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Soft Computing

, Volume 22, Issue 6, pp 2025–2043 | Cite as

Optimization algorithms for the disjunctively constrained knapsack problem

  • Mariem Ben Salem
  • Raouia Taktak
  • A. Ridha Mahjoub
  • Hanêne Ben-Abdallah
Methodologies and Application
  • 156 Downloads

Abstract

This paper deals with the Knapsack Problem with conflicts, also known as the Disjunctively Constrained Knapsack Problem. The conflicts are represented by a graph whose vertices are the items such that adjacent items cannot be packed in the knapsack simultaneously. We consider a classical formulation for the problem, study the polytope associated with this formulation and investigate the facial aspect of its basic constraints. We then present new families of valid inequalities and describe necessary and sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities. Using these results, we develop a Branch-and-Cut algorithm for the problem. An extensive computational study is also presented.

Keywords

Knapsack problem Disjunctive constraints Polytope Facet Separation Branch-and-cut 

Notes

Acknowledgements

We would like to thank the referees for their valuable comments which helped to improve the presentation of the paper.

Compliance with ethical standards

Conflict of interest

Mariem Ben Salem declares that she has no conflict of interest. Dr. Raouia Taktak declares that she has no conflict of interest. Prof. Dr. A. Ridha Mahjoub declares that he has no conflict of interest. Prof. Dr. Hanêne Ben-Abdallah declares that she has no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.FSEGS/MIRACL, Université de SfaxSfaxTunisia
  2. 2.ISIMS/CRNS, Université de SfaxSfaxTunisia
  3. 3.Université Paris-Dauphine, PSL Research University, CNRS, LAMSADEParisFrance
  4. 4.King Abdulaziz UniversityJeddahSaudi Arabia

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