Minimizing makespan in a blocking flowshop using genetic algorithms

We consider the problem of minimizing the makespan of n jobs in an m-machine #owshop operating without bu!ers. Since there is no intermediate storage, a job here cannot leave a machine until the machine downstream is free. When that is the case, the job is said to be blocked. Thisblocking #owshopa problem is known to be strongly NP-hard for the shop having more than two machines. In this paper, we develop a genetic algorithmic approach to solve large size restricted slowdown #owshop problems of which blocking #owshop problems are a special case. Abadi (Flowshop scheduling problems with no-wait and blocking environments: A mathematical programming approach. Ph.D Thesis, Department of Industrial Engineering, University of Toronto, Canada, 1995) has established a connection between the blocking #owshop problem and a no-wait #owshop in which jobs do not wait between operations. He uses the idea of deliberately slowing down the processing of certain operations. We utilize this concept to evaluate the makespan ("tness) of the solutions generated by genetic algorithms. Computational results indicate that a genetic algorithm with optimized parameters for controlling the evolution of solutions consistently performs signi"cantly better than the heuristic for blocking #owshops developed in a recent Ph.D. thesis by Abadi. The comparison is made for the problems with sizes up to 20 machines and 250 jobs. 2001 Published by Elsevier Science B.V. All rights reserved.

[1]  J. Piehler,et al.  Ein Beitrag zum Reihenfolgeproblem , 1960, Unternehmensforschung.

[2]  Chuen-Lung Chen,et al.  An application of genetic algorithms for flow shop problems , 1995 .

[3]  Hisao Ishibuchi,et al.  Performance evaluation of genetic algorithms for flowshop scheduling problems , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[4]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[5]  T. B. Tate,et al.  Machine Scheduling Problems , 1978 .

[6]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[7]  Michael Pinedo,et al.  Sequencing in an Assembly Line with Blocking to Minimize Cycle Time , 1989, Oper. Res..

[8]  L. Lei,et al.  DETERMINING OPTIMAL CYCLIC HOIST SCHEDULES IN A SINGLE-HOIST ELECTROPLATING LINE , 1994 .

[9]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[10]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Sidney Addelman,et al.  trans-Dimethanolbis(1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionato)zinc(II) , 2008, Acta crystallographica. Section E, Structure reports online.

[13]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[14]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[15]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[16]  David Connolly,et al.  General Purpose Simulated Annealing , 1992 .

[17]  A. J. Clewett,et al.  Introduction to sequencing and scheduling , 1974 .

[18]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[19]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[20]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[21]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[22]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[23]  Chelliah Sriskandarajah,et al.  A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process , 1996, Oper. Res..

[24]  É. Taillard.  Some efficient heuristic methods for the flow shop sequencing problem , 1990 .

[25]  Gilbert Laporte,et al.  New Insertion and Postoptimization Procedures for the Traveling Salesman Problem , 1992, Oper. Res..

[26]  Yih-Long Chang,et al.  A new heuristic for the n-job, M-machine flow-shop problem , 1991 .

[27]  Chelliah Sriskandarajah,et al.  Minimizing Cycle Time in a Blocking Flowshop , 2000, Oper. Res..