带释放时间的并行机调度问题的ILS & SS算法

研究工件带释放时间的两类并行机最小化总完成时间的调度问题.针对问题提出了一种新的基于变深度环交换邻域结构的Iterated local search(ILS)算法.1)提出了变深度环交换邻域结构.2)基于变深度环交换和传统Swap的混合邻域,提出了带有两种kick策略的ILS算法.3)为了加强ILS逃出局部最优的能力,将Scatter search (SS)搜索方法引入了ILS算法中;算法将当前最好解和次好解进行分散处理,再从处理后的解开始继续迭代.为了验证算法的有效性,对两类并行机问题分别随机产生100组数据进行试验.实验结果表明:对于同构并行机问题,引入SS的ILS算法的计算结果与下界的平均偏差为0.99%,而没有引入SS的ILS算法的为1.06%;对于无关并行机问题,引入SS搜索方法后,ILS算法的计算结果 改进了6.06%,并明显优于多点下降算法.     

An ant colony-based algorithm for integrated scheduling on batch machines with non-identical capacities

In this paper, a production–distribution scheduling problem with non-identical batch machines and multiple vehicles is considered. In the production stage, n jobs are grouped into batches, which are processed on m parallel non-identical batch machines. In the distribution stage, there are multiple vehicles with identical capacities to deliver jobs to customers after the jobs are processed. The objective is to minimize the total weighted tardiness of the jobs. Considering the NP-hardness of the studied problem, an algorithm based on ant colony optimization is presented. A new local optimization strategy called LOC is proposed to improve the local exploitation ability of the algorithm and further search the neighborhood solution to improve the quality of the solution. Moreover, two interval candidate lists are proposed to reduce the search for the feasible solution space and improve the search speed. Furthermore, three objective-oriented heuristics are developed to accelerate the convergence of the algorithm. To verify the performance of the proposed algorithm, extensive experiments are carried out. The experimental results demonstrate that the proposed algorithm can provide better solutions than the state-of-the-art algorithms within a reasonable time.

     

Dual-Objective Mixed Integer Linear Program and Memetic Algorithm for an Industrial Group Scheduling Problem

Group scheduling problems have attracted much attention owing to their many practical applications. This work proposes a new bi-objective serial-batch group scheduling problem considering the constraints of sequence-dependent setup time, release time, and due time. It is originated from an important industrial process, i.e., wire rod and bar rolling process in steel production systems. Two objective functions, i.e., the number of late jobs and total setup time, are minimized. A mixed integer linear program is established to describe the problem. To obtain its Pareto solutions, we present a memetic algorithm that integrates a population-based nondominated sorting genetic algorithm II and two single-solution-based improvement methods, i.e., an insertion-based local search and an iterated greedy algorithm. The computational results on extensive industrial data with the scale of a one-week schedule show that the proposed algorithm has great performance in solving the concerned problem and outperforms its peers. Its high accuracy and efficiency imply its great potential to be applied to solve industrial-size group scheduling problems.      

A novel artificial immune system for solving multiobjective scheduling problems subject to special process constraint

This study presents a novel artificial immune system for solving a multiobjective scheduling problem on parallel machines (MOSP), which has the following characteristics: (1) parallel machines are nonidentical, (2) the type of jobs processed on each machine can be restricted, and (3) the multiobjective scheduling problem includes minimizing the maximum completion time among all the machines (makespan) and minimizing the total earliness/tardiness penalty of all the jobs. In this proposed algorithm, the cells are represented by a vector group, and a local search algorithm is incorporated to facilitate the exploitation of the search space. Specially, a new diversity technique is proposed to preserve the diversity of the population and enhance the exploration of the solution space. Simulation results show the proposed algorithm outperforms the vector immune genetic algorithm (VIGA).     

有准备时间无等待流水车间调度的搜索算法

利用迭代变化邻域搜索算法(IVNS)求解最小化总完工时间的有准备时间无等待流水车间调度问题.设计局部搜索算法需要考虑3个关键因素:所用邻域、解评估和局部最优的克服.因此,定义了3个较大规模邻域以扩大搜索范围.为加速解评估,利用目标增量来避免重新计算每个解的目标函数值,使相邻解比较只需常量时间,NEH插入算法的时间复杂度降低一阶.IVNS通过切换邻域和扰动重启,来克服局部搜索易于陷入局部最优解的缺点.通过与求解该问题的当前最好算法在5400个标准算上,以相同CPU时间进行的实算比较,实验结果统计分析验证了IVNS的寻优性能明显优于参照算法.     

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．     

Minimizing makespan for flow shop scheduling problem with intermediate buffers by using hybrid approach of artificial immune system

In this study, three new meta-heuristic algorithms artificial immune system (AIS), iterated greedy algorithm (IG) and a hybrid approach of artificial immune system (AIS-IG) are proposed to minimize maximum completion time (makespan) for the permutation flow shop scheduling problem with the limited buffers between consecutive machines. As known, this category of scheduling problem has wide application in the manufacturing and has attracted much attention in academic fields. Different from basic artificial immune systems, the proposed AIS-IG algorithm is combined with destruction and construction phases of iterated greedy algorithm to improve the local search ability. The performances of these three approaches were evaluated over Taillard, Carlier and Reeves benchmark problems. It is shown that the AIS-IG and AIS algorithms not only generate better solutions than all of the well-known meta heuristic approaches but also can maintain their quality for large scale problems.     

