Robust Optimization of Unconstrained Binary Quadratic Problems

Mark Lewis; Gary Kochenberger; John Metcalfe

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arXiv · 1709.07511

Robust Optimization of Unconstrained Binary Quadratic Problems

Mark Lewis·Gary Kochenberger·John Metcalfe

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Abstract

In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, 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 x_i variables is considered by examining the range of Q values over which the x_i are predetermined.

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Mark Lewis, Gary Kochenberger, John Metcalfe. 2017-09-21. Robust Optimization of Unconstrained Binary Quadratic Problems. https://arxiv.org/abs/1709.07511

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