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Polynomial-size formulations and relaxations for the quadratic multiple knapsack problem
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DOI：10.1016/j.ejor.2020.10.047.png)
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Abstract
En 中文
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. (C) 2020 Elsevier B.V. All rights reserved.
Keywords:
Combinatorial optimization
Quadratic multiple knapsack
Binary quadratic programming
Lagrangian relaxation
Reformulation linearization technique
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