An effective genetic algorithm for the flexible job-shop scheduling problem

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Abstract

In this paper, we proposed an effective genetic algorithm for solving the flexible job-shop scheduling problem (FJSP) to minimize makespan time. In the proposed algorithm, Global Selection (GS) and Local Selection (LS) are designed to generate high-quality initial population in the initialization stage. An improved chromosome representation is used to conveniently represent a solution of the FJSP, and different strategies for crossover and mutation operator are adopted. Various benchmark data taken from literature are tested. Computational results prove the proposed genetic algorithm effective and efficient for solving flexible job-shop scheduling problem.

Research highlights

► Global Selection and Local Selection generate high-quality initial population. ► An improved chromosome representation is used to represents the solution of the FJSP. ► Different strategies for crossover and mutation operator are adopted.

Introduction

Scheduling is one of the most important issues in the planning and operation of manufacturing systems (Chen, Ihlow, & Lehmann, 1999), and scheduling has gained much attention increasingly in recent years (Ho, Tay, Edmund, & Lai, 2007). The classical job-shop scheduling problem (JSP) is one of the most difficult problems in this area. It consists of scheduling a set of jobs on a set of machines with the objective to minimize a certain criterion. Each machine is continuously available from time zero, processing one operation at a time without preemption. Each job has a specified processing order on the machines which are fixed and known in advance. Moreover, processing time is also fixed and known.

The flexible job-shop scheduling problem (FJSP) is a generalization of the classical JSP for flexible manufacturing systems (Pezzella, Morganti, & Ciaschetti, 2007). Each machine may have the ability of performing more than one type of operations, i.e., for a given operation must be associated with at least one machine. The problem of scheduling jobs in FJSP could be decomposed into two sub-problems: the routing sub-problem that assigns each operation to a machine selected out of a set of capable machines, the scheduling sub-problem that consists of sequencing the assigned operations on all machines in order to obtain a feasible schedule to minimize the predefined objective function.

Unlike the classical JSP where each operation is processed on a predefined machine, each operation in the FJSP can be processed on one out of several machines. This makes FJSP more difficult to solve due to the consideration of both routing of jobs and scheduling of operations. Moreover, it is a complex combinatorial optimization problem. JSP is known to be NP-hard (Garey, Johnson, & Sethi, 1976). FJSP is therefore NP-hard too.

In this paper, we propose an effective GA to solve the FJSP. Global Selection (GS) and Local Selection (LS) are designed to generate high-quality initial population in the initialization stage which could accelerate convergent speed. In order to assist the initialization method and assure the algorithm perform well, we design an improved chromosome representation method “Machine Selection and Operation Sequence”. In this method, we try to find an efficient coding scheme of the individuals which respects all constraints of the FJSP. At the same time, different strategies for crossover and mutation operator are employed. Computational results show that the proposed algorithm could get good solutions.

The paper is organized as follows. Section 2 gives the formulation of FJSP and shows an illustrative instance. An overview of relevant literature on the subject is provided in Section 3. Section 4 presents the approach of Machine Selection and Operation Sequence, encoding and decoding scheme, Global Selection, Local Selection and genetic operators. Section 5 presents and analyzes the performance results of effective genetic algorithm when it is applied to solve some common benchmarks from literature. Some final concluding remarks and future study directions are given in Section 6.

Section snippets

Problem formulation

The flexible job-shop scheduling problem can be formulated as follows. There is a set of N jobs J = {J1, J2, …, Ji, …, JN} and a set of M machines M = {M1, M2, …, Mk, …, MM}. Each job Ji consists of a predetermined sequence of operations. Each operation requires one machine selected out of a set of available machines, namely the first sub-problem: the routing sub-problem. In addition, the FJSP sets its starting and ending time on each machine, namely the second sub-problem: the scheduling sub-problem. The

Literature review

Brucker and Schile (1990) were the first to address this problem in 1990. They developed a polynomial graphical algorithm for a two-job problem. However, exact algorithms are not effective for solving FJSP and large instances (Pezzella et al., 2007). Several heuristic procedures such as dispatching rules, tabu search (TS), simulated annealing (SA) and genetic algorithm (GA) have been developed in recent years for the FJSP. They could produce reasonably good schedules in a reasonable

An effective GA for FJSP

The advantage of GA with respect to other local search algorithms is due to the fact that more strategies could be adopted together to find good individuals to add to the mating pool in a GA framework, both in the initial population phase and in the dynamic generation phase (Pezzella et al., 2007). In this paper, the proposed GA adopts an improved chromosome representation and a novel initialization approach, which can balance the workload of the machines well and converge to suboptimal

Computational results

The proposed effective genetic algorithm (eGA) was implemented in C++ on a Pentium IV running at 1.8 GHz and tested on a large number of instances from the literature. Test problems include both the P-FJSP and the T-FJSP. We know the P-FJSP is more complex than the T-FJSP from above, when considering the search space and the computational cost, the approach for solving it is very important. However, in our experiments, the approach matches the P-FJSP well because of the mechanism of adopting

Conclusions and future study

In this paper, we proposed an effective genetic algorithm for solving the flexible job-shop scheduling problem (FJSP). An improved chromosome representation scheme is proposed and an effective decoding method interpreting each chromosome into a feasible active schedule is designed. In order to enhance the quality of initial solution, a new initial assignment method (GS + LS + RS) is designed to generate high-quality initial population integrating different strategies to improve the convergence

Acknowledgements

This project is supported by 863 High Technology Plan Foundation of China under Grant No. 2006AA04Z131, the National Natural Science Foundation of China No. 50825503 and Program for New Century Excellent Talents in University under Grant No. NCET-08-0232. And we wish to thank the anonymous referees for their constructive and useful comments.

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