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On exact solution approaches for bilevel quadratic 0–1 knapsack problem

Author

Listed:
  • Gabriel Lopez Zenarosa

    (UNC Charlotte)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

  • Eduardo L. Pasiliao

    (AFRL Munitions Directorate)

Abstract

We consider the bilevel quadratic knapsack problem (BQKP) that model settings where a leader appropriates a budget for a follower, who solves a quadratic 0–1 knapsack problem. BQKP generalizes the bilevel knapsack problem introduced by Dempe and Richter (Cent Eur J Oper Res 8(2):93–107, 2000), where the follower solves a linear 0–1 knapsack problem. We present an exact-solution approach for BQKP based on extensions of dynamic programs for QKP bounds and the branch-and-backtrack algorithm. We compare our approach against a two-phase method computed using an optimization solver in both phases: it first computes the follower’s value function for all feasible leader’s decisions, and then solves a single-level, value-function reformulation of BQKP as a mixed-integer quadratically constrained program. Our computational experiments show that our approach for solving BQKP outperforms the two-phase method computed by a commercial state-of-the-art optimization software package.

Suggested Citation

  • Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    • Handle: RePEc:spr:annopr:v:298:y:2021:i:1:d:10.1007_s10479-018-2970-4
    DOI: 10.1007/s10479-018-2970-4
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    References listed on IDEAS

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