Regression and Kriging metamodels with their experimental designs in simulation: A review

This article reviews the design and analysis of simulation experiments. It focusses on analysis via either low-order polynomial regression or Kriging (also known as Gaussian process) metamodels. The type of metamodel determines the design of the experiment, which determines the input combinations of the simulation experiment. For