Optimization algorithms for the disjunctively constrained knapsack problem
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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.
KeywordsKnapsack problem Disjunctive constraints Polytope Facet Separation Branch-and-cut
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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