The strategies and parameters of tabu search for job-shop scheduling

This paper presents a tabu search approach for the job-shop scheduling problem. Although the problem is NP-hard, satisfactory solutions have been obtained recently by tabu search. However, tabu search has a problem-specific and parametric structure. Therefore, in the paper, we focussed on the tabu search strategies and parameters such as initial solution, neighborhood structure, tabu list, aspiration criterion, elite solutions list, intensification, diversification and the number of iteration. In order to compare some neighborhood strategies and tabu list length methods, a computational study is done on the benchmark problems.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

基于两次禁忌搜索的军事物资装运方案研究

针对当前军事物资装载与运输问题,映射建立数学模型,运用两次禁忌搜索算法自动输出较优的可行运输方案.第一次禁忌搜索用于确定较优的初始解,针对初始解,运用第二次禁忌搜索,保证在一定时间限制条件下,对运输问题进行优化求解.计算结果表明,该模型通过两次禁忌搜索算法可以得出在满足时间限制条件下的成本较小的装运方案,使用该模型可以有效提高载具的利用率,避免运力的浪费.     

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.     

针对移动云计算任务迁移的快速高效调度算法

计算量较大的应用程序由于需要大量的能耗,因此在电池容量有限的移动设备上运行时十分受限。云计算迁移技术是保证此类应用程序在资源有限的设备上运行的主流方法。针对无线网络中应用程序任务图的调度和迁移问题,提出了一种快速高效的启发式算法。该算法将能够迁移到云端的任务都安排在云端完成这种策略作为初始解,通过逐次计算可迁移任务在移动端运行的能耗节省量,依次将节省量最大的任务迁移到移动端,并依据任务间的通讯时间及时更新各个任务的能耗节省量。为了寻找全局最优解,构造了适用于此问题的禁忌搜索算法,给出了相应的编码方法、禁忌表、邻域解以及算法终止准则。构造的禁忌搜索算法以提出的启发式解为初始解进行全局搜索,并实现对启发解的进一步优化。通过 实验 将所提方法与无迁移、随机迁移、饱和迁移3类算法进行对比,结果表明提出的启发式算法能够快速有效地给出能耗更小的解。例如,在宽度为10的任务图上,当深度为8时,无迁移、随机迁移与饱和迁移的能耗分别为5461、3357和2271能量单位,而给出的启发解对应的能耗仅为2111。在此基础上禁忌搜索算法又将其能耗降低到1942, 这进一步说明了提出的启发式算法能够产生高质量的近似解。     

Problem difficulty for tabu search in job-shop scheduling

Tabu search algorithms are among the most effective approaches for solving the job-shop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from similar models developed for SAT and other NP-complete problems. We show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical, random JSPs. Additionally, this model accounts for the cost of locating sub-optimal solutions, and provides an explanation for differences in the relative difficulty of square versus rectangular JSPs. We also identify two important limitations of our model. First, model accuracy is inversely correlated with problem difficulty, and is exceptionally poor for rare, very high-cost problem instances. Second, the model is significantly less accurate for structured, non-random JSPs. Our results are also likely to be useful in future research on difficulty models of local search in SAT, as local search cost in both SAT and the JSP is largely dictated by the same search space features. Similarly, our research represents the first attempt to quantitatively model the cost of tabu search for any NP-complete problem, and may possibly be leveraged in an effort to understand tabu search in problems other than job-shop scheduling.     

Steelmaking and refining coordinated scheduling problem with waiting time and transportation consideration

This article explores the coordinated scheduling problem between production and transportation in a steelmaking shop. Two models arising from steelmaking and refining operations are considered. The first model assumes that there is a converter at the steelmaking operation and a refining furnace at the refining operation. A transporter with capacity one is available to carry out jobs from converter to a refining furnace. The objective is to minimize the maximum completion time. For this model, we provide an algorithm with worst case ratio of two and show the computational results. The second model considers more practical situation in which jobs are processed in identical parallel converters first, and then the jobs coming from same converter are transported by a dedicated trolley with capacity one to the next operations. Two objectives are considered in the second model. One is to minimize the sum of maximum completion time, idle time penalties and waiting time penalties satisfying waiting time constraints. The other is to minimize the sum of maximum completion time, idle times penalties and hot consumption penalties related to waiting times while satisfying waiting time constraints. For the model, we develop a tabu search algorithm, provide the computational results and then give the worst case analysis.     

