Efficient simulation budget allocation with regression

Simulation can be a very powerful tool to help decision making in many applications; however, exploring multiple courses of actions can be time consuming. Numerous Ranking & Selection (R&S) procedures have been developed to enhance the simulation efficiency of finding the best design. This article explores the potential of further enhancing R&S efficiency by incorporating simulation information from across the domain into a regression metamodel. This article assumes that the underlying function to be optimized is one-dimensional as well as approximately quadratic or piecewise quadratic. Under some common conditions in most regression-based approaches, the proposed method provides approximations of the optimal rules that determine the design locations to conduct simulation runs and the number of samples allocated to each design location. Numerical experiments demonstrate that the proposed approach can dramatically enhance efficiency over existing efficient R&S methods and can obtain significant savings over regression-based methods. In addition to utilizing concepts from the Design Of Experiments (DOE) literature, it introduces the probability of correct selection optimality criterion that underpins our new R&S method to the DOE literature.