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Improved row-by-row method for binary quadratic optimization problems

Author

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  • Rupaj Kumar Nayak

    (International Institute of Information Technology)

  • Nirmalya Kumar Mohanty

    (International Institute of Information Technology)

Abstract

The research presented here is an improved row-by-row (RBR) algorithm for the solution of boolean quadratic programming (BQP) problems. While a faster and implementable RBR method has been widely used for semidefinite programming (SDP) relaxed BQPs, it can be challenged by SDP relaxations because of the fact that it produce a tighter lower bounds than RBR on BQPs. On the other hand, solving SDP by interior point method (IPM) is computationally expensive for large scale problems. Departing from IPM, our methods provides better lower bound than the RBR algorithm by Wai et al. (IEEE international conference on acoustics, speech and signal processing ICASSP, 2011) and competitive with SDP solved by IPM. The method includes the SDP cut relaxation on the SDP and is solved by a modified RBR method. The algorithm has been tested on MATLAB platform and applied to several BQPs from BQPLIB (a library by the authors). Numerical experiments show that the proposed method outperform the previous RBR method proposed by several authors and the solution of BQP by IPM as well.

Suggested Citation

  • Rupaj Kumar Nayak & Nirmalya Kumar Mohanty, 2019. "Improved row-by-row method for binary quadratic optimization problems," Annals of Operations Research, Springer, vol. 275(2), pages 587-605, April.
    • Handle: RePEc:spr:annopr:v:275:y:2019:i:2:d:10.1007_s10479-018-2978-9
    DOI: 10.1007/s10479-018-2978-9
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    References listed on IDEAS

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    1. Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.
    2. Rupaj Kumar Nayak & Mahendra Prasad Biswal, 2018. "A low complexity semidefinite relaxation for large-scale MIMO detection," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 473-492, February.
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    Cited by:

    1. Rupaj Kumar Nayak & Nirmalya Kumar Mohanty, 2020. "Solution of boolean quadratic programming problems by two augmented Lagrangian algorithms based on a continuous relaxation," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 792-825, April.

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