Skip to main content
SpringerLink
Log in
Book cover

International Conference on Computational Science and Its Applications

ICCSA 2017: Computational Science and Its Applications – ICCSA 2017 pp 133–147Cite as

A Hybrid CPU-GPU Scatter Search for Large-Sized Generalized Assignment Problems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10404))

Abstract

In the Generalized Assignment Problem, tasks must be allocated to machines with limited resources, in order to minimize processing costs. This problem has several industrial applications and often appears as substructure of other combinatorial optimization problems. By harnessing the massive computational power of Graphics Processing Units in a Scatter Search metaheuristic framework, we propose a method that efficiently generates a solution pool using a Tabu list criteria and an Ejection Chain mechanism. Common characteristics are extracted from the pool and solutions are combined by exploring a restricted search space, as a Binary Programming model. Classic instances vary from 100–1600 jobs and 5–80 agents, but due to the big amount of optimal and near-optimal solutions found by our method, we propose novel large-sized instances up to 9000 jobs and 600 agents. Results indicate that the method is competitive with state-of-the-art algorithms in literature.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    The proposed instances are available on the website: https://drive.google.com/open?id=0B20uFG9WVmWMM2t1MlIxNG5aNW8.

References

  1. Avella, P., Boccia, M., Vasilyev, I.: A computational study of exact knapsack separation for the generalized assignment problem. Comput. Optim. Appl. 45(3), 543–555 (2010). Springer, Heidelberg

    Article  MathSciNet  MATH  Google Scholar 

  2. Cattrysse, D.G., Van Wassenhove, L.N.: A survey of algorithms for the generalized assignment problem. Eur. J. Oper. Res. 60(3), 260–272 (1992). Elsevier, Amsterdam

    Article  MATH  Google Scholar 

  3. Chu, P.C., Beasley, J.E.: A genetic algorithm for the generalised assignment problem. Comput. Oper. Res. 24(1), 17–23 (1997). Elsevier, Amsterdam

    Article  MathSciNet  MATH  Google Scholar 

  4. Czapiński, M., Barnes, S.: Tabu Search with two approaches to parallel flowshop evaluation on CUDA platform. J. Parallel Distrib. Comput. 71(6), 802–811 (2011). Elsevier, Amsterdam

    Article  Google Scholar 

  5. Danna, E., Rothberg, E., Pape, C.L.: Exploring relaxation induced neighborhoods to improve MIP solutions. Math. Program. 102(1), 71–90 (2005). Springer, Heidelberg

    Article  MathSciNet  MATH  Google Scholar 

  6. Diaz, J.A., Fernández, E.: A Tabu search heuristic for the generalized assignment problem. Eur. J. Oper. Res. 132(1), 22–38 (2001). Elsevier, Amsterdam

    Article  MathSciNet  MATH  Google Scholar 

  7. Feltl, H., Raidl, G.R.: An improved hybrid genetic algorithm for the generalized assignment problem. In: Proceedings of the 2004 ACM Symposium on Applied Computing, pp. 990–995. ACM, New York (2004)

    Google Scholar 

  8. Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977). Wiley Online Library, New Jersey

    Article  Google Scholar 

  9. Glover, F.: Tabu search-part I. ORSA J. Comput. 1(3), 190–206 (1989). INFORMS, Catonsville

    Article  MATH  Google Scholar 

  10. Glover, F.: Tabu search-part II. ORSA J. Comput. 2(1), 4–32 (1990). INFORMS, Catonsville

    Article  MATH  Google Scholar 

  11. Glover, F., Laguna, M.: Tabu Search. Springer, New York (2013)

    MATH  Google Scholar 

  12. Glover, F., Rego, C.: Ejection chain and filter-and-fan methods in combinatorial optimization. 4OR: Q. J. Oper. Res. 4(4), 263–296 (2006). Springer, Heidelberg

    Article  MathSciNet  MATH  Google Scholar 

  13. Higgins, A.J.: A dynamic Tabu search for large-scale generalised assignment problems. Comput. Oper. Res. 28(10), 1039–1048 (2001). Elsevier, Amsterdam

    Article  MathSciNet  MATH  Google Scholar 

  14. Kirk, D.B., Wen-Mei, W.H.: Programming Massively Parallel Processors: A Hands-on Approach, vol. 2, pp. 10–14. Morgan Kaufmann, San Francisco (2012)