An efficient hybrid evolutionary algorithm for scheduling with setup times and weighted tardiness minimization

We confront the job shop scheduling problem with sequence-dependent setup times and weighted tardiness minimization. To solve this problem, we propose a hybrid metaheuristic that combines the intensification capability of tabu search with the diversification capability of a genetic algorithm which plays the role of long term memory for tabu search in the combined approach. We define and analyze a new neighborhood structure for this problem which is embedded in the tabu search algorithm. The efficiency of the proposed algorithm relies on some elements such as neighbors filtering and a proper balance between intensification and diversification of the search. We report results from an experimental study across conventional benchmarks, where we analyze our approach and demonstrate that it compares favorably to the state-of-the-art methods.     

Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery

The vehicle routing problem with simultaneous pick-up and delivery is the problem of optimally integrating goods distribution and waste collection, when no precedence constraints are imposed on the order in which the operations must be performed. The purpose of this paper is to present heuristic algorithms to solve this problem approximately in a small amount of computing time. We present and compare constructive algorithms, local search algorithms and tabu search algorithms, reporting on our computational experience with all of them. In particular we address the issue of applying the tabu search paradigm to algorithms based on complex and variable neighborhoods. For this purpose we combine arc-exchange-based and node-exchange-based neighborhoods, employing different and interacting tabu lists. All the algorithms presented in this paper are applicable to problems in which each customer may have either a pick-up demand or a delivery demand as well as to problems in which each customer may require both kinds of operation.     

微电子生产过程调度问题基于指标快速预报的分解算法

微电子生产过程调度问题具有规模大和约束复杂等特点,如菜单、Setup时间和组批约束等,其优化调度具有一定难度.针对以最小化平均流经时间为调度目标的较大规模微电子生产过程调度问题,提出一种基于指标快速预报的分解方法(DM-IFP).首先,通过松弛不可中断约束,设计一种代理方法,即基于机器负载的操作完工时间快速预测方法(CTP-ML);其次,设计基于CTP-ML的问题分解方法,将原问题迭代分解为多个连续交迭的子问题;然后,提出一种基于双信息素的蚁群算法(ACO-D)用于求解分解后的子问题,其全局调度目标采用CTP-ML获取,有效保证了全局优化性能;最后,针对一些不同规模的仿真数据,将所提出方法与一些代表性的算法进行详尽的数值对比,计算结果表明所提出方法在所获解的质量和收敛性上均有改善.     

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.     

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.     

大型钢铁企业原料场存储分配问题的研究

为钢铁企业原料存储分配问题建立了以降低成本并保持原料成分稳定为目标函数的非线性数学模型,并提出了改进禁忌搜索算法进行求解.该算法利用基于随机kick移动的迭代局域搜索策略作为跳出局部最优的策略,其中迭代局域搜索策略的邻域以环交换移动产生.通过150组随机数据的实验证明,引入迭代局域搜索策略的禁忌搜索算法具有较强的全局搜索能力,是解决该类实际工业问题的快速有效的近优算法.     

Multiagent scheduling method with earliness and tardiness objectives in flexible job shops.

Flexible job-shop scheduling problems are an important extension of the classical job-shop scheduling problems and present additional complexity. Such problems are mainly due to the existence of a considerable amount of overlapping capacities with modern machines. Classical scheduling methods are generally incapable of addressing such capacity overlapping. We propose a multiagent scheduling method with job earliness and tardiness objectives in a flexible job-shop environment. The earliness and tardiness objectives are consistent with the just-in-time production philosophy which has attracted significant attention in both industry and academic community. A new job-routing and sequencing mechanism is proposed. In this mechanism, two kinds of jobs are defined to distinguish jobs with one operation left from jobs with more than one operation left. Different criteria are proposed to route these two kinds of jobs. Job sequencing enables to hold a job that may be completed too early. Two heuristic algorithms for job sequencing are developed to deal with these two kinds of jobs. The computational experiments show that the proposed multiagent scheduling method significantly outperforms the existing scheduling methods in the literature. In addition, the proposed method is quite fast. In fact, the simulation time to find a complete schedule with over 2000 jobs on ten machines is less than 1.5 min.     

