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Computational Comparison of Exact Solution Methods for 0‐1 Quadratic Programs: Recommendations for Practitioners

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  • Richard J. Forrester
  • Noah Hunt-Isaak

Abstract

This paper is concerned with binary quadratic programs (BQPs), which are among the most well‐studied classes of nonlinear integer optimization problems because of their wide variety of applications. While a number of different solution approaches have been proposed for tackling BQPs, practitioners need techniques that are both efficient and easy to implement. We revisit two of the most widely used linearization strategies for BQPs and examine the effectiveness of enhancements to these formulations that have been suggested in the literature. We perform a detailed large‐scale computational study over five different classes of BQPs to compare these two linearizations with a more recent linear reformulation and direct submission of the nonlinear integer program to an optimization solver. The goal is to provide practitioners with guidance on how to best approach solving BQPs in an effective and easily implemented manner.

Suggested Citation

  • Richard J. Forrester & Noah Hunt-Isaak, 2020. "Computational Comparison of Exact Solution Methods for 0‐1 Quadratic Programs: Recommendations for Practitioners," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:5974820
    DOI: 10.1155/2020/5974820
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    References listed on IDEAS

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    1. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    2. Richard J. Forrester & Warren P. Adams & Paul T. Hadavas, 2010. "Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 1-12, February.
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