    Google Scholar 

  15. Laguna, M., Kelly, J.P., Gonzlez-Velarde, J., Glover, F.: Tabu search for the multilevel generalized assignment problem. Eur. J. Oper. Res. 82(1), 176–189 (1995). Elsevier, Amsterdam

    Article  MATH  Google Scholar 

  16. Martí, R., Duarte, A., Laguna, M.: Advanced scatter search for the max-cut problem. INFORMS J. Comput. 21(1), 26–38 (2009). INFORMS, Catonsville

    Article  MathSciNet  MATH  Google Scholar 

  17. Martí, R., Laguna, M., Glover, F.: Principles of scatter search. Eur. J. Oper. Res. 169(2), 359–372 (2006). Elsevier, Amsterdam

    Article  MathSciNet  MATH  Google Scholar 

  18. Nauss, R.M.: Solving the generalized assignment problem: an optimizing and heuristic approach. INFORMS J. Comput. 15(3), 249–266 (2003). INFORMS, Catonsville

    Article  MathSciNet  MATH  Google Scholar 

  19. Öncan, T.: A survey of the generalized assignment problem and its applications. INFOR: Inf. Syst. Oper. Res. 45(3), 123–141 (2007). Canadian Operational Research Society, Ottawa

    MathSciNet  Google Scholar 

  20. Osman, I.H.: Heuristics for the generalised assignment problem: simulated annealing and Tabu search approaches. Oper.-Res.-Spektrum 17(4), 211–225 (1995). Springer, Heidelberg

    Article  MATH  Google Scholar 

  21. Pigatti, A., De Aragao, M.P., Uchoa, E.: Stabilized branch-and-cut-and-price for the generalized assignment problem. Electron. Notes Discret. Math. 19, 389–395 (2005). Optimization Online, North-Holland

    Article  MathSciNet  MATH  Google Scholar 

  22. Posta, M., Ferland, J.A., Michelon, P.: An exact method with variable fixing for solving the generalized assignment problem. Comput. Optim. Appl. 52(3), 629–644 (2012). Springer, Heidelberg

    Article  MathSciNet  MATH  Google Scholar 

  23. Resende, M.G., Ribeiro, C.C., Glover, F., Martí, R.: Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of metaheuristics, pp. 87–107. Springer, Heidelberg (2010). doi:10.1007/978-1-4419-1665-5_4

    Chapter  Google Scholar 

  24. Ross, G.T., Soland, R.M.: A branch and bound algorithm for the generalized assignment problem. Math. Program. 8(1), 91–103 (1975). Springer, Heidelberg

    Article  MathSciNet  MATH  Google Scholar 

  25. Sahni, S., Gonzalez, T.: P-complete approximation problems. J. ACM (JACM) 23(3), 555–565 (1976). ACM, New York

    Article  MathSciNet  MATH  Google Scholar 

  26. Savelsbergh, M.: A branch-and-price algorithm for the generalized assignment problem. Oper. Res. 45(6), 831–841 (1997). INFORMS, Catonsville

    Article  MathSciNet  MATH  Google Scholar 

  27. Sulewski, D., Edelkamp, S., Kissmann, P.: Exploiting the computational power of the graphics card: optimal state space planning on the GPU. In: 21st International Conference on Automated Planning and Scheduling - ICAPS, Freiburg (2011)

    Google Scholar 

  28. Wilson, J.M.: A genetic algorithm for the generalised assignment problem. J. Oper. Res. Soc. 48(8), 804–809 (1997). Elsevier, Amsterdam

    Article  MATH  Google Scholar 

  29. Yagiura, M., Ibaraki, T., Glover, F.: A path relinking approach with ejection chains for the generalized assignment problem. Eur. J. Oper. Res. 169(2), 548–569 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Brazilian funding agencies CAPES, CNPq, FAPEMIG and FAPERJ for supporting the current work.

Author information

Authors and Affiliations

  1. Federal University of Ouro Preto, Ouro Preto, MG, Brazil

    Danilo S. Souza, Haroldo G. Santos & Janniele A. S. Araujo

  2. State University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Igor M. Coelho

Authors
  1. Danilo S. Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haroldo G. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Igor M. Coelho
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Janniele A. S. Araujo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Danilo S. Souza .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Souza, D.S., Santos, H.G., Coelho, I.M., Araujo, J.A.S. (2017). A Hybrid CPU-GPU Scatter Search for Large-Sized Generalized Assignment Problems. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10404. Springer, Cham. https://doi.org/10.1007/978-3-319-62392-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-62392-4_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62391-7

  • Online ISBN: 978-3-319-62392-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation