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.     

Minimizing Total Weighted Tardiness in a Generalized Job Shop

We consider a generalization of the classical job shop scheduling problem with release times, positive end–start time lags, and a general precedence graph. As objective we consider the total weighted tardiness. We use a tabu search algorithm to search for the order in which the operations are processed on each machine. Given a sequence of operations on each machine, we determine optimal starting times by solving a maximum cost flow problem. This solution is used to determine the neighborhood for our tabu search algorithm. All sequences in our neighborhood are obtained by swapping certain pairs of adjacent operations. We show that only swaps that possess a certain property can improve the current solution; if no such swap is available in the neighborhood, then the current solution is globally optimal. In the computational results we compare our method with other procedures proposed in literature. Our tabu search algorithm seems to be effective both with respect to time and solution quality. The research was carried out at the Technische Universiteit Eindhoven and the Universiteit Utrecht with support of Baan and the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).     

A tabu search algorithm with a new neighborhood structure for the job shop scheduling problem

Tabu search (TS) algorithms are among the most effective approaches for solving the job shop scheduling problem (JSP) which is one of the most difficult NP-complete problems. However, neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the tabu search for the JSP. In this paper, a new enhanced neighborhood structure is proposed and applied to solving the job shop scheduling problem by TS approach. Using this new neighborhood structure combined with the appropriate move evaluation strategy and parameters, we tested the TS approach on a set of standard benchmark instances and found a large number of better upper bounds among the unsolved instances. The computational results show that for the rectangular problem our approach dominates all others in terms of both solution quality and performance.     

铁路行包基地及配送点选址问题禁忌搜索算法

分析了铁路行包运输物流化发展背景及行包运输物流配送的特点，给出了铁路行包基地及配送点选址的数学模型，应用改进的扫描法构造问题尽可能好的初始解，并通过巧妙地设计罚函数、合理构造邻域及随机选取禁忌长度的一种禁忌搜索算法对初始解优化．计算结果表明，扫描法和禁忌搜索算法结合的两阶段法，不仅可以得到良好的计算结果，而且具有搜索空间小、求解速度快的优点，该方法是有效、可行的．     

A comparison of five heuristics for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problem consists of determining least-cost schedules for vehicles assigned to several depots such that each task is accomplished exactly once by a vehicle. In this paper, we propose to compare the performance of five different heuristics for this well-known problem, namely, a truncated branch-and-cut method, a Lagrangian heuristic, a truncated column generation method, a large neighborhood search heuristic using truncated column generation for neighborhood evaluation, and a tabu search heuristic. The first three methods are adaptations of existing methods, while the last two are new in the context of this problem. Computational results on randomly generated instances show that the column generation heuristic performs the best when enough computational time is available and stability is required, while the large neighborhood search method is the best alternative when looking for good quality solutions in relatively fast computational times.     

约束满足混合算法求解提前/拖期Job Shop调度问题

针对提前/拖期Job Shop调度问题,建立其约束满足优化问题模型,提出了一种约束满足与禁忌搜索结合的混合算法。该算法基于约束满足思想,通过约束传播技术和启发式修复算法,得到可行调度作为禁忌搜索算法的初始解;再进行关键路径上的邻域变换,优化当前解;并采用一种全局邻域交换策略,扩大搜索空间,改善优化结果。数据实验表明了该混合算法的可行性和有效性。     

混合流水车间调度的变邻域禁忌搜索算法

针对混合流水车间系统的最小化Makespan调度问题,提出一种基于关键路径理论的变邻域禁忌搜索算法,讨论其关键技术。在该算法中,提出基于关键路径的毗邻域概念,防止搜索算法陷入局部最优解,采用变邻域搜索策略,在无法改进解时,实现对移动毗邻域的搜索。仿真结果表明,该算法获得的调度结果优于简化禁忌搜索和启发式算法。     

An artificial immune system heuristic for two-stage multi-machine assembly scheduling problem to minimize total completion time

We address the two-stage multi-machine assembly scheduling problem. The first stage consists of m independently working machines where each machine produces its own component. The second stage consists of two independent and identical assembly machines. The objective is to come up with a schedule that minimizes total or mean completion time for all jobs. The problem has been addressed in the scheduling literature and several heuristics have been proposed. In this paper, we propose a new heuristic called artificial immune system (AIS). We conduct experimental analysis for comparing the newly proposed heuristic AIS with the best known heuristic in the literature. Experimental results show that our proposed heuristic AIS performs better than the best known existing heuristic. More specifically, our new heuristic AIS reduces the error of the best known heuristic by 60% while the computational times of both AIS and the best known heuristic are almost the same.     

