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A Parallel Distributed Algorithm for the Permutation Flow Shop Scheduling Problem

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Book cover Algorithms and Architectures for Parallel Processing (ICA3PP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6082))

Abstract

This paper describes a new parallel Branch-and-Bound algorithm for solving the classical permutation flow shop scheduling problem as well as its implementation on a cluster of six computers. The experimental study of our distributed parallel algorithm gives promising results and shows clearly the benefit of the parallel paradigm to solve large-scale instances in moderate CPU time.

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References

  1. Bendjoudi, A., Melab, N., Talbi, E.-G.: P2P design and implementation of a parallel B&B algorithm for grids. International Journal of Grid and Utility Computing 1, 159–168 (2009)

    Article  Google Scholar 

  2. Land, A.H., Doig, A.G.: An automatic method for solving discrete programming problems. Econometrika 28, 497–520 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gendron, B., Crainic, T.G.: Parallel B&B Algorithms: Survey and synthesis. Operation Research 42(6), 1042–1066 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Le Cun, B., Crainic, T.G., Roucairol, C.: Parallel Branchand-Bound algorithms. In: Parallel combinatorial optimization, Wiley, John & Sons incorporated, Chichester (2006)

    Google Scholar 

  5. Benjamin, Wah, W., Ma, Y.W.: MANIP-a parallel computer system for implementing B&B algorithm. In: International Symposium on Computer Architecture, pp. 239–262 (1981)

    Google Scholar 

  6. Phillips, C.A., Eckstein, J., Hart, W.E.: Pico: An object oriented framework for parallel branch-andbound. Technical report, RUTCOR Research Report (2000)

    Google Scholar 

  7. Caromel, D., Di Costanzo, A., Baduel, L., Matsuoka, S.: Grid’BnB: A parallel B&B Framework for Grids. In: International conference on high performance computing, HIPC (2007)

    Google Scholar 

  8. Bader, D.A.: Parallel algorithm design for branch and bound. International Series in Operations Research & Management Science 76, 5-1-5-44 (2004)

    Google Scholar 

  9. Ignall, E., Schrage, L.E.: Application of the branch-and-bound technique to some flow shop problems. Operations Research 12, 400–412 (1965)

    Article  MathSciNet  Google Scholar 

  10. Anderson, E.J., Glass, C.A., Potts, C.N.: Local search in combinatorial optimization: Machine Scheduling. In: Local Search in Combinatorial Optimization, pp. 361–414. John Wiley and Sons, Chichester

    Google Scholar 

  11. Taillard, E.: Benchmarks for basic scheduling problems. European Journal of Operational Research 64, 278–285 (1993)

    Article  MATH  Google Scholar 

  12. McMahon, G.B., Burton, P.G.: Flow-Shop Scheduling with the Branch-and-Bound Method. Operations Research 15(3), 473–481 (1967)

    Article  Google Scholar 

  13. Carlier, J., Rebai, I.: Two branch-and-bound algorithms for the permutation flowshop problem. European Journal of Operational Research 90(2), 238–251 (1996)

    Article  MATH  Google Scholar 

  14. Lenstra, J.K., Rinnooy Kan, A.H.G., Bruker, P.: Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1–343 (1977)

    Google Scholar 

  15. Lemesre, J., Dhaenens, C., Talbi, E.G.: An exact parallel method for a bi-objective permutation flowshopproblem. European Journal of Operational Research 177(3), 1641–1655 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Aida, K., Natsume, W., Futakata, Y.: Distributed computing with hierarchical master-worker paradigm for parallel B&B algorithm. In: CCGrid 2003, 3rd IEEE/ACM International Symposium on Cluster Computing and the Grid, pp. 156–163 (2003)

    Google Scholar 

  17. Mitten, L.: Branch-and-bound methods: general formulation and properties. Operations Research 18, 24–34 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  18. Haouari, M., Ladhari, T.: A branch-and-bound-based local search method for the flow shop problem. The Journal of the Operational Research Society 54(10), 1076–1084 (2003)

    Article  MATH  Google Scholar 

  19. Haouari, M., Ladhari, T.: Minimising maximum lateness in a two-machine flowshop. The Journal of the Operational Research Society 51(9), 1100–1106 (2000)

    MATH  Google Scholar 

  20. Mezmaz, M., Melab, N., Talbi, E.-G.: B&B@Grid: une approche efficace pour la gridification d’un algorithme Branch and Bound. INRIA, number: RR-6937, Mai (2009)

    Google Scholar 

  21. Mezmaz, M., Melab, N., Talbi, E.-G.: A Grid-enabled B&B Algorithm for Solving Challenging Combinatorial Optimization Problems. In: Parallel and Distributed Processing Symposium, IEEE International, March 2007, pp. 1–9 (2007)

