Skip to main content
SpringerLink
Log in

The Knapsack Problem with Forfeits

  • Conference paper
  • First Online:
Combinatorial Optimization (ISCO 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12176))

Included in the following conference series:

Abstract

In this paper we introduce and study the Knapsack Problem with Forfeits. With respect to the classical definition of the problem, we are given a collection of pairs of items, such that the inclusion of both in the solution involves a reduction of the profit. We propose a mathematical formulation and two heuristic algorithms for the problem. Computational results validate the effectiveness of our approaches.

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 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

Institutional subscriptions

Change history

  • 22 July 2020

    The original version of this chapter was revised. A typo in the second author’s family name was inadvertently introduced during the publication process. The family name has been corrected to “D’Ambrosio.”

References

  1. Bettinelli, A., Cacchiani, V., Malaguti, E.: A branch-and-bound algorithm for the knapsack problem with conflict graph. INFORMS J. Comput. 29(3), 457–473 (2017)

    Article  MathSciNet  Google Scholar 

  2. Carrabs, F., Cerrone, C., D’Ambrosio, C., Raiconi, A.: Column generation embedding carousel greedy for the maximum network lifetime problem with interference constraints. In: Sforza, A., Sterle, C. (eds.) ODS 2017. SPMS, vol. 217, pp. 151–159. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67308-0_16

    Chapter  Google Scholar 

  3. Carrabs, F., Cerulli, R., D’Ambrosio, C., Raiconi, A.: Prolonging lifetime in wireless sensor networks with interference constraints. In: Au, M.H.A., Castiglione, A., Choo, K.-K.R., Palmieri, F., Li, K.-C. (eds.) GPC 2017. LNCS, vol. 10232, pp. 285–297. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57186-7_22

    Chapter  MATH  Google Scholar 

  4. Carrabs, F., Cerulli, R., Pentangelo, R., Raiconi, A.: Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach. Ann. Oper. Res. 1–14 (2018). https://doi.org/10.1007/s10479-018-2895-y

  5. Cerrone, C., Cerulli, R., Golden, B.: Carousel greedy: a generalized greedy algorithm with applications in optimization. Comput. Oper. Res. 85, 97–112 (2017)

    Article  MathSciNet  Google Scholar 

  6. Cerrone, C., D’Ambrosio, C., Raiconi, A.: Heuristics for the strong generalized minimum label spanning tree problem. Networks 74(2), 148–160 (2019)

    Article  MathSciNet  Google Scholar 

  7. Darmann, A., Pferschy, U., Schauer, J.: Minimal spanning trees with conflict graphs. Optimization online (2009)

    Google Scholar 

  8. Epstein, L., Levin, A.: On bin packing with conflicts. SIAM J. Optim. 19(3), 1270–1298 (2008)

    Article  MathSciNet  Google Scholar 

  9. Gendreau, M., Laporte, G., Semet, F.: Heuristics and lower bounds for the bin packing problem with conflicts. Comput. Oper. Res. 31(3), 347–358 (2004)

    Article  MathSciNet  Google Scholar 

  10. Gurski, F., Rehs, C.: The knapsack problem with conflict graphs and forcing graphs of bounded clique-width. In: Fortz, B., Labbé, M. (eds.) Operations Research Proceedings 2018. ORP, pp. 259–265. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-18500-8_33

    Chapter  Google Scholar 

  11. Hadi, K., Lasri, R., El Abderrahmani, A.: An efficient approach for sentiment analysis in a big data environment. Int. J. Eng. Adv. Technol. 8(4), 263–266 (2019)

    Google Scholar 

  12. Hifi, M., Otmani, N.: An algorithm for the disjunctively constrained knapsack problem. Int. J. Oper. Res. 13(1), 22–43 (2012)

    Article  Google Scholar 

  13. Kanté, M.M., Laforest, C., Momège, B.: Trees in graphs with conflict edges or forbidden transitions. In: Chan, T.-H.H., Lau, L.C., Trevisan, L. (eds.) TAMC 2013. LNCS, vol. 7876, pp. 343–354. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38236-9_31

    Chapter  MATH  Google Scholar 

  14. Kong, H., Kang, Q., Li, W., Liu, C., Kang, Y., He, H.: A hybrid iterated carousel greedy algorithm for community detection in complex networks. Physica A: Stat. Mech. Appl. 536 (2019). Article Number 122124

    Google Scholar 

  15. Muritiba, A.E.F., Iori, M., Malaguti, E., Toth, P.: Algorithms for the bin packing problem with conflicts. Informs J. Comput. 22(3), 401–415 (2010)

    Article  MathSciNet  Google Scholar 

  16. Pferschy, U., Schauer, J.: The knapsack problem with conflict graphs. J. Graph Algorithms Appl. 13(2), 233–249 (2009)

    Article  MathSciNet  Google Scholar 

  17. Pferschy, U., Schauer, J.: The maximum flow problem with conflict and forcing conditions. In: Pahl, J., Reiners, T., Voß, S. (eds.) INOC 2011. LNCS, vol. 6701, pp. 289–294. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21527-8_34

    Chapter  Google Scholar 

  18. Pferschy, U., Schauer, J.: Approximation of knapsack problems with conflict and forcing graphs. J. Comb. Optim. 33(4), 1300–1323 (2016). https://doi.org/10.1007/s10878-016-0035-7

    Article  MathSciNet  MATH  Google Scholar 

  19. Sadykov, R., Vanderbeck, F.: Bin packing with conflicts: a generic branch-and-price algorithm. INFORMS J. Comput. 25(2), 244–255 (2013)

    Article  MathSciNet  Google Scholar 

  20. Samer, P., Urrutia, S.: A branch and cut algorithm for minimum spanning trees under conflict constraints. Optim. Lett. 9(1), 41–55 (2014). https://doi.org/10.1007/s11590-014-0750-x

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang, R., Kabadi, S.N., Punnen, A.P.: The minimum spanning tree problem with conflict constraints and its variations. Discret. Optim. 8(2), 191–205 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Salerno, 84084, Fisciano, Italy

    Raffaele Cerulli, Ciriaco D’Ambrosio, Andrea Raiconi & Gaetano Vitale

Authors
  1. Raffaele Cerulli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ciriaco D’Ambrosio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrea Raiconi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gaetano Vitale
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Raiconi .

Editor information

Editors and Affiliations

  1. CNRS and Université Clermont Auvergne, Aubière, France

    Mourad Baïou

  2. Département d'informatique et de recherche opérationnelle & CIRRELT, University of Montreal, Montréal, QC, Canada

    Bernard Gendron

  3. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA

    Oktay Günlük

  4. Laboratoire LAMSADE, Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cerulli, R., D’Ambrosio, C., Raiconi, A., Vitale, G. (2020). The Knapsack Problem with Forfeits. In: Baïou, M., Gendron, B., Günlük, O., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2020. Lecture Notes in Computer Science(), vol 12176. Springer, Cham. https://doi.org/10.1007/978-3-030-53262-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-53262-8_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-53261-1

  • Online ISBN: 978-3-030-53262-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation