无等待流水车间调度问题的优化

文中研究了以生产周期为目标的无等待流水车间调度问题.首先,结合问题特征,提出了一种复杂度为O(n)的快速生产周期算法.其次,研究了两种插入邻域结构:基本插入邻域和多重插入邻域,并提出了快速基本插入邻域算法和最大多重插入移动算法.在此基础上,将离散粒子群算法与上述两种邻域搜索算法相结合,得到了离散粒子群优化调度算法.第三,根据问题生产周期的不规则性,给出了一种通过延长工序加工时间进一步改进调度方案的方法.最后,仿真实验表明了所得算法的可行性和有效性.     

Application of a modified GA,ACO and a random search procedure to solve the production scheduling of a case study bakery

Based on the constraints and frame conditions given by the real processes the production in bakeries can be modelled as a no-wait permutation flow-shop, following the definitions in scheduling theory. A modified genetic algorithm, ant colony optimization and a random search procedure were used to analyse and optimize the production planning of a bakery production line that processes 40 products on 26 production stages. This setup leads to 8.2 × 10⁴⁷ different possible schedules in a permutation flow-shop model and is thus not solvable in reasonable time with exact methods. Two objective functions of economical interest were analysed, the makespan and the total idle time of machines. In combination with the created model, the applied algorithms proved capable to provide optimized results for the scheduling operation within a predefined runtime of 15 min, reducing the makespan by up to 8.6% and the total idle time of machines by up to 23%.     

Efficient non-population-based algorithms for the permutation flowshop scheduling problem with makespan minimisation subject to a maximum tardiness

This paper focuses on the problem of scheduling jobs in a permutation flowshop with the objective of makespan minimisation subject to a maximum allowed tardiness for the jobs, a problem that combines two desirable manufacturing objectives related to machine utilisation and to customer satisfaction. Although several approximate algorithms have been proposed for this NP-hard problem, none of them can use the excellent speed-up method by Taillard (1990) [22] for makespan minimisation due to the special structure of the problem under consideration. In this paper, several properties of the problem are defined in order to be able to partly apply Taillard׳s acceleration. This mechanism, together with a novel feasible tabu local search method, allows us to further exploit the structure of solutions of the problem, and are incorporated in two proposed algorithms: a bounded-insertion-based constructive heuristic and an advanced non-population-based algorithm. These algorithms are compared with state-of-the-art algorithms under the same computer conditions. The results show that both algorithms improve existing ones and therefore, constitute the new state-of-art approximate solution procedures for the problem.     

A DE-based approach to no-wait flow-shop scheduling

This paper proposes an effective hybrid differential evolution (HDE) for the no-wait flow-shop scheduling problem (FSSP) with the makespan criterion, which is a typical NP-hard combinational optimization problem. Firstly, a largest-order-value (LOV) rule is presented to transform individuals in DE from real vectors to job permutations so that the DE can be applied for solving FSSPs. Secondly, the DE-based parallel evolution mechanism and framework is applied to perform effective exploration, and a simple but efficient local search developed according to the landscape of FSSP is applied to emphasize problem-dependent local exploitation. Thirdly, a speed-up evaluation method and a fast Insert-based neighborhood examining method are developed based on the properties of the no-wait FSSPs. Due to the hybridization of DE-based evolutionary search and problem-dependent local search as well as the utilization of the speed-up evaluation and fast neighborhood examining, the no-wait FSSPs can be solved efficiently and effectively. Simulations and comparisons based on well-known benchmarks demonstrate the efficiency, effectiveness, and robustness of the proposed HDE.     

A revised discrete particle swarm optimization algorithm for permutation flow-shop scheduling problem

This research proposes a revised discrete particle swarm optimization (RDPSO) to solve the permutation flow-shop scheduling problem with the objective of minimizing makespan (PFSP-makespan). The candidate problem is one of the most studied NP-complete scheduling problems. RDPSO proposes new particle swarm learning strategies to thoroughly study how to properly apply the global best solution and the personal best solution to guide the search of RDPSO. A new filtered local search is developed to filter the solution regions that have been reviewed and guide the search to new solution regions in order to keep the search from premature convergence. Computational experiments on Taillard’s benchmark problem sets demonstrate that RDPSO significantly outperforms all the existing PSO algorithms.     

Iterated greedy algorithms for the blocking flowshop scheduling problem with makespan criterion

Recently, iterated greedy algorithms have been successfully applied to solve a variety of combinatorial optimization problems. This paper presents iterated greedy algorithms for solving the blocking flowshop scheduling problem (BFSP) with the makespan criterion. Main contributions of this paper can be summed up as follows. We propose a constructive heuristic to generate an initial solution. The constructive heuristic generates better results than those currently in the literature. We employ and adopt well-known speed-up methods from the literature for both insertion and swap neighborhood structures. In addition, an iteration jumping probability is proposed to change the neighborhood structure from insertion neighborhood to swap neighborhood. Generally speaking, the insertion neighborhood is much more effective than the swap neighborhood for the permutation flowshop scheduling problems. Instead of considering the use of these neighborhood structures in a framework of the variable neighborhood search algorithm, two powerful local search algorithms are designed in such a way that the search process is guided by an iteration jumping probability determining which neighborhood structure will be employed. By doing so, it is shown that some additional enhancements can be achieved by employing the swap neighborhood structure with a speed-up method without jeopardizing the effectiveness of the insertion neighborhood. We also show that the performance of the iterated greedy algorithm significantly depends on the speed-up method employed. The parameters of the proposed iterated greedy algorithms are tuned through a design of experiments on randomly generated benchmark instances. Extensive computational results on Taillard’s well-known benchmark suite show that the iterated greedy algorithms with speed-up methods are equivalent or superior to the best performing algorithms from the literature. Ultimately, 85 out of 120 problem instances are further improved with substantial margins.     

A tabu search heuristic for a sequence-dependent and time-dependent scheduling problem on a single machine

This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.     

A hybrid discrete differential evolution algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion

This paper presents a hybrid discrete differential evolution (HDDE) algorithm for the no-idle permutation flow shop scheduling problem with makespan criterion, which is not so well studied. The no-idle condition requires that each machine must process jobs without any interruption from the start of processing the first job to the completion of processing the last job. A novel speed-up method based on network representation is proposed to evaluate the whole insert neighborhood of a job permutation and employed in HDDE, and moreover, an insert neighborhood local search is modified effectively in HDDE to balance global exploration and local exploitation. Experimental results and a thorough statistical analysis show that HDDE is superior to the existing state-of-the-art algorithms by a significant margin.     

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．     

An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems

This paper proposes an effective hybrid tabu search algorithm (HTSA) to solve the flexible job-shop scheduling problem. Three minimization objectives – the maximum completion time (makespan), the total workload of machines and the workload of the critical machine are considered simultaneously. In this study, a tabu search (TS) algorithm with an effective neighborhood structure combining two adaptive rules is developed, which constructs improved local search in the machine assignment module. Then, a well-designed left-shift decoding function is defined to transform a solution to an active schedule. In addition, a variable neighborhood search (VNS) algorithm integrating three insert and swap neighborhood structures based on public critical block theory is presented to perform local search in the operation scheduling component. The proposed HTSA is tested on sets of the well-known benchmark instances. The statistical analysis of performance comparisons shows that the proposed HTSA is superior to four existing algorithms including the AL + CGA algorithm by Kacem, Hammadi, and Borne (2002b), the PSO + SA algorithm by Xia and Wu (2005), the PSO + TS algorithm by Zhang, Shao, Li, and Gao (2009), and the Xing’s algorithm by Xing, Chen, and Yang (2009a) in terms of both solution quality and efficiency.     

