We consider the problem of finding a set of feasible or near-feasible systems among a finite number of simulated systems in the presence of stochastic constraints. When the constraints are subjective, a decision maker may want to test multiple threshold values for the constraints. Or the decision maker may simply want to determine how a set of feasible systems changes as constraints become more strict with the objective of pruning systems or finding the system with the best performance. When only the constraint thresholds change for the same set of underlying systems, it is natural to reuse observations collected from the feasibility check with a different threshold value. We present an indifference-zone procedure that recycles observations and provide an overall probability of correct decision for all threshold values. Our numerical experiments show that the proposed procedure performs well in reducing the required number of observations while providing a statistical guarantee on the probability of correct decision. Summary of Contribution: We consider the problem of determining the feasibility of a finite number of systems in the presence of subjective constraints on performance measures that can be estimated only by stochastic simulation. Specifically, our work focuses on the situation where the decision maker is willing to relax some constraint thresholds if necessary to achieve feasibility. Also, we discuss how our proposed procedures can help select the best system in the presence of multiple objectives. This is the first work that considers subjective constraints in the field of ranking and selection in simulation and it provides a practically useful decision-making tool with more flexibility on feasibility determination. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.1227 .

We propose an asymptotically optimal set (AOS) approach for solving stochastic optimization problems with discrete or continuous feasible regions. Our AOS approach is a framework for designing provably convergent algorithms that are adaptive in seeking new points and in resampling or discarding already sampled points. The framework is an improvement over the adaptive search with resampling (ASR) method for stochastic optimization in that it spends less effort on inferior points and uses a more robust estimate of the optimal solution. We present conditions guaranteeing that the AOS approach is globally convergent and will eventually discard suboptimal sampled points with probability one, compare the algorithms, and analyze when (additional) resampling (beyond the minimum) is desirable. Our theoretical results show that AOS has stronger performance guarantees than ASR. Our numerical results suggest that AOS makes substantial improvements over ASR, especially for difficult problems with large numbers of local optima. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0811 .

The replicated batch means (RBM) method for steady-state simulation output analysis generalizes both the independent replications (IR) and batch means (BM) methods. We analyze the performance of RBM in situations where the underlying stochastic process possesses an additive initial transient. Our analysis differs from prior work in that the initial transient is stochastic, and hence the sample paths of the transient process may be replication dependent, and possibly also correlated across replications. We provide asymptotic expressions for the mean and variance of the RBM estimators of the steady-state mean and variance parameter of the stochastic process being simulated. We then use our results to study the performance of RBM as a function of the number of replications, initialization method for the replications, and decay rate of the associated initialization bias. Our results provide guidance on when IR, BM, or a combination thereof is the best choice, and also on effective choices of initial states for the replications.

We discuss desirable features that optimization algorithms should possess to exhibit good empirical performance when applied to solve simulation optimization problems possessing little known structure. Our framework emphasizes maintaining an appropriate balance between exploration, exploitation, and estimation. With the exception of estimation, our ideas are also applicable in (unstructured) deterministic optimization. Exploration refers to (globally) searching the entire feasible region for promising solutions, exploitation refers to the (local) search for improved solutions in promising subregions, and estimation refers to obtaining enhanced estimates of the objective function values at promising solutions and of the optimal solution. We also present two new random search methods that possess these desirable features, prove their almost-sure global convergence, and provide preliminary numerical results that suggest that the proposed framework is promising from a practical point of view.

In decision analysis, it is frequently necessary to obtain reasonably precise estimates of unknown quantities, including both probabilities and utilities. Decomposition is often used for this purpose, under the assumption that it is preferable to direct elicitation. In this context, decomposition involves estimating the conditional means of the quantity of interest for a finite number of conditioning events, and weighting the means by the estimated probabilities of these events. We propose a model for how the precision of estimates obtained using decomposition depends on the choice of conditioning events. A novel feature of this model is that it captures how the choice of conditioning events influences both the conditional means and the conditional variances simultaneously. This makes it possible to characterize not only when decomposition is preferable to direct elicitation, but also when highly informative decompositions are preferred to less informative ones. Intuitive explanations of these results are provided. In addition, when the estimated probabilities of the conditioning events are reasonably precise, our results are consistent with conventional wisdom in decision analysis, and bear strong similarity to results on the construction of strata in stratified sampling.