Robust Optimization of Unconstrained Binary Quadratic Problems
  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.
