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Matheuristics for solving the Multiple Knapsack Problem with Setup

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The knapsack problem is one of the most investigated and applicable combinatorial optimization problems. In this paper we consider a generalized problem called the Multiple Knapsack Problem with Setup (MKPS) in which a set of families of items and a set of knapsacks are available. Each item is characterized by a knapsack-dependent profit and each family is associated with a knapsack-dependent cost. We formally present a mixed-integer linear program of the MKPS and we propose a multi-level matheuristic to solve large size instances of the problem. The matheuristic takes advantage of the structure of the problem and the decomposition principle. Furthermore, we enhance our solution approach combining it with tabu search. We carry out a computational study to assess...

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