Polynomial-size formulations and relaxations for the quadratic multiple knapsack problem

Laura Galli, Silvano Martello, Carlos Rey and Paolo Toth

European Journal of Operational Research, 2021, vol. 291, issue 3, 871-882

Abstract: The Quadratic Multiple Knapsack Problem generalizes, simultaneously, two well-known combinatorial optimization problems that have been intensively studied in the literature: the (single) Quadratic Knapsack Problem and the Multiple Knapsack Problem. The only exact algorithm for its solution uses a formulation based on an exponential-size number of variables, that is solved via a Branch-and-Price algorithm. This work studies polynomial-size formulations and upper bounds. We derive linear models from classical reformulations of 0-1 quadratic programs and analyze theoretical properties and dominances among them. We define surrogate and Lagrangian relaxations, and we compare the effectiveness of the Lagrangian relaxation when applied to a quadratic formulation and to a Level 1 reformulation linearization that leads to a decomposable structure. The proposed methods are evaluated through extensive computational experiments.

Keywords: Combinatorial optimization; Quadratic multiple knapsack; Binary quadratic programming; Lagrangian relaxation; Reformulation linearization technique (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:291:y:2021:i:3:p:871-882

DOI: 10.1016/j.ejor.2020.10.047

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