8 research outputs found
Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget
In stochastic simulation, input uncertainty (IU) is caused by the error in
estimating the input distributions using finite real-world data. When it comes
to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the
failure of many existing selection procedures. In this paper, we study R&S
under IU by allowing the possibility of acquiring additional data. Two
classical R&S formulations are extended to account for IU: (i) for fixed
confidence, we consider when data arrive sequentially so that IU can be reduced
over time; (ii) for fixed budget, a joint budget is assumed to be available for
both collecting input data and running simulations. New procedures are proposed
for each formulation using the frameworks of Sequential Elimination and Optimal
Computing Budget Allocation, with theoretical guarantees provided accordingly
(e.g., upper bound on the expected running time and finite-sample bound on the
probability of false selection). Numerical results demonstrate the
effectiveness of our procedures through a multi-stage production-inventory
problem
Finite Simulation Budget Allocation for Ranking and Selection
We consider a simulation-based ranking and selection (R&S) problem under a
fixed budget setting. Existing budget allocation procedures focus either on
asymptotic optimality or on one-step-ahead allocation efficiency. Neither of
them depends on the fixed simulation budget, the ignorance of which could lead
to an inefficient allocation, especially when the simulation budget is finite.
In light of this, we develop a finite-budget allocation rule that is adaptive
to the simulation budget. Theoretical results show that the budget allocation
strategies are distinctively different between a finite budget and a
sufficiently large budget. Our proposed allocation rule can dynamically
determine the ratio of budget allocated to designs according to different
simulation budget and is optimal when the simulation budget goes to infinity,
indicating it not only possesses desirable finite-budget properties but also
achieves asymptotic optimality. Based on the proposed allocation rule, two
efficient finite simulation budget allocation algorithms are developed. In the
numerical experiments, we use both synthetic examples and a case study to show
the superior efficiency of our proposed allocation rule
Selection of the Most Probable Best
We consider an expected-value ranking and selection problem where all k
solutions' simulation outputs depend on a common uncertain input model. Given
that the uncertainty of the input model is captured by a probability simplex on
a finite support, we define the most probable best (MPB) to be the solution
whose probability of being optimal is the largest. To devise an efficient
sampling algorithm to find the MPB, we first derive a lower bound to the large
deviation rate of the probability of falsely selecting the MPB, then formulate
an optimal computing budget allocation (OCBA) problem to find the optimal
static sampling ratios for all solution-input model pairs that maximize the
lower bound. We devise a series of sequential algorithms that apply
interpretable and computationally efficient sampling rules and prove their
sampling ratios achieve the optimality conditions for the OCBA problem as the
simulation budget increases. The algorithms are benchmarked against a
state-of-the-art sequential sampling algorithm designed for contextual ranking
and selection problems and demonstrated to have superior empirical performances
at finding the MPB