An efficient incremental evaluation function for optimizing truck scheduling in a resource-constrained crossdock using metaheuristics

This paper addresses truck scheduling optimization in a resource-constrained crossdock. The truck scheduling problem decides on the succession of incoming and outgoing trucks at the dock doors of a crossdocking terminal such that the total crossdocking operation time is minimized. The paper tackles the optimization from the computational perspective by developing an incremental evaluation of the objective function in the body of single-solution based metaheuristics. It consists in evaluating only the transformation applied to the current solution rather than the complete evaluation of the neighbor solution. The proposed incremental neighborhood evaluation is integrated into two metaheuristics including tabu search (TS) and variable neighborhood search (VNS). In terms of solution quality vs. runtime, experimental results show that the incremental mechanism helps the two algorithms with dedicating their runtime to solution optimization rather than spending it on fitness evaluation when compared with a deterministic local search (LS) algorithm that exploits a simple complete evaluation of the objective function. This is in particular evident for the TS algorithm which obtains comparable results to LS while achieving on average 67.6% reduction in runtime for huge instances of scheduling 2048 trucks in a 256-door crossdock. Our findings on the efficiency of the proposed incremental evaluation are reinforced when the two metaheuristics are re-assessed with a complete evaluation of the objective function.     

Sequence-dependent group scheduling problem on unrelated-parallel machines

In this research we address a sequence-dependent group scheduling problem on a set of unrelated-parallel machines where the run time of each job differs on different machines. To benefit both producer and customers we attempt to minimize a linear combination of total weighted completion time and total weighted tardiness. Since the problem is shown to be NP-hard, meta-heuristic algorithms based on tabu search are developed to find the optimal/near optimal solution. For some small size yet complex problems, the results from these algorithms are compared to the optimal solutions found by CPLEX. The result obtained in all of these problems is that the tabu search algorithms could find solutions at least as good as CPLEX but in drastically shorter computational time, thus signifying the high degree of efficiency and efficacy attained by the former.     

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.     

具有可调时间窗的动态车辆调度问题研究

提出一种新的时间窗可调整的动态车辆调度模型,设计求解该问题的算法。算法能够有效地处理预约需求和实时需求,给出时间窗的调整策略、初始路径的禁忌搜索改进策略以及实时需求的插入算法。实验计算结果表明,该算法与时间窗硬约束算法相比能够大量减少被拒绝服务的顾客数量,高效地处理实时产生的动态需求。提出的禁忌搜索算法能够显著改进初始解的质量,有效减少行驶费用,降低运输成本。     

SOLVING THE OPEN SHOP SCHEDULING PROBLEM VIA A HYBRID GENETIC-VARIABLE NEIGHBORHOOD SEARCH ALGORITHM

In this article, a hybrid metaheuristic method for solving the open shop scheduling problem (OSSP) is proposed. The optimization criterion is the minimization of makespan and the solution method consists of four components: a randomized initial population generation, a heuristic solution included in the initial population acquired by a Nawaz-Enscore-Ham (NEH)-based heuristic for the flow shop scheduling problem, and two interconnected metaheuristic algorithms: a variable neighborhood search and a genetic algorithm. To our knowledge, this is the first hybrid application of genetic algorithm (GA) and variable neighborhood search (VNS) for the open shop scheduling problem. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches a high quality solution in short computational times. Moreover, 12 new hard, large-scale open shop benchmark instances are proposed that simulate realistic industrial cases.     

Effective constructive heuristics and meta-heuristics for the distributed assembly permutation flowshop scheduling problem

This paper addresses a novel distributed assembly permutation flowshop scheduling problem that has important applications in modern supply chains and manufacturing systems. The problem considers a number of identical factories, each one consisting of a flowshop for part-processing plus an assembly line for product-processing. The objective is to minimize the makespan. To suit the needs of different CPU time and solution quality, we present a mixed integer linear model, three constructive heuristics, two variable neighborhood search methods, and an iterated greedy algorithm. Important problem-specific knowledge is obtained to enhance the effectiveness of the algorithms. Accelerations for evaluating solutions are proposed to save computational efforts. The parameters and operators of the algorithms are calibrated and analyzed using a design of experiments. To prove the algorithms, we present a total of 16 adaptations of other well-known and recent heuristics, variable neighborhood search algorithms, and meta-heuristics for the problem and carry out a comprehensive set of computational and statistical experiments with a total of 810 instances. The results show that the proposed algorithms are very effective and efficient to solve the problem under consideration as they outperform the existing methods by a significant margin.     

