Advancing Constrained Ranking and Selection With Regression in Partitioned Domains

Ranking and selection (R&S) procedures are powerful tools to enhance the efficiency of simulation-based optimization. In this paper, we consider the R&S problem subject to stochastic constraints and seek to improve the selection efficiency by incorporating the information from across the domain into quadratic regression metamodels. To better fulfill the quadratic assumption of the regression metamodel used in this paper, we divide the solution space into adjacent partitions such that the underlying functions of both the objective and constraint measures in each partition are approximately quadratic with homogeneous noise. Using the large deviations theory, we characterize the asymptotically optimal allocation rule by maximizing the rate at which the probability of false selection tends to zero. Numerical experiments demonstrate that our approach dramatically improves the selection efficiency by 50%-90% on some typical selection examples compared with the existing approaches.