一种求解车间作业调度问题的混合邻域结构搜索算法

车间作业调度问题是优化组合中一个著名的难题,问题的目标是在满足约束条件的前提下,使调度的加工周期尽可能小。文章中提出了利用新的混合邻域结构进行搜索来求解车间作业调度问题。对于算法关键的邻域构造问题以及跳坑策略给出了提高算法优度的解决方案。采用43个不同规模和难度的国际标准算例做为本算法的测试实验集,39个算例找到了最优解,其中包括著名的难例FT10。与当前国外学者提出的一种先进算法进行了比较,算法的优度高于被比较的先进算法。     

求解无等待流水调度的基于禁忌搜索的混合算法

本文提出了解决最小完工时间的无等待流水调度问题的基于禁忌搜索的混合算法。算法结合了调度规则和禁忌搜索算法的优点,首先利用调度规则构造较好的初始解,既可以加快禁忌搜索算法的收敛速度,也可以降低整个算法的运算量,使算法有更好的工程实用性;然后使用变邻域结构的禁忌搜索算法改进当前解。在保持可达性的基础上,该算法缩小了邻域规模和减少了计算时间。数值仿真实验表明,该算法是有效的。     

Inverse scheduling: two-machine flow-shop problem

We study an inverse counterpart of the two-machine flow-shop scheduling problem that arises in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find job sequence(s) for which the value of the makespan is minimum, in the inverse scheduling the exact values of processing times are unknown and they should be selected within given boundaries so that pre-specified job sequence(s) become optimal. We derive necessary and sufficient conditions of optimality of a given solution for the general case of the flow-shop problem when the job sequences on the machines can be different. Based on these conditions we prove that the inverse flow-shop problem is NP-hard even in the case of the same job sequence on both machines and produce a linear programming formulation for a special case which can be solved efficiently.     

强化Dynasearch & TS算法求解酸轧生产调度问题

酸轧生产调度的主要任务是在满足酸轧机组生产工艺和能力约束下, 考虑下游机组的流向需求,为保证生产连续性和平滑过渡的要求,从给定候选池中选择适合的板卷构成一个酸轧调度单元. 针对此问题, 本文建立了以最小化过渡费用和调度单元剩余容量惩罚费用为目标的整数规划模型, 提出了一种嵌入强化Dynasearch算法的禁忌搜索混合算法. 该混合算法采用基于最小插入法的两阶段启发式产生初始解, 根据采用邻域结构的不同设计双禁忌表, 为了避免算法陷入局部最优, 在禁忌搜索的每次迭代过程中嵌入Swap邻域和Inner-insert邻域相结合的多交换Dynasearch邻域, 并设计了多项式动态规划算法搜索该邻域. 针对问题的特征, 提出了Block分区结构, 基于此分析了多个可行解性质, 有效降低了搜索空间. 与一般禁忌搜索算法比较, 结果表明所提出的强化Dynsearch TS (Tabu search)算法求解效果明显优于一般TS算法, 平均改进量为3.62%, 算法运行时间大大缩短. 验证了该算法在解决此类问题的有效性.     

Artificial intelligence search methods for multi-machine two-stage scheduling with due date penalty,inventory, and machining costs

