Sequential Procedures for the "Selection" Problems in Discrete Simulation Optimization
thesisposted on 17.10.2019 by Wenyu Wang
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The simulation optimization problems refer to the nonlinear optimization problems whose objective function can be evaluated through stochastic simulations. We study two significant discrete simulation optimization problems in this thesis: Ranking and Selection (R&S) and Factor Screening (FS). Both R&S and FS are the "selection" problems defined upon a finite set of candidate systems or factors. They vary mainly in their objectives: the R&S 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.
In this thesis, we develop efficient sequential procedures for these two problems. For the R&S problem, we propose fully-sequential procedures for selecting the "best" systems with a guaranteed probability of correct selection (PCS). The main features of the stated methods are: (1) a Bonferroni-free model, these procedures overcome the conservativeness of the Bonferroni correction and deliver the exact probabilistic guarantee without overshooting; (2) asymptotic optimality, these procedures achieve the lower bound of average sample size asymptotically; (3) an indifference-zone-flexible formulation, these procedures bridge 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. We establish the validity and asymptotic efficiency for the proposed procedure and conduct numerical studies to investigates the performance under multiple 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. These procedures identify the Pareto front with a guaranteed probability of correct selection (PCS). In particular, these procedures are fully sequential using the test statistics built upon the Generalized Sequential Probability Ratio Test (GSPRT). The main features are: 1) an objective-dimension-free model, the performance of these procedures do not deteriorate as the number of objectives increases, and achieve the same efficiency as KN family procedures for single-objective ranking and selection problem; 2) an indifference-zone-flexible formulation, the new methods eliminate the necessity of indifference-zone parameter while makes use of the indifference-zone information 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 offer 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 comparisons; SORTIP uses the Holms procedure to overcome the conservative of the Bonferroni method, and MIP combines both SUMIP and SORTIP to work efficiently in the parallel computing environment. Numerical studies are provided to demonstrate the validity and efficiency, and a case study is presented.