The simulation optimization problems refer to the nonlinear optimization problems whose objective function can be evaluated through stochastic simulations. Two important discrete simulation optimization problems are studied in this thesis: Ranking and Selection (R&S) and Factor Screening (FS). Both RS and FS are the “selection” problems that are defined on a finite set of candidate systems or factors. They vary mainly in their objectives: the RS problems is to find the “best” system(s) among all alternatives; whereas the FS is to select important factors that are critical to the stochastic systems.

 

For the R&S problem, we propose a fully sequential procedure for selecting the “best” systems with a guaranteed probability of correct selection (PCS). The main features of the proposed procedure are: (1) a Bonferroni-free model, the proposed frameworks overcome the conservativeness of the Bonferroni correction and deliver the exact probabilistic guarantee without overshooting; (2) asymptotic optimality, the first framework achieves the lower bound of average sample size asymptotically; (3) an indifference-zone-flexible formulation, the new formulation bridges the gap between the indifference-zone formulation and the indifference-zone-free formulation so that the indifference-zone parameter is not indispensable but could be helpful if provided; (4) adaptive implementations, the frameworks can be adopted to various assumptions on underlying distributions. We establish the validity and asymptotic efficiency for the proposed procedure and conduct numerical studies to investigates the efficiency under various configurations.

 

We also consider the multi-objective R&S (MOR&S) problem. To the best of our knowledge, the procedure proposed is the first frequentist approach for MOR&S. The newly proposed procedure identifies the Pareto front with a guaranteed probability of correct selection (PCS). In particular, the proposed procedure is fully sequential using the test statistics built upon the generalized sequential probability ratio test (GSPRT). The main features of the new proposed procedure are: 1) a dimension-free model, the performance of the new procedure does not deteriorate as the number of objectives increases, and achieves the same efficiency as KN family procedures for single-objective ranking and selection; 2) an indifference-zone-flexible formulation, the new procedure eliminates the necessity of indifference-zone parameter while makes use of the it if provided. A numerical evaluation demonstrates the validity efficiency of the new procedure.

 

For the FS problem, our objective is to identify important factors for simulation experiments with controlled Family-Wise Error Rate. We assume a Multi-Objective first-order linear model where the responses follow a multivariate normal distribution. We propose three fully sequential procedures: Sum Intersection Procedure (SUMIP), Sort Intersection Procedure (SORTIP), and Mixed Intersection procedure (MIP). SUMIP uses the Bonferroni correction to adjust for multiple comparison; SORTIP uses the Holms procedure to overcome the conservative of the Bonferroni method; and MIP combines both SUMIP and SORTIP to form a procedure that work efficiently in parallel computing environment.