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.     

Local search heuristics for two-stage flow shop problems with secondary criterion

This paper develops and compares different local search heuristics for the two-stage flow shop problem with makespan minimization as the primary criterion and the minimization of either the total flow time, total weighted flow time, or total weighted tardiness as the secondary criterion. We investigate several variants of simulated annealing, threshold accepting, tabu search, and multi-level search algorithms. The influence of the parameters of these heuristics and the starting solution are empirically analyzed. The proposed heuristic algorithms are empirically evaluated and found to be relatively more effective in finding better quality solutions than the existing algorithms.Scope and purposeTraditional research to solve multi-stage scheduling problems has focused on single criterion. However, in industrial scheduling practices, managers develop schedules based on multi-criteria. Scheduling problems involving multiple criteria require significantly more effort in finding acceptable solutions and hence have not received much attention in the literature. This paper considers one such multiple criteria scheduling problem, namely, the two-machine flow shop problem where the primary criterion is the minimization of makespan and the secondary criterion is one of the three most popular performance measures, namely, the total flow time, total weighted flow time, or total weighted tardiness. Based on the principles of local search, development of heuristic algorithms, that can be adapted for several multi-criteria scheduling problems, is discussed. Using the example of the two-machine flow shop problem with secondary criterion, computational experiments are used to evaluate the utility of the proposed algorithms for solving scheduling problems with a secondary criterion.     

A GES/TS algorithm for the job shop scheduling

The job shop scheduling problem is a difficult combinatorial optimization problem. This paper presents a hybrid algorithm which combines global equilibrium search, path relinking and tabu search to solve the job shop scheduling problem. The proposed algorithm used biased random sampling to have a better covering of the solution space. In addition, a new version of N6 neighborhood is applied in a tabu search framework. In order to evaluate the algorithm, comprehensive tests are applied to it using various standard benchmark sets. Computational results confirm the effectiveness of the algorithm and its high speed. Besides, 19 new upper bounds among the unsolved problems are found.     

Metaheuristics for the waste collection vehicle routing problem with time windows,driver rest period and multiple disposal facilities

In this problem there is a set of waste disposal facilities, a set of customers at which waste is collected and an unlimited number of homogeneous vehicles based at a single depot. Empty vehicles leave the depot and collect waste from customers, emptying themselves at the waste disposal facilities as and when necessary. Vehicles return to the depot empty. We take into consideration time windows associated with customers, disposal facilities and the depot. We also have a driver rest period. The problem is solved heuristically. A neighbour set is defined for each customer as the set of customers that are close, but with compatible time windows. A procedure that attempts to fully utilise a vehicle is used to obtain an initial solution, with this initial solution being improved using an interchange procedure. We present two metaheuristic algorithms using tabu search and variable neighbourhood search that are based around the neighbour sets. We also present a metaheuristic based on variable neighbourhood tabu search, where the variable neighbourhood is searched via tabu search. Computational results are presented for publicly available waste collection problems involving up to 2092 customers and 19 waste disposal facilities, which indicate that our algorithms produce better quality solutions than previous work presented in the literature.     

Two-phase neighborhood search algorithm for two-agent hybrid flow shop scheduling problem

In this paper hybrid flow shop scheduling problem with two agents is studied and its feasibility model is considered. A two-phase neighborhood search (TNS) algorithm is proposed to minimize objectives of two agents simultaneously under the given upper bounds. TNS is constructed through the combination of multiple variable neighborhood mechanisms and a new perturbation strategy for new current solution. A new replacement principle is also applied to decide if the current solution can be updated. TNS is tested on a number of instances and compared with the existing methods. The computational results show the promising advantage of TNS on the considered problem.     

A Tabu search approach for designing a non-hierarchical video-on-demand network architecture

In this paper, we present a tabu search to design a non-hierarchical and decentralized video-on-demand (VOD) network architecture. To optimize the VOD network resource, we consider optimization of both video server locations and storage allocation subject to the tradeoffs among installation cost for video servers, program storage cost, and transmission (or communication) cost. In applying a tabu search technique to the problem, neighborhood structure and search strategy are elaborated to improve solution quality and to reduce computation time. We report the results of the computational experiments to demonstrate the performance of the proposed tabu search. A comparative study shows that our algorithm is promising.