinatorial optimization problems. A new ant colony algorithm has been developed in this paper to solve the flowshop scheduling problem with the consideration of sequence-dependent setup times of jobs. The objective is to minimize the makespan. Artificial ants are used to construct solutions for flowshop scheduling problems, and the solutions are subsequently improved by a local search procedure. An existing ant colony algorithm and the proposed ant colony algorithm were compared with two existing heuristics. It was found after extensive computational investigation that the proposed ant colony algorithm gives promising and better results, as compared to those solutions given by the existing ant colony algorithm and the existing heuristics, for the flowshop scheduling problem under study.     

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。     

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.     

An improved particle swarm optimization for the resource-constrained project scheduling problem

In this paper, an improved particle swarm optimization (PSO) algorithm is proposed for the resource-constrained project scheduling problem (RCPSP) which is widely applied in advanced manufacturing, production planning, and project management. The algorithm treats the solutions of RCPSP as particle swarms and employs a double justification skill and a move operator for the particles, in association with rank-priority-based representation, greedy random search, and serial scheduling scheme, to execute the intelligent updating process of the swarms to search for better solutions. The integration combines and overhauls the characteristics of both PSO and RCPSP, resulting in enhanced performance. The computational experiments are subsequently conducted to set the adequate parameters and compare the proposed algorithm with other approaches. The results suggest that the proposed PSO algorithm augments the performance by 9.26, 16.17, and 10.45 % for the J30, J60, and J120 instances against the best lower bound-based PSO currently available, respectively. Moreover, the proposed algorithms demonstrate obvious advantage over other proposals in exploring solutions for large-scale RCPSP problems such as the J60 and J120 instances.     

A hybrid particle swarm optimization for parallel machine total tardiness scheduling

The parallel machine scheduling problem has received increasing attention in recent years. This research considers the problem of scheduling jobs on parallel machines with a total tardiness objective. In the view of its non-deterministic polynomial-time hard nature, the particle swarm optimization (PSO), which is inspired by the swarming or collaborative behavior of biological populations, is employed to solve the parallel machine total tardiness problem (PMTP). Since it is very hard to directly apply standard PSO to this problem, a new solution representation is designed based on real number encoding, which can conveniently convert the job sequences of PMTP to continuous position values. Moreover, in order to enhance the performance of PSO, we introduce clonal selection algorithm (CSA) into PSO and therefore propose a new CSPSO method. The incorporation of CSA can greatly improve the swarm diversity and avoid premature convergence. We further investigate three parameters of PSO and CSPSO, finding that the parameters have marginal impact on CSPSO, which indicates that CSPSO is a very stable and robust method. The performance of CSPSO is evaluated in comparison with traditional genetic algorithm (GA) and standard PSO on 250 benchmark instances. Experimental results show that CSPSO significantly outperforms GA and PSO, with obtaining the optimal solutions of 237 instances. Additionally, PSO appears more effective than GA.     

Reentrant two-stage multiprocessor flow shop scheduling with due windows

Reentrant flow shop scheduling allows a job to revisit a particular machine several times. The topic has received considerable interest in recent years; with related studies demonstrating that particle swarm algorithm (PSO) is an effective and efficient means of solving scheduling problems. By selecting a wafer testing process with the due window problem as a case study, this study develops a farness particle swarm optimization algorithm (FPSO) to solve reentrant two-stage multiprocessor flow shop scheduling problems in order to minimize earliness and tardiness. Computational results indicate that either small- or large-scale problems are involved in which FPSO outperforms PSO and ant colony optimization with respect to effectiveness and robustness. Importantly, this study demonstrates that FPSO can solve such a complex scheduling problem efficiently.     

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.     

A multistage stochastic programming approach in project selection and scheduling

In this paper, the joint problem of project selection and project scheduling under uncertain environment is formulated, analyzed, and solved by multistage stochastic programs. First of all, a general mathematical formulation which can address several versions of the problem is presented. A multi-period project selection and scheduling problem is introduced and modeled by multistage stochastic programs, which are effective for solving long-term planning problems under uncertainty. A set of scenarios and corresponding probabilities is applied to model the multivariate random data process (costs or revenues, available budget, chance of success). Then, due to computational complexity, a scenario tree of the resulted scenarios is constructed by scenario reduction algorithms. Finally, assuming resources of the projects to be limited and renewable, and present worth of profit of projects as the objective, the objective of the problem is maximized. Eventually, a case study is introduced and solved, and the results are presented. The effectiveness of the proposed algorithm is shown by the numerical results.     