    Google Scholar 

  22. Pinedo, M.: Scheduling: theory, algorithms, and systems. Prentice-Hall, Englewood CliKs (1995)

    MATH  Google Scholar 

  23. Garey, M.R., Johnson, D.S., Sethi, R.: The complexity of flow shop and job shop scheduling. Mathematics of Operations Research 29, 1–117 (1976)

    MathSciNet  Google Scholar 

  24. Santoro, N.: Design and analysis of distributed algorithms. Wiley, Chichester (2006)

    Book  Google Scholar 

  25. Kacsuk, P., Fahringer, T., Németh, Z.: Distributed and parallel systems from cluster to grid computing. Springer, New York (2007)

    Google Scholar 

  26. Bellman, R., Esogbue, A.O., Nabeshima, I.: Mathematical Aspects of scheduling and Applications, p. 202. Pergamon Press, Oxford (1982)

    MATH  Google Scholar 

  27. Čiegis, R., Baravykaite, M.: Implementation of a Black-Box Global Optimization Algorithm with a Parallel B&B Template. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds.) PARA 2006. LNCS, vol. 4699, pp. 1115–1125. Springer, Heidelberg (2007)

    Google Scholar 

  28. Okamoto, S., Wantanabe, I., Lizuka, H.: A new Par. algorithm for the n-job, m-machine flow-shop scheduling problem. Systems and Computers in Japan 26(2) (1995)

    Google Scholar 

  29. Johnson, S.M.: Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly 8, 1–61 (1954)

    Google Scholar 

  30. Ladhari, T., Haouari, M.: A computational study of the PFSP based on a tight lower bound. Computers & Operations Research 32, 1831–1847 (2005)

    Article  MATH  Google Scholar 

  31. Crainic, T.G.: Parallel Branch-and-Branch Algorithms: Survey and synthesis. Operations Research 42(6), 1042–1066 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  32. Bozejko, W.: Solving the flow shop problem by parallel programming. Journal of parallel and distributed computing 69(5), 470–481 (2009)

    Article  Google Scholar 

  33. Yu, W., Hoogeveen, H., Lenstra, J.K.: Minimizing Makespan in a Two-Machine Flowshop with Delays and Unit-Time Operations is NP-Hard. Journal of Scheduling 7, 333–348 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  34. http://www2.lifl.fr/~talbi/challenge2007/

  35. http://www.utic.rnu.tn

  36. http://www-sop.inria.fr/oasis/plugtest2005/2ndGridPlugtestsReport/

  37. Wang, X., Cheng, T.C.E.: Two-machine flowshop scheduling with job class setups to minimize total flowtime. Computers and Operations Research 32(11), 2751–2770 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  38. Masahiro, Y.S., Higaki, M., Hirabayashi, R.: A generalized utility for parallel B&B algorithms. In: 7th IEEE Sym. on Parallel and Distr. Processing (October 1995)

    Google Scholar 

  39. Lomnicki, Z.: A branch-and-bound algorithm for the exact solution of the three-machine scheduling problem. Operational Research Quarterly, 89–105 (1965)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Research Laboratory UTIC, Ecole Supérieure des Sciences et Techniques de Tunis, Tunis, Tunisia

    Samia Kouki & Mohamed Jemni

  2. Ecole Supérieure des Sciences Economiques et Commerciales, Tunis, Tunisia

    Talel Ladhari

Authors
  1. Samia Kouki
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  2. Talel Ladhari
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  3. Mohamed Jemni
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, Chung Hua University, 300, Hsinchu, Taiwan, China

    Ching-Hsien Hsu

  2. Department of Computer Science, St. Francis Xavier University, B2G 2W5, Antigonish, NS, Canada

    Laurence T. Yang

  3. Department of Computer Science ad Engineering, Seoul National University of Technology, 172 Gongreund 2-dong, Nowon-gou, 139-742, Seoul, Korea

    Jong Hyuk Park

  4. Division of Computer Engineering, Mokwon University, 302-729, Daejeon, Korea

    Sang-Soo Yeo

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Kouki, S., Ladhari, T., Jemni, M. (2010). A Parallel Distributed Algorithm for the Permutation Flow Shop Scheduling Problem. In: Hsu, CH., Yang, L.T., Park, J.H., Yeo, SS. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2010. Lecture Notes in Computer Science, vol 6082. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13136-3_34

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  • DOI: https://doi.org/10.1007/978-3-642-13136-3_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13135-6

  • Online ISBN: 978-3-642-13136-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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