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

Gabriel Lopez Zenarosa, Oleg A. Prokopyev () and Eduardo L. Pasiliao
Additional contact information
Gabriel Lopez Zenarosa: UNC Charlotte
Oleg A. Prokopyev: University of Pittsburgh
Eduardo L. Pasiliao: AFRL Munitions Directorate

Annals of Operations Research, 2021, vol. 298, issue 1, No 25, 555-572

Abstract: 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.

Keywords: Bilevel programming; Bilevel knapsack problem; Quadratic knapsack problem; Dynamic programming; 90C20; 90C27; 90C39; 90C57 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-018-2970-4

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