改进人工蜂群求解多目标柔性作业车间调度问题

针对多个目标约束的柔性作业车间问题,本文采用基于Pareto解集的改进离散人工蜂群算法来求解.由于经典人工蜂群算法的选择概率不适用于多目标问题,本文对选择概率进行了重定义,将排序引入选择概率中;同时采用基于变异操作的邻域搜索方法进行局部搜索,并使用混合列交叉算子提高种群的多样性;采用Harmonic平均距离对Pareto解集进行裁剪,完成对Pareto解集的更新.最后通过实例测试及仿真实验,验证了本文算法在求解多目标柔性作业车间调度时的有效性.     

求解柔性作业车间调度问题的鸟群算法

柔性作业车间调度问题是生产调度领域中非常重要的一类带约束优化问题。根据其求解特性,提出一种基于改进的鸟群算法求解以最小化最大完工时间为目标的柔性作业车间调度问题的方法。该方法采用随机黑洞策略改进鸟群的觅食方式,自适应的动态调整策略改善鸟群的迁移步长,从而提高种群的多样性并加速算法的收敛速度;通过对关键路径上工序的领域搜索加强算法的局部搜索能力。最后利用实际制造企业的生产加工数据以及标准测试实例进行仿真实验,实验结果表明,该算法在问题的求解精度和收敛速度上具有一定的优势,是一种有效的求解柔性作业车间调度问题的新方法。     

A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints

The capacitated vehicle routing problem with three-dimensional loading constraints combines capacitated vehicle routing and three-dimensional loading with additional packing constraints concerning, for example, unloading operations. An efficient hybrid algorithm including a tabu search algorithm for routing and a tree search algorithm for loading is introduced. Computational results are presented for all publicly available test instances. Most of the best solutions previously reported in literature have been improved while the computational effort is drastically reduced compared to other methods.     

Solving job shop scheduling with setup times through constraint-based iterative sampling: an experimental analysis

This paper presents a heuristic algorithm for solving a job-shop scheduling problem with sequence dependent setup times and min/max separation constraints among the activities (SDST-JSSP/max). The algorithm relies on a core constraint-based search procedure, which generates consistent orderings of activities that require the same resource by incrementally imposing precedence constraints on a temporally feasible solution. Key to the effectiveness of the search procedure is a conflict sampling method biased toward selection of most critical conflicts and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This constraint-based search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically both on a set of previously studied job-shop scheduling benchmark problems with sequence dependent setup times and by introducing a new benchmark with setups and generalized precedence constraints.     

A hybrid simulated annealing algorithm for location and routing scheduling problems with cross-docking in the supply chain

The location and routing scheduling problems with cross-docking can be regarded as new research directions for distribution networks in the supply chain. The aims of these problems are to concurrently design a cross-docking center location and a vehicle routing scheduling model, known as NP-hard problems. This paper presents a two-stage mixed-integer programming (MIP) model for the location of cross-docking centers and vehicle routing scheduling problems with cross-docking due to potential applications in the distribution networks. Then, a new algorithm based on a two-stage hybrid simulated annealing (HSA) with a tabu list taken from tabu search (TS) is proposed to solve the presented model. This proposed HSA not only prevents revisiting the solution but also maintains the stochastic nature. Finally, small and large-scale test problems are randomly generated and solved by the HSA algorithm. The computational results for different problems show that the proposed HSA performs well and converges fast to reasonable solutions.     

Flexible job-shop scheduling with parallel variable neighborhood search algorithm

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. FJSP is NP-hard and mainly presents two difficulties. The first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on the machines. This paper proposes a parallel variable neighborhood search (PVNS) algorithm that solves the FJSP to minimize makespan time. Parallelization in this algorithm is based on the application of multiple independent searches increasing the exploration in the search space. The proposed PVNS uses various neighborhood structures which carry the responsibility of making changes in assignment and sequencing of operations for generating neighboring solutions. The results obtained from the computational study have shown that the proposed algorithm is a viable and effective approach for the FJSP.