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A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem

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  • Lamanna, Leonardo
  • Mansini, Renata
  • Zanotti, Roberto

Abstract

The Multidimensional Multiple-choice Knapsack Problem (MMKP) is a complex combinatorial optimization problem for which finding high quality feasible solutions is very challenging. Recently, several heuristic approaches and a few exact algorithms have been proposed for its solution. These methods have been able to provide new best-known values for benchmark instances although many of them still remain unclosed to optimality. In this paper, we provide a new variant of the heuristic framework Kernel Search and apply it to the MMKP. The proposed variant keeps the method’s main idea of solving a sequence of restricted mixed-integer subproblems but innovates by partitioning the solution process into two different phases with complementary goals. The first phase strives for feasibility and collects important information to dynamically adapt subproblems’ dimension and solution time in the second phase that is focused on getting high quality solutions. This makes the global approach more scalable and efficient.

Suggested Citation

  • Lamanna, Leonardo & Mansini, Renata & Zanotti, Roberto, 2022. "A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 53-65.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:1:p:53-65
    DOI: 10.1016/j.ejor.2021.05.007
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    References listed on IDEAS

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