Skip to main content
SpringerLink
Log in

New MIP model for multiprocessor scheduling problem with communication delays

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper we consider scheduling tasks on a multiprocessor system, taking into account communication delays. We propose a new Mixed Integer Program (MIP) formulation that drastically reduces both the number of variables and the number of constraints, when compared to the best mathematical programming formulations from the literature. In addition, we propose pre-processing procedures that generates cuts and bounds on all variables, reducing the solution space of the problem as well. Cuts are obtained by using forward and backward critical path method from project management field, while the upper bound is derived from the new greedy heuristic. Computational experience shows advantages of our approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Ali, H., El-Rewini, H.: An optimal algorithm for scheduling interval ordered tasks with communication on N processor, University of Nebraska at Omaha, Math. and Computer Science Department, Technical Report, 9120 (1990)

  2. Cakici, E., Mason, S.J.: Parallel machine scheduling subject to auxiliary resource constraints. Prod. Plan. Control. 18, 217225 (2007)

    Article  Google Scholar 

  3. Chen, W.H., Lin, C.S.: A hybrid heuristic to solve a task allocation problem. Comput. Oper. Res. 27(3), 287303 (2000)

    Article  Google Scholar 

  4. Chrétienne, P., Picouleau, C.: Scheduling with communication delays: a survey. In: Chrétienne, P., Coffman, E.G., Lenstra, J.K., Liu, Z. (eds.) Scheduling theory and its applications, p. 6590. Wiley, New York (1995)

    Google Scholar 

  5. Darte, A., Robert, Y., Vivien, F.: Scheduling and automatic parallelization. Birkhuser, Boston (2000)

    Book  MATH  Google Scholar 

  6. Dauzère-Pérès, S., Sevaux, M.: Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine. Nav. Res Logist. 50(3), 273288 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Davidović, T., Crainic, T.G.: Benchmark-problem instances for static scheduling of task graphs with communication delays on homogeneous multiprocessor systems. Comput. Oper. Res. 33, 21552177 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Davidović, T., Hansen, P., Mladenović, N.: Permutation-based genetic, tabu and variable neigh-borhood search heuristics for multiprocessor scheduling with communication delays. Asia Pacific J. Oper. Res. 22(3), 297326 (2005)

    MATH  Google Scholar 

  9. Davidović, T., Liberti, L., Maculan, N., Mladenović, N.: Towards the optimal solution of the multiprocessor scheduling problem with communication delays. MISTA Proceedings (2007)

  10. Djordjević, G.L., Tošić, M.B.: A heuristic for scheduling task graphs with communication delays onto multiprocessors. Parallel Comput. 22(9), 11971214 (1996)

    MathSciNet  MATH  Google Scholar 

  11. Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. WH Freeman & Co., San Francisco (1979)

    MATH  Google Scholar 

  12. Harris, J.M.: Combinatorics and graph theory. Springer, New York (2000)

    Book  MATH  Google Scholar 

  13. Hartmann, S., Briskorn, D.: A survey of variants and extensions of the resource-constrained project scheduling problem. Eur. J. Oper. Res. 207, 114 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hwang, R., Gen, M., Katayama, H.: A comparison of multiprocessor task scheduling algorithms with communication costs. Comput. Oper. Res. 35, 976993 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Isaak, G.: Scheduling rooted forests with communication delays. Order 11, 309316 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Knuth, D.E.: The art of computer programming, vol. 1, 3rd edn. Addison-Wesley, Boston (1991)

    Google Scholar 

  17. Luo, P., L, K., Shi, Z.: A revisit of fast greedy heuristics for mapping a class of independent tasks onto heterogeneous computing systems. J. Parallel Distrib. Comput. 67, 695714 (2007)

    Article  Google Scholar 

  18. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 10971100 (1997)

    MathSciNet  MATH  Google Scholar 

  19. Murty, K.G.: Operations research: deterministic optimization models. Prentice-Hall, Englewood Cliffs (1994)

    MATH  Google Scholar 

  20. Pinedo, M.: Scheduling: theory, algorithms, and systems, 2nd edn. Prentice-Hall, New Jersey (2002)

    MATH  Google Scholar 

  21. Prastein, M.: Precedence-constrained scheduling with minimum time and communication. MS Thesis, University of Illinois at Urbana-Champaign (1987)

  22. Rayward-Smith, V.J.: UET scheduling with unit interprocessor communication delays. Discret. Appl. Math. 18, 5571 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  23. Sousa, J.P., Wolsey, L.A.: A time-indexed formulation of nonpreemptive single machine scheduling problems. Math. Progr. 54, 353367 (1992)

    Article  MathSciNet  Google Scholar 

  24. Unlu, Y., Mason, S.J.: Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Comput. Ind. Eng., Pergamon Press Inc., 58, 785800 (2010)

  25. Urban, T.L.: Note. Optimal balancing of U-shaped assembly lines. Manag. Sci. 44(5), 738741 (1998)

    Article  Google Scholar 

  26. Venugopalan, S., Sinnen, O.: Optimal linear programming solutions for multiprocessor scheduling with communication delays. In: Xiang, Y., Stojmenovic, I., Apduhan, B.O., Wang, G., Nakano, K., Zomaya, A. (eds.) Algorithms and architectures for parallel processing, pp. 129138. Springer, Heidelberg, 7439, (2012)

Download references

Acknowledgments

The authors would like to gratefully thank the IRT (Institut de recherche technologique) Railenium for the financial support to achieve this research. Also, the authors thank the International Chair Professor N. Mladenović, for his contribution to this work. This Chair position at the University of Valenciennes is co-funded by the region Nord-Pas-de-Calais and the IRT Railenium.

Author information

Authors and Affiliations

  1. UVHC-LAMIH CNRS UMR 8201, F-59313, Valenciennes Cedex 9, France

    Abdessamad Ait El Cadi, Rabie Ben Atitallah, Saïd Hanafi, Nenad Mladenović & Abdelhakim Artiba

Authors
  1. Abdessamad Ait El Cadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rabie Ben Atitallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saïd Hanafi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nenad Mladenović
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Abdelhakim Artiba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdessamad Ait El Cadi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ait El Cadi, A., Ben Atitallah, R., Hanafi, S. et al. New MIP model for multiprocessor scheduling problem with communication delays. Optim Lett 11, 1091–1107 (2017). https://doi.org/10.1007/s11590-014-0802-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-014-0802-2

Keywords

Search

Navigation