Abstract
The hybrid flow-shop scheduling problem with multiprocessor tasks finds its applications in real-time machine-vision systems among others. Motivated by this application and the computational complexity of the problem, we propose a genetic algorithm in this paper. We first describe the implementation details, which include a new crossover operator. We then perform a preliminary test to set the best values of the control parameters, namely the population size, crossover rate and mutation rate. Next, given these values, we carry out an extensive computational experiment to evaluate the performance of four versions of the proposed genetic algorithm in terms of the percentage deviation of the solution from the lower bound value. The results of the experiments demonstrate that the genetic algorithm performs the best when the new crossover operator is used along with the insertion mutation. This genetic algorithm also outperforms the tabu search algorithm proposed in the literature for the same problem.
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References
Błażewicz, J., M. Drabowski, and J. Weglarz, “Scheduling multiprocessor tasks to minimize schedule length,” IEEE Transactions on Computers, C-35(5), 389–393 (1986).
Błażewicz, J., M. Drozdowski, G. Schmidt, and D. de Werra, “Scheduling independent two-processor tasks on a uniform duo-processor system,” Discrete Applied Mathematics, 28, 11–20 (1990).
Błażewicz, J., K. H. Ecker, E. Pesch, G. Schmidt, and J. Weglarz,” Scheduling Computer and Manufacturing Processes, 2nd edition, Springer-Verlag, Berlin, 2001.
Brucker, P., S. Knust, D. Roper, and Y. Zinder, “Scheduling UET tasks systems with concurrency on two parallel identical processors,” Mathematical Methods of Operations Research, 52(3), 369–387 (2000).
Brucker, P. and A. Krämer, “Shop scheduling problems with multiprocessor tasks on dedicated processors,” Annals of Operations Research, 57, 13–27 (1995).
Brucker, P. and A. Krämer, “Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems,” European Journal of Operational Research, 90, 214–226 (1996).
Caraffa, V., S. Ianes, T. P. Bagchi, and C. Sriskandarajah, “Minimizing makespan in a blocking flowshop using genetic algorithms,” International Journal Production Economics, 70, 101–115 (2001).
Chen, J. and C.-Y. Lee, “General multiprocessor task schduling,” Naval Research Logistics, 46, 57–74 (1999).
Chen, C.-L., V. S. Vempati, and N. Aljaber, “An application of genetic algorithms for flow shop problems,” European Journal of Operational Research, 80, 389–396 (1995).
Della Croce, F., R. Tadei, and G. Volta, “A genetic algorithm for the job shop problem,” Computers and Operations Research, 22, 15–24 (1995).
Dorndorf, U. and E. Pesch, “Evolution based learning in a job shop scheduling environment,” Computers and Operations Research, 22, 25–40 (1995).
Drozdowski, M., “Scheduling multiprocessor tasks—An overview,” European Journal of Operational Research, 94, 215–230 (1996).
Drozdowski, M., “Selected problems of scheduling tasks in multiprocessor computer systems,”Monograph No. 321, Poznan University of Technology Press, 1997. (Downloadable from website http://www.cs.put.poznan.pl/mdrozdowski#prepr).
Du, J. and J. Y.-T. Leung, “Complexity of scheduling parallel task systems,” SIAM Journal on Discrete Mathematics, 2, 473–487 (1989).
Ercan, M. F. and Y.-F. Fung, “Real-time image interpretation on a multi-layer architecture,” in Proceedings of the IEEE TENCON’99, 1999, pp. 1303–1306.
Gen, M. and R. Cheng, Genetic Algorithms and Engineering Design, Wiley, New York, 1997.
Goldberg, D. and R. Lingle, “Alleles, loci, and the traveling salesman problem,” in J. Grefenstette (ed.), Proceedings of the First International Conference on Genetic Algorithms and their Applications, Hillsdale, 1985, pp. 154–159.
Gupta, J. N. D., “Two stage hybrid flowshop scheduling problem,” Journal of Operational Research Society, 39(4), 359–364 (1988).
Haouari, M. and R. M’Hallah, “Heuristic algorithms for the two-stage hybrid flowshop problems,” Operations Research Letters, 21, 43–53 (1997).
Holland, J. H., Adaption in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975.
Iyer, S. K. and B. Saxena, “Improved genetic algorithm for the permutation flowshop scheduling problem,” Computers and Operations Research, 31, 593–606 (2004).
Krawczyk, H. and M. Kubale, “An approximation algorithm for diagnostic test scheduling in multicomputer systems,” IEEE Transactions on Computers, 34, 869–872 (1985).
Lee, C.-Y. and X. Cai, “Scheduling one and two-processor tasks on two parallel processors,” IIE Transaction, 31, 445–455 (1999).
Lee, C.-Y., L. Lei, and M. Pinedo, “Current trends in deterministic scheduling,” Annals of Operations Research, 70, 1–41 (1997).
Lloyd, E. L., “Concurrent task systems,” Operations Research, 29, 189–201 (1981).
Michalewicz, Z., Genetic Algorithms+Data Structures = Evolution Programs, 3rd edition, Springer-Verlag, Berlin, 1996.
Moursli O. and Y. Pochet, “A branch-and-bound algorithm for the hybrid flowshop,” International Journal of Production Economics, 64, 113–125 (2000).
Oĝuz, C. and M. F. Ercan, “Scheduling multiprocessor tasks in a two-stage flow-shop environment,” Computers and Industrial Engineering, 33, 269–272 (1997).
Oĝuz, C., M. F. Ercan, T. C. E. Cheng, and Y.-F. Fung, “Heuristic algorithms for multiprocessor task scheduling in a two-stage hybrid flow-shop,” European Journal of Operational Research, 149, 390–403 (2003).
Oĝuz, C., Y. Zinder, V. H. Do, A. Janiak, and M. Lichtenstein, “Hybrid flow-shop scheduling problems with multiprocessor task systems,” European Journal of Operational Research, 152, 115–131 (2004).
Portmann, M.-C., A. Vignier, D. Dardilhac, and D. Dezalay, “Branch and bound crossed with GA to solve hybrid flow shops,” European Journal of Operational Research, 107, 389–400 (1998).
Reeves, C. R., “A genetic algorithm for flowshop sequencing,” Computers and Operations Research, 22, 5–13 (1995).
Riane, F., A. Artiba, and S. E. Elmaghraby, “A hybrid three-stage flowshop problem: Efficient heuristics to minimize makespan,” European Journal of Operational Research, 109, 321–329 (1998).
Santos, D. L., J. L. Hunsucker, and D. E. Deal, “Global lower bounds for flow shops with multiple processors,” European Journal of Operational Research, 80, 112–120 (1995).
Vignier, A., J.-C. Billaut, and C. Proust, “Hybrid flowshop scheduling problems: State of the art,” Rairo-Recherche Operationnelle-Operations Research, 33, 117–183 (1999).
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Oĝuz, C., Ercan, M.F. A Genetic Algorithm for Hybrid Flow-shop Scheduling with Multiprocessor Tasks. J Sched 8, 323–351 (2005). https://doi.org/10.1007/s10951-005-1640-y
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DOI: https://doi.org/10.1007/s10951-005-1640-y