Skip to main content
SpringerLink
Log in

Using Bound Sets in Multiobjective Optimization: Application to the Biobjective Binary Knapsack Problem

  • Conference paper
Experimental Algorithms (SEA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6049))

Included in the following conference series:

Abstract

This paper is devoted to a study of the impact of using bound sets in biobjective optimization. This notion, introduced by Villareal and Karwan [19], has been independently revisited by Ehrgott and Gandibleux [9], as well as by Sourd and Spanjaard [17]. The idea behind it is very general, and can therefore be adapted to a wide range of biobjective combinatorial problem. We focus here on the biobjective binary knapsack problem. We show that using bound sets in a two-phases approach [18] based on biobjective dynamic programming yields numerical results that outperform previous ones, both in execution times and memory requirements.

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

Access this chapter

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aneja, Y.R., Nair, K.P.K.: Bicriteria transportation problem. Management Science 25, 73–78 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bazgan, C., Hugot, H., Vanderpooten, D.: An efficient implementation for the 0-1 multi-objective knapsack problem. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 406–419. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Bazgan, C., Hugot, H., Vanderpooten, D.: Solving efficiently the 0-1 multi-objective knapsack problem. Computers & Operations Research 36(1), 260–279 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bitran, G., Rivera, J.M.: A combined approach to solve binary multicriteria problems. Naval Research Logistics Quarterly 29, 181–201 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Captivo, M.E., Clìmaco, J., Figueira, J., Martins, E., Santos, J.L.: Solving bicriteria 0-1 knapsack problems using a labeling algorithm. Computers & Operations Research 30(12), 1865–1886 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Daellenbach, H.G., De Kluyver, C.A.: Note on multiple objective dynamic programming. Journal of the Operational Research Society 31, 591–594 (1980)

    MATH  Google Scholar 

  7. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  8. Ehrgott, M., Gandibleux, X.: Approximative solution methods for multiobjective combinatorial optimization. Journal of the Spanish Statistical and Operations Research Society 12(1), 1–88 (2004)

    MATH  MathSciNet  Google Scholar 

  9. Ehrgott, M., Gandibleux, X.: Bound sets for biobjective combinatorial optimization problems. Computers & Operations Research 34(9), 2674–2694 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin (2004)

    MATH  Google Scholar 

  11. Kiziltan, G., Yucaoglu, E.: An algorithm for multiobjective zero-one linear programming. Management Science 29(12), 1444–1453 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  12. Klamroth, K., Wiecek, M.M.: Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics 47, 57–76 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Martin, P.D., Shmoys, D.B.: A new approach to computing optimal schedules for the job shop scheduling problem. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 389–403. Springer, Heidelberg (1996)

    Google Scholar 

  14. Mavrotas, G., Diakoulaki, D.: A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research 107, 530–541 (1998)

    Article  MATH  Google Scholar 

  15. Pisinger, D.: A minimal algorithm for the 0-1 knapsack problem. Operations Research 45, 758–767 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Serafini, P.: Some considerations about computational complexity for multiobjective combinatorial problems. In: Recent advances and historical development of vector optimization. LNEMS, vol. 294 (1986)

    Google Scholar 

  17. Sourd, F., Spanjaard, O.: A multi-objective branch-and-bound framework. Application to the bi-objective spanning tree problem. INFORMS Journal of Computing 20(3), 472–484 (2008)

    Article  MathSciNet  Google Scholar 

  18. Ulungu, B., Teghem, J.: The two-phase method: An efficient procedure to solve bi-objective combinatorial optimization problems. Foundations of Computing and Decision Sciences 20(2), 149–165 (1995)

    MATH  MathSciNet  Google Scholar 

  19. Villareal, B., Karwan, M.H.: Multicriteria integer programming: A (hybrid) dynamic programming recursive approach. Mathematical Programming 21, 204–223 (1981)

    Article  MathSciNet  Google Scholar 

  20. Visée, M., Teghem, J., Pirlot, M., Ulungu, B.: Two-phases method and branch and bound procedures to solve the bi–objective knapsack problem. J. of Global Optimization 12(2), 139–155 (1998)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIP6-CNRS, Université Pierre et Marie Curie (UPMC), 4 Place Jussieu, F-75005, Paris, France

    Charles Delort & Olivier Spanjaard

Authors
  1. Charles Delort
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olivier Spanjaard
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Applications, University of Napoli Federico II, Compl. MSA, Via Cintia, 80126, Napoli, Italy

    Paola Festa

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Delort, C., Spanjaard, O. (2010). Using Bound Sets in Multiobjective Optimization: Application to the Biobjective Binary Knapsack Problem. In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13193-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13192-9

  • Online ISBN: 978-3-642-13193-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation