A neuro-tabu search heuristic for the flow shop scheduling problem

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Abstract

Flow shop scheduling deals with the sequencing of different jobs that visit a set of machines in the same order. A neural networks-based tabu search method, namely EXTS, is proposed for the flow shop scheduling. Unlike the other tabu search-based methods, the proposed approach helps diminishing the tabu effect in an exponential way rather than most commonly used way of diminishing it in a sudden manner. On the basis of the conducted tests, some rules are evolved to set the values for different parameters. The effectiveness of the proposed method is tested with 23 problems selected from literature. The computational results indicate that the proposed approach is effective in terms of reduced makespan for the attempted problems.

Introduction

The flow shop scheduling is a well-known problem among researchers and practitioners. It deals with sequencing N jobs that have to be processed on M machines so that the manufacturing system performs better in terms of performance measures such as minimum makespan, minimum tardiness, minimum work-in-process, etc. In flow shop scheduling, the processing routes are the same for all the jobs. Emergence of advanced manufacturing systems such as CAD/CAM, FMS, CIM, etc. has increased the importance of flow shop scheduling. In these systems, similar parts are grouped in manufacturing cells. Since the manufacturing processes of parts within a cell are almost similar, the parts need to visit machines in the same order. The research attempted in this paper bridges the flow shop scheduling and neural networks, which has not been explored so far. The following assumptions are made for the flow shop scheduling problem in this paper:

  • all jobs are available for processing at time zero,

  • each job can be processed only once on each machine (if a job does not need processing on a particular machine, the related processing time is set to zero),

  • once an operation is started on a machine, it has to be completed without breaking (non-preemption),

  • all machines are available at time zero,

  • every machine can process only one job at a time,

  • each job can be processed on only one machine at a time,

  • the setup times are independent of the sequence and therefore can be incorporated in processing times.

Section snippets

Literature review

Sequencing methods in the literature can be broadly categorized into two types of approaches, namely optimization and heuristic. Optimization approaches guarantee to obtain the optimum sequence, whereas heuristic approaches mostly obtain near-optimal sequences. Among the optimization approaches, the algorithm developed by Johnson [1] is the widely cited research dealing with sequencing N jobs on two machines. Lomnicki [2] proposed a branch and bound technique to find the optimum permutation of

Formulation of problem

The flow shop scheduling problem concerns a set of N jobs called J={1,2,…,N} that are to be processed on a set of M machines called I={1,2,…,M}. Without losing generality, it is assumed that jobs are processed in the order of indices of machines. Each part contains M operations and each operation is processed on one machine. Let Π denote the set of all permutations of jobs belonging to J. A permutation of all jobs belonging to J is represented by π where πΠ. The jth element of permutation π is

Elements of tabu search

The TS algorithm proposed in this paper contains the following elements:

  • initial solution,

  • move mechanism,

  • neighborhood,

  • TS mechanism,

  • stopping condition.

There are some other optional elements, such as aspiration function, etc. that some TS-based methods exploit. For a more detailed description of these elements, Glover [23], [24] may be referred. In the following sub-sections, we discuss how the elements mentioned above have been implemented in this paper.

The proposed method

In the proposed method, a variable called as bad_counter is used to count the number of iterations throughout which no improvement in makespan is obtained. Once the variable bad_counter exceeds a predefined control parameter, say max_bad, the algorithm jumps back and the best permutation obtained so far is considered as current permutation. This action is also called as diversification scheme in the terminology of TS algorithm. The number of jumps to back is counted by a variable called

Computational results

Osman and Potts [11] and Ogbu and Smith [14] have developed simulated annealing-based algorithms for solving flow shop scheduling problems. Ogbu and Smith [25] reported that the performance of these algorithms is comparable in terms of the quality of solutions and efficiency of computation. Also, Reeves [26] used a genetic algorithm to solve the benchmark problems of Taillard [27] and reported that the simulated annealing algorithm proposed by Osman and Potts [11] performs slightly better than

Discussion and conclusion

In this paper, a neural network-based TS method, termed as EXTS, is developed to solve the flow shop scheduling problem. The EXTS algorithm is an improvement method. It gets an initial permutation from a constructive method such as NEH algorithm. The EXTS exploits a neuro-dynamical structure to iteratively improve the initial permutation. The proposed EXTS algorithm is different from the other TS-based methods, as it reduces the tabu effect exponentially. Based on experimental tests, some rules

Acknowledgements

The authors would like to put on record their appreciation to the anonymous referees for their valuable suggestions, which have enhanced the quality of the paper over its earlier versions.

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