解决JOB SHOP问题的粒子群优化算法

设计了2种解决Job shop问题的粒子群算法,即实数编码的粒子群调度算法和工序编码的粒子群调度算法。工序编码的粒子群调度算法更符合Job shop问题的特点,优化性能相对高。但粒子群调度算法容易陷入局部最优。为了提高优化性能,将粒子群算法和模拟退火算法结合,得到了粒子群-模拟退火混合调度算法。仿真结果表明了算法的有效性。     

Scheduling jobs on dynamic parallel machines with sequence-dependent setup times

Dynamic parallel machine scheduling problems (DPMSPs) with sequence-dependent setup times represent a very important production scheduling problem but remain under-represented in the research literature. In this study, a restricted simulated annealing (RSA) algorithm that incorporates a restricted search strategy with the elimination of non-effect job moves to find the best neighborhood schedule is presented. The proposed RSA algorithm can reduce search efforts significantly while minimizing maximum lateness on DPMSPs. Extensive computational experiments demonstrate that the proposed RSA algorithm is highly effective as compared to the basic simulated annealing and existing algorithms on the same benchmark problem data set.     

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。     

An effective hybrid particle swarm optimization for no-wait flow shop scheduling

The no-wait flow shop scheduling that requires jobs to be processed without interruption between consecutive machines is a typical NP-hard combinatorial optimization problem, and represents an important area in production scheduling. This paper proposes an effective hybrid algorithm based on particle swarm optimization (PSO) for no-wait flow shop scheduling with the criterion to minimize the maximum completion time (makespan). In the algorithm, a novel encoding scheme based on random key representation is developed, and an efficient population initialization, an effective local search based on the Nawaz-Enscore-Ham (NEH) heuristic, as well as a local search based on simulated annealing (SA) with an adaptive meta-Lamarckian learning strategy are proposed and incorporated into PSO. Simulation results based on well-known benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed hybrid algorithm.     

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.     

APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOPSCHEDULING PROBLEM

A new heuristic algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling problem. The new algorithm is based on the principles of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which is inspired by the social behavior of bird flocking. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs certain probability to avoid becoming trapped in a local optimum and the search process can be controlled by the cooling schedule. By reasonably combining these two different search algorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, is developed. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated by applying it to some benchmark job-shop scheduling problems and comparing results with other algorithms in literature. Comparing results indicate that PSO-based a     

A multi-product multi-period inventory control problem under inflation and discount: a parameter-tuned particle swarm optimization algorithm

In this paper, a seasonal multi-product multi-period inventory control problem is modeled in which the inventory costs are obtained under inflation and all-unit discount policy. Furthermore, the products are delivered in boxes of known number of items, and in case of shortage, a fraction of demand is considered backorder and a fraction lost sale. Besides, the total storage space and total available budget are limited. The objective is to find the optimal number of boxes of the products in different periods to minimize the total inventory cost (including ordering, holding, shortage, and purchasing costs). Since the integer nonlinear model of the problem is hard to solve using exact methods, a particle swarm optimization (PSO) algorithm is proposed to find a near-optimal solution. Since there is no bench mark available in the literature to justify and validate the results, a genetic algorithm is presented as well. In order to compare the performances of the two algorithms in terms of the fitness function and the required CPU time, they are first tuned using the Taguchi approach, in which a metric called “smaller is better” is used to model the response variable. Then, some numerical examples are provided to demonstrate the application and to validate the results obtained. The results show that, while both algorithms have statistically similar performances, PSO tends to be the better algorithm in almost all problems.     

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.     

A hybrid algorithm based on particle swarm optimization and simulated annealing for a periodic job shop scheduling problem

Generating schedules such that all operations are repeated every constant period of time is as important as generating schedules with minimum delays in all cases where a known discipline is desired or obligated by stakeholders. In this paper, a periodic job shop scheduling problem (PJSSP) based on the periodic event scheduling problem (PESP) is presented, which deviates from the cyclic scheduling. The PESP schedules a number of recurring events as such that each pair of event fulfills certain constraints during a given fixed time period. To solve such a hard PJSS problem, we propose a hybrid algorithm, namely PSO-SA, based on particle swarm optimization (PSO) and simulated annealing (SA) algorithms. To evaluate this proposed PSO-SA, we carry out some randomly constructed instances by which the related results are compared with the proposed SA and PSO algorithms as well as a branch-and-bound algorithm. In addition, we compare the results with a hybrid algorithm embedded with electromagnetic-like mechanism and SA. Moreover, three lower bounds (LBs) are studied, and the gap between the found LBs and the best found solutions are reported. The outcomes prove that the proposed hybrid algorithm is an efficient and effective tool to solve the PJSSP.