Block approach—tabu search algorithm for single machine total weighted tardiness problem

Problem of scheduling on a single machine to minimize total weighted tardiness of jobs can be described as follows: there are n jobs to be processed, each job has an integer processing time, a weight and a due date. The objective is to minimize the total weighted tardiness of jobs. The problem belongs to the class of NP-hard problems. Some new properties of the problem associated with the blocks have been presented and discussed. These properties allow us to propose a new fast local search procedure based on a tabu search approach with a specific neighborhood which employs blocks of jobs and a compound moves technique. A compound move consists in performing several moves simultaneously in a single iteration of algorithm and allows us to accelerate the convergence to good solutions. In the algorithm, we use an idea which decreases the complexity for the search of neighborhood from O(n³) to O(n²). Additionally, the neighborhood is reduced by using some elimination criteria. The method presented in this paper is deterministic one and has not any random element, as distinct from other effective but non-deterministic methods proposed for this problem, such as tabu search of Crauwels, H. A. J., Potts, C. N., & Van Wassenhove, L. N. (1998). Local search heuristics for the single machine total weighted tardiness Scheduling Problem. INFORMS Journal on Computing, 10(3), 341–350, iterated dynasearch of Congram, R. K., Potts C. N., & Van de Velde, S. L. (2002). An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS Journal on Computing, 14(1), 52–67 and enhanced dynasearch of Grosso, A., Della Croce, F., & Tadei, R. (2004). An enhanced dynasearch neighborhood for single-machine total weighted tardiness scheduling problem. Operations Research Letters, 32, 68–72. Computational experiments on the benchmark instances from OR-Library (http://people.brunel.ac.uk/mastjjb/jeb/info.html) are presented and compared with the results yielded by the best algorithms discussed in the literature. These results show that the algorithm proposed allows us to obtain the best known results for the benchmarks in a short time. The presented properties and ideas can be applied in any local search procedures.     

A heuristic for job shop scheduling to minimize total weighted tardiness

This paper considers the job shop scheduling problem to minimize the total weighted tardiness with job-specific due dates and delay penalties, and a heuristic algorithm based on the tree search procedure is developed for solving the problem. A certain job shop scheduling to minimize the maximum tardiness subject to fixed sub-schedules is solved at each node of the search tree, and the successor nodes are generated, where the sub-schedules of the operations are fixed. Thus, a schedule is obtained at each node, and the sub-optimum solution is determined among the obtained schedules. Computational results on some 10 jobs and 10 machines problems and 15 jobs and 15 machines problems show that the proposed algorithm can find the sub-optimum solutions with a little computation time.     

Minimizing weighted earliness–tardiness on parallel machines using hybrid metaheuristics

We consider the problem of scheduling a set of jobs on a set of identical parallel machines where the objective is to minimize the total weighted earliness and tardiness penalties with respect to a common due date. We propose a hybrid heuristic algorithm for constructing good solutions, combining priority rules for assigning jobs to machines and a local search with exact procedures for solving the one-machine subproblems. These solutions are then used in two metaheuristic frameworks, Path Relinking and Scatter Search, to obtain high quality solutions for the problem.The algorithms are tested on a large number of test instances to assess the efficiency of the proposed strategies.The results show that our algorithms consistently outperform the best reported results for this problem.     

A new heuristic for workload balancing on identical parallel machines and a statistical perspective on the workload balancing criteria

We consider the multiprocessor scheduling problem in which independent jobs are scheduled on identical parallel machines, with the objective of minimizing the normalized sum of square for workload deviations (NSSWD) criterion in order to obtain workload balancing. NSSWD and other criteria for the related problem of number partitioning are presented from a statistical viewpoint, which allows to derive some insightful connections with statistical measures of dispersion. A new local search algorithm is also developed. The algorithm at first generates and merges a set of partial solutions in order to obtain a feasible solution for the multiprocessor scheduling problem. Then a set of interchange procedures are utilized in order to improve the solution. The effectiveness of this approach is evaluated by solving a large number of benchmark instances.     

An Enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes

This paper addresses a sequence- and machine-dependent batch scheduling problem on a set of unrelated-parallel machines where the objective is to minimize a linear combination of total weighted completion time and total weighted tardiness. In particular, batch scheduling disregards the group technology assumptions by allowing for the possibility of splitting pre-determined groups of jobs into batches with respect to desired lower bounds on batch sizes. With regard to bounds on batch sizes, the MILP model is developed as two integrated batching and scheduling phases to present the problem. A benchmark of small-size instances on group scheduling shows the superior performance of batch scheduling up to 37% reduction in the objective function value. An efficient meta-heuristic algorithm based on tabu search with multi-level diversification and multi-tabu structure is developed at three levels, which moves back and forth between batching and scheduling phases. To eliminate searching in ineffective neighborhoods and thus enhance computational efficiency of search algorithms, several lemmas are proposed and proven. The results of applying lemmas reflect up to 40% reduction in computational times. Comparing the optimal solutions found by CPLEX and tabu search shows that the tabu search algorithm could find solutions, at least as good as CPLEX but in incredibly shorter computational time. In order to trigger the search algorithm, two different initial solution finding mechanisms have been developed and implemented. Also, due to lack of a qualified benchmark for unrelated-parallel machines, a comprehensive data generation mechanism has been developed in a way that it fairly reflects the real world situations encountered in practice. The machine availability times and job release times are considered to be dynamic and the run time of each job differs on different machines based upon the capability of the machines.     

An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.     

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 new model for the preemptive earliness–tardiness scheduling problem

This paper addresses a new model for the one-machine earliness–tardiness scheduling problem where jobs can be interrupted. Some dominance rules and a lower bound are derived. A new timing algorithm is also presented and a local search algorithm based on this timing algorithm permits the computation of good feasible solutions. We experimentally compare our timing algorithm with a previously published timing algorithm. The tests show that the execution time of the new timing algorithm is significantly faster, especially for large instances. The values of the solutions are compared to the lower bound.     

Bi-objective parallel machines scheduling with sequence-dependent setup times using hybrid metaheuristics and weighted min–max technique

In the literature of multi-objective problem, there are different algorithms to solve different optimization problems. This paper presents a min–max multi-objective procedure for a dual-objective, namely make span, and sum of the earliness and tardiness of jobs in due window machine scheduling problems, simultaneously. In formulation of min–max method when this method is combined with the weighting method, the decision maker can have the flexibility of mixed use of weights and distance parameter to yield a set of Pareto-efficient solutions. This research extends the new hybrid metaheuristic (HMH) to solve parallel machines scheduling problems with sequence-dependent setup time that comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) as an evolutionary algorithm employs certain probability to avoid becoming trapped in a local optimum, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. In addition, two VNS-based HMHs, which are a combination of two methods, SA/VNS and ACO/VNS, are also proposed to solve the addressed scheduling problems. A design of experiments approach is employed to calibrate the parameters. The non-dominated sets obtained from HMH and two best existing bi-criteria scheduling algorithms are compared in terms of various indices and the computational results show that the proposed algorithm is capable of producing a number of high-quality Pareto optimal scheduling plans. Aside, an extensive computational experience is carried out to analyze the different parameters of the algorithm.     

A memetic algorithm for minimizing total weighted tardiness on parallel batch machines with incompatible job families and dynamic job arrival

This paper addresses a scheduling problem motivated by scheduling of diffusion operations in the wafer fabrication facility. In the target problem, jobs arrive at the batch machines at different time instants, and only jobs belonging to the same family can be processed together. Parallel batch machine scheduling typically consists of three types of decisions—batch forming, machine assignment, and batch sequencing. We propose a memetic algorithm with a new genome encoding scheme to search for the optimal or near-optimal batch formation and batch sequence simultaneously. Machine assignment is resolved in the proposed decoding scheme. Crossover and mutation operators suitable for the proposed encoding scheme are also devised. Through the experiment with 4860 problem instances of various characteristics including the number of machines, the number of jobs, and so on, the proposed algorithm demonstrates its advantages over a recently proposed benchmark algorithm in terms of both solution quality and computational efficiency.     

Scheduling two-stage hybrid flow shops with parallel batch, release time, and machine eligibility constraints

This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10?min.     

Unrelated parallel machine scheduling with setup times using simulated annealing

This paper presents a scheduling problem for unrelated parallel machines with sequence-dependent setup times, using simulated annealing (SA). The problem accounts for allotting work parts of L jobs into M parallel unrelated machines, where a job refers to a lot composed of N items. Some jobs may have different items while every item within each job has an identical processing time with a common due date. Each machine has its own processing times according to the characteristics of the machine as well as job types. Setup times are machine independent but job sequence dependent. SA, a meta-heuristic, is employed in this study to determine a scheduling policy so as to minimize total tardiness. The suggested SA method utilizes six job or item rearranging techniques to generate neighborhood solutions. The experimental analysis shows that the proposed SA method significantly outperforms a neighborhood search method in terms of total tardiness.     

Flowshop scheduling problems with transportation or deterioration between the batching and single machines

In this paper, we consider two new types of the two-machine flowshop scheduling problems where a batching machine is followed by a single machine. The first type is that normal jobs with transportation between machines are scheduled on the batching and single machines. The second type is that normal jobs are processed on the batching machine while deteriorating jobs are scheduled on the single machine. For the first type, we formulate the problem to minimize the makespan as a mixed integer programming model and prove that it is strongly NP-hard. Furthermore, a heuristic algorithm along with a worst case error bound is derived and the computational experiments are also carried out to verify the effectiveness of the proposed heuristic algorithm. For the second type, the two objectives are considered. For the problem with minimizing the makespan, we find an optimal polynomial algorithm. For the problem with minimizing the sum of completion time, we show that it is strongly NP-hard and propose an optimal polynomial algorithm for its special case.