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Robust optimisation of unconstrained binary quadratic problems

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  • Mark Lewis
  • John Metcalfe
  • Gary Kochenberger

Abstract

In this paper we focus on the unconstrained binary quadratic optimisation model, maximise xtQx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix. We are motivated to find robust, or stable, solutions because of the uncertainty inherent in the big data origins of Q and limitations in computer numerical precision, particularly in a new class of quantum annealing computers. Experimental design techniques are used to generate a diverse subset of possible scenarios, from which robust solutions are identified. An illustrative example with practical application to business decision making is examined. The approach presented also generates a surface response equation which is used to estimate upper bounds in constant time for Q instantiations within the scenario extremes. In addition, a theoretical framework for the robustness of individual xi variables is considered by examining the range of Q values over which the xi are predetermined.

Suggested Citation

  • Mark Lewis & John Metcalfe & Gary Kochenberger, 2019. "Robust optimisation of unconstrained binary quadratic problems," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 36(4), pages 441-454.
    • Handle: RePEc:ids:ijores:v:36:y:2019:i:4:p:441-454
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    Cited by:

    1. Ricardo N. Liang & Eduardo A. J. Anacleto & Cláudio N. Meneses, 2022. "Data structures for speeding up Tabu Search when solving sparse quadratic unconstrained binary optimization problems," Journal of Heuristics, Springer, vol. 28(4), pages 433-479, August.

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