Routing and scheduling in a flexible job shop by tabu search

A hierarchical algorithm for the flexible job shop scheduling problem is described, based on the tabu search metaheuristic. Hierarchical strategies have been proposed in the literature for complex scheduling problems, and the tabu search metaheuristic, being able to cope with different memory levels, provides a natural background for the development of a hierarchical algorithm. For the case considered, a two level approach has been devised, based on the decomposition in a routing and a job shop scheduling subproblem, which is obtained by assigning each operation of each job to one among the equivalent machines. Both problems are tackled by tabu search. Coordination issues between the two hierarchical levels are considered. Unlike other hierarchical schemes, which are based on a one-way information flow, the one proposed here is based on a two-way information flow. This characteristic, together with the flexibility of local search strategies like tabu search, allows to adapt the same basic algorithm to different objective functions. Preliminary computational experience is reported.     

Cyclic job shop scheduling problems with blocking

A tabu search algorithm for a cyclic job shop problem with blocking is presented. Operations are blocking if they must stay on a machine after finishing when the next machine is occupied by another job. During this stay the machine is blocked for other jobs. For this problem traditional tabu search moves often lead to infeasible solutions. Recovering procedures are developed which construct nearby feasible solutions. Computational results are presented for the approach.     

An Ant Colony Optimization Algorithm for Shop Scheduling Problems

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure derived by Nowicki and Smutnicki for the job shop scheduling problem. Then, we develop an ant colony optimization approach, which uses a strong non-delay guidance for constructing solutions and which employs black-box local search procedures to improve the constructed solutions. We compare this algorithm to an adaptation of the tabu search by Nowicki and Smutnicki to group shop scheduling. Despite its general nature, our algorithm works particularly well when applied to open shop scheduling instances, where it improves the best known solutions for 15 of the 28 tested instances. Moreover, our algorithm is the first competitive ant colony optimization approach for job shop scheduling instances.     

A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem

This paper deals with a general job shop scheduling problem with multiple constraints, coming from printing and boarding industry. The objective is the minimization of two criteria, the makespan and the maximum lateness, and we are interested in finding an approximation of the Pareto frontier. We propose a fast and elitist genetic algorithm based on NSGA-II for solving the problem. The initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm, that minimizes a linear combination of the two criteria. Both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method.     

No-wait Job Shop Scheduling: Tabu Search and Complexity of Subproblems

This paper deals with the no-wait job shop problem with a makespan objective. We present some new theoretical properties on the complexity of subproblems associated with a well-known decomposition approach. Justified by the complexity results, we implement a fast tabu search algorithm for the problem at hand. It is extensively tested on known benchmark instances and compares favorably to the best existing algorithms for the no-wait job shop as well as the no-wait flow shop.     

An integrated tabu search algorithm for the lot streaming problem in job shops

In this paper, we focus on solving the lot streaming problem in a job shop environment, where consistent sublots are considered. The presented three-phase algorithm incorporates the predetermination of sublot sizes, the determination of schedules based on tabu search and the variation of sublot sizes. With regard to tabu search implementation, a constructive multi-level neighbourhood is developed, which effectively connects three isolated neighbourhood functions. Moreover, enhancements of the basic version of tabu search are conducted. Combined with the procedure for varying sublot sizes, the algorithm further exploits the improvement potential. All tested instances show a rapid convergence to their lower bounds. The well-known difficult benchmark problems also achieve substantial makespan reduction. In addition, the performance of specific components is intensively examined in our study.     

Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.     

Tabu search for graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.     

A new neighborhood and tabu search for the Blocking Job Shop

The Blocking Job Shop is a version of the job shop scheduling problem with no intermediate buffers, where a job has to wait on a machine until being processed on the next machine. We study a generalization of this problem which takes into account transfer operations between machines and sequence-dependent setup times. After formulating the problem in a generalized disjunctive graph, we develop a neighborhood for local search. In contrast to the classical job shop, there is no easy mechanism for generating feasible neighbor solutions. We establish two structural properties of the underlying disjunctive graph, the concept of closures and a key result on short cycles, which enable us to construct feasible neighbors by exchanging critical arcs together with some other arcs. Based on this neighborhood, we devise a tabu search algorithm and report on extensive computational experience, showing that our solutions improve most of the benchmark results found in the literature.     

Local search algorithms for the multiprocessor flow shop scheduling problem

The multiprocessor flow shop scheduling problem is a generalization of the ordinary flow shop scheduling problem. The problem consists of both assigning operations to machines and scheduling the operations assigned to the same machine. We review the literature on local search methods for flow shop and job shop scheduling and adapt them to the multiprocessor flow shop scheduling problem. Other local search approaches we consider are variable-depth search and simulated annealing. We show that tabu search and variable-depth search with a neighborhood originated by Nowicki and Smutnicki outperform the other algorithms.     

Job Shop Scheduling with Tooling Constraints: a Tabu Search Approach

Flexible manufacturing systems (FMSs) are automated factories in which many different part types are produced simultaneously. The tool-loading problem now adds further to the delicate task of finding an optimal schedule for such systems. In this paper, a tabu search approach is developed to solve the job shop scheduling problem with tooling constraints.     

A Branch-and-Bound Approach for a Two-machine Flowshop Scheduling Problem

In this paper, we present a branch-and-bound approach for solving a two-machine flow shop scheduling problem, in which the objective is to minimize a weighted combination of job flowtime and schedule makespan. Experimental results show that the algorithm works very well for certain special cases and moderately well for others. In fact, it is able to produce optimal schedules for 500-job problems in which the second machine dominates the first machine. It is also shown that the algorithm developed to provide an upper bound for the branch-and-bound is optimal when processing times for jobs are the same on both machines. The primary reason for developing the branch-and-bound approach is that its results can be used to guide other heuristic techniques, such as simulated annealing, tabu search and genetic algorithms, in their search for optimal solutions for larger problems.     

A fast tabu search algorithm for the permutation flow-shop problem

A fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented. The algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion. Computational experiments (up to 500 jobs and 20 machines) show its excellent numerical properties.     

Constraint-Based Job Shop Scheduling with IILOG SCHEDULER

We introduce constraint-based scheduling and discuss its main principles. An approximation algorithm based on tree search is developed for the job shop scheduling problem using ILOG SCHEDULER. A new way of calculating lower bounds on the makespan of the job shop scheduling problem is presented and we show how such results can be used within a constraint-based approach. An empirical performance analysis shows that the algorithm we developed performs well. Finally, taking the job shop scheduling problem as a start point, we discuss how constraint-based scheduling can be used to solve more general scheduling problems.     

A comparison of local search methods for flow shop scheduling

Local search techniques are widely used to obtain approximate solutions to a variety of combinatorial optimization problems. Two important categories of local search methods are neighbourhood search and genetic algorithms. Commonly used neighbourhood search methods include descent, threshold accepting, simulated annealing and tabu search. In this paper, we present a computational study that compares these four neighbourhood search methods, a genetic algorithm, and a hybrid method in which descent is incorporated into the genetic algorithm. The performance of these six local search methods is evaluated on the problem of scheduling jobs in a permutation flow shop to minimize the total weighted completion time. Based on the results of extensive computational tests, simulated annealing is found to generate better quality solutions than the other neighborhood search methods. However, the results also indicate that the hybrid genetic descent algorithm is superior to simulated annealing.     

Iterated tabu search for the car sequencing problem

This paper introduces an iterated tabu search heuristic for the daily car sequencing problem in which a set of cars must be sequenced so as to satisfy requirements from the paint shop and the assembly line. The iterated tabu search heuristic combines a classical tabu search with perturbation operators that help escape from local optima. The resulting heuristic is flexible, easy to implement, and fast. It has produced very good results on a set of test instances provided by the French car manufacturer Renault.     

A priority list based heuristic for the job shop problem

A priority list for the job shop scheduling problem is defined to be any permutation of a set of symbols where the symbol for each job appears as many times as the number of its operations. Every priority list can be associated in a natural way with a feasible schedule, and every feasible schedule arises in this way. Priority lists are therefore a representation of feasible schedules that avoid the problems normally associated with schedule infeasibility. As a result, the three ingredients of local search heuristics, namely picking initial starting schedules, constructing search neighbourhoods and computing makespans, become faster and easier when performed in the space of priority lists rather than in the space of feasible schedules. As an illustration of their usefulness, a priority list based simulated annealing heuristic is presented, which, although simple, is competitive with the current leading schedule based simulated annealing and tabu search heuristics.     

一种改进的禁忌搜索算法及其在选址问题中的应用

本文研究了选址问题中无容量限制的p-中值问题,在Rolland等人提出的有效禁忌搜索算法基础上,提出了一种以目标函数变化量作为评价函数的改进禁忌搜索算法,并进行了理论分析,然后将其与有效禁忌搜索算法作了性能比较.通过比较三个公共测试数据集的计算结果,验证了本文提出的禁忌搜索算法的可行性和有效性.     

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Evaluating the performance of tabu search procedures for flow shop sequencing

We address the problem of minimising makespan in a flow shop by using tabu search procedures. By combining different neighbourhood structures, neighbourhood examinations, and stopping conditions we obtain alternative tabu search procedures. Starting from a common initial solution we evaluate the relative performance of such procedures considering both the solution quality and computational effort.