This paper evaluates artificial intelligence search methods for multi-machine two-stage scheduling problems with due date penalty, inventory, and machining costs. We compare four search methods: tabu search, simulated annealing, genetic algorithm, and neighborhood search. Computational results show that the tabu search performs best in terms of solution quality. The tabu search also requires much less computational time than the genetic algorithm and simulated annealing. As expected, the neighborhood search needs the smallest computational time, but gives the worst solution quality. To further improve the solution quality and computational time, this paper proposes a two-phase tabu search. The two-phase tabu search sequentially addresses two aspects of sequencing for the same problem, order- and component-based sequencing. The order-based tabu search identifies a sequence for customers’ orders. Starting from the sequence identified for customers’ orders, the component-based tabu search fine-tunes the sequence for components produced at the fabrication stage. The results show that the two-phase tabu search is better in solution quality and computational time than the one-phase tabu search. The difference in solution quality is more pronounced at the early stage of the search.Scope and purposeMost manufacturing firms have some form of separate fabrication and assembly stages. Raw materials are transformed into components at the fabrication stage and the components are then assembled into finished products at the assembly stage. The components and assembly items are typically routed in batch quantities through several machines/work centers in a predetermined order before the finished products are delivered to customers.In this study, we model fabrication and assembly work centers as multi-machine two-stage manufacturing systems where a given machine is used to assemble/produce at least one component/product. The scheduling problem considered in this study involves a scheduling decision that achieves three objectives concurrently: (1) meeting customers’ due dates, (2) minimizing inventory cost, and (3) minimizing machining cost. Each order is an indivisible scheduling element that needs to be delivered to customers on the due date. Each order triggers successive production events from upstream to downstream according to the bill-of-material structure between components and end products.The objective of this paper are three-fold: (1) to present a solution representation for the multi-machine two-stage scheduling problem, (2) to identify the best artificial intelligence search method for this problem based on extensive computational experiments, and (3) to propose a modified tabu search method to further improve the solution quality and computational time.     

A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems

This paper presents a new, carefully designed algorithm for five bi-objective permutation flow shop scheduling problems that arise from the pairwise combinations of the objectives (i) makespan, (ii) the sum of the completion times of the jobs, and (iii) both, the weighted and non-weighted total tardiness of all jobs. The proposed algorithm combines two search methods, two-phase local search and Pareto local search, which are representative of two different, but complementary, paradigms for multi-objective optimization in terms of Pareto-optimality. The design of the hybrid algorithm is based on a careful experimental analysis of crucial algorithmic components of these two search methods. We compared our algorithm to the two best algorithms identified, among a set of 23 candidate algorithms, in a recent review of the bi-objective permutation flow-shop scheduling problem. We have reimplemented carefully these two algorithms in order to assess the quality of our algorithm. The experimental comparison in this paper shows that the proposed algorithm obtains results that often dominate the output of the two best algorithms from the literature. Therefore, our analysis shows without ambiguity that the proposed algorithm is a new state-of-the-art algorithm for the bi-objective permutation flow-shop problems studied in this paper.     

A new encoding scheme-based hybrid algorithm for minimising two-machine flow-shop group scheduling problem

This article investigates the two-machine flow-shop group scheduling problem (GSP) with sequence-dependent setup and removal times, and job transportation times between machines. The objective is to minimise the total completion time. As known, this problem is an NP-hard problem and generalises the typical two-machine GSPs. In this article, a new encoding scheme based on permutation representation is proposed to transform a random job permutation to a feasible permutation for GSPs. The proposed encoding scheme simultaneously determines both the sequence of jobs in each group and the sequence of groups. By reasonably combining particle swarm optimisation (PSO) and genetic algorithm (GA), we develop a fast and easily implemented hybrid algorithm (HA) for solving the considered problems. The effectiveness and efficiency of the proposed HA are demonstrated and compared with those of standard PSO and GA by numerical results of various tested instances with group numbers up to 20. In addition, three different lower bounds are developed to evaluate the solution quality of the HA. Limited numerical results indicate that the proposed HA is a viable and effective approach for the studied two-machine flow-shop group scheduling problem.     

基于多维EDA算法的低碳分布式装配流水车间调度

针对低碳分布式装配置换流水车间调度问题(LC_DAPFSP),建立以同时最小化总能耗和总完工时间为优化目标的数学模型,进而提出一种多维分布估计算法(MEDA)以进行求解.首先,采用随机方法和启发式算法共同生成初始化种群;其次,建立基于矩阵立方体的概率模型,用于合理学习并积累优质解的块结构信息和序关系信息,同时设计有效采...     

Genetic tabu search for the fuzzy flexible job shop problem

This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances.