Fully sequential procedures for comparing constrained systems via simulation

Abstract

We consider the problem of finding the system with the best primary performance measure among a finite number of simulated systems in the presence of a stochastic constraint on a single real‐valued secondary performance measure. Solving this problem requires the identification and removal from consideration of infeasible systems (Phase I) and of systems whose primary performance measure is dominated by that of other feasible systems (Phase II). We use indifference zones in both phases and consider two approaches, namely, carrying out Phases I and II sequentially and carrying out Phases I and II simultaneously, and we provide specific example procedures of each type. We present theoretical results guaranteeing that our approaches (general and specific, sequential and simultaneous) yield the best system with at least a prespecified probability, and we provide a portion of an extensive numerical study aimed at evaluating and comparing the performance of our approaches. The experimental results show that both new procedures are useful for constrained ranking and selection, with neither procedure showing uniform superiority over the other.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Optimal Sampling Laws for Stochastically Constrained Simulation Optimization on Finite Sets

“…As illustrated in Table 1, Andradóttir and Kim (2010) provide finitetime guarantees on the probability of false selection for stochastically constrained SO problems and parallels traditional R&S work. Similarly, recent work by Lee et al (2011) provide an asymptotically efficient procedure to solve stochastically constrained SO problems that parallels the previous OCBA work in the unconstrained context.…”

Guessing preferences: A new approach to multi-attribute ranking and selection

“…This work includes Andradóttir, Goldsman, and Kim (2005), Andradóttir and Kim (2010). This use of constraints has been considered by Morrice and Butler (2006), Merrick (2009), which argues that utility functions are a more appropriate way to handle multiple attributes in many applications.…”

Procedures for Feasibility Detection in the Presence of Multiple Constraints

“…Andradóttir, Goldsman, and Kim (2005) present a procedure that detects feasibility of systems in the presence of one constraint with a pre-specified probability of correctness. We extend their procedure to the case of multiple constraints by the use of the Bonferroni inequality.…”

“…As a remedy, we present a screening procedure that uses an aggregated observation, which is a linear combination of the collected observations across stochastic constraints. Then, we present an accelerated procedure that combine the extension of Andradóttir, Goldsman, and Kim (2005) with the procedure that uses aggregated observations. Some experimental results that compare the performance of the proposed procedures are presented.…”

“…However, their methods are either very hard to apply in practice or focused on only a special case. Andradóttir, Goldsman, and Kim (2005) present a R&S procedure that determines the feasibility of a system for one stochastic constraint. This procedure can handle a general stochastic constraint on a secondary performance measure and determines the feasibility of systems in consideration correctly with high probability.…”