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This paper studies the allocation of simulation effort in a ranking-and-selection (R&S) problem with the goal of selecting a system whose performance is within a given tolerance of the best. We apply large-deviations theory to derive an optimal allocation for maximizing the rate at which the so-called probability of good selection (PGS) asymptotically approaches one, assuming that systems’ output distributions are known. An interesting property of the optimal allocation is that some good systems may receive a sampling ratio of zero. We demonstrate through numerical experiments that this property leads to serious practical consequences, specifically when designing adaptive R&S algorithms. In particular, we observe that the convergence and even consistency of a simple plug-in algorithm designed for the PGS goal can be negatively impacted. We offer empirical evidence of these challenges and a preliminary exploration of a potential correction. 

Screening procedures for ranking and selection have received less attention than selection procedures, yet they serve as a cheap and powerful tool for decision making under uncertainty. Research on screening procedures has been less active in recent years, just as the advent of parallel computing has dramatically reshaped how selection procedures are designed and implemented. As a result, screening procedures used in modern practice continue to largely operate offline on fixed data. In this tutorial, we provide an overview of screening procedures with the goal of clarifying the current state of research and laying out opportunities for future development. We discuss several guarantees delivered by screening procedures and their role in different decision-making settings and investigate their impact on screening power and sampling efficiency in numerical experiments. We also study the implementation of screening procedures in parallel computing environments and how they can be combined with selection procedures. 

Stochastic constraints, which constrain an expectation in the context of simulation optimization, can be hard to conceptualize and harder still to assess. As with a deterministic constraint, a solution is considered either feasible or infeasible with respect to a stochastic constraint. This perspective belies the subjective nature of stochastic constraints, which often arise when attempting to avoid alternative optimization formulations with multiple objectives or an aggregate objective with weights. Moreover, a solution’s feasibility with respect to a stochastic constraint cannot, in general, be ascertained based on only a finite number of simulation replications. We introduce different means of estimating how “close” the expected performance of a given solution is to being feasible with respect to one or more stochastic constraints. We explore how these metrics and their bootstrapped error estimates can be incorporated into plots showing a solver’s progress over time when solving a stochastically constrained problem. 

Simulation optimization involves optimizing some objective function that can only be estimated via stochastic simulation. Many important problems can be profitably viewed within this framework. Whereas many solvers—implementations of simulation-optimization algorithms—exist or are in development, comparisons among solvers are not standardized and are often limited in scope. Such comparisons help advance solver development, clarify the relative performance of solvers, and identify classes of problems that defy efficient solution, among many other uses. We develop performance measures and plots, and estimators thereof, to evaluate and compare solvers and diagnose their strengths and weaknesses on a testbed of simulation-optimization problems. We explain the need for two-level simulation in this context and provide supporting convergence theory. We also describe how to use bootstrapping to obtain error estimates for the estimators. History: Accepted by Bruno Tuffin, area editor for simulation. Funding: This work was supported by the National Science Foundation [Grants CMMI-2035086, CMMI-2206972, and TRIPODS+X DMS-1839346]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1261 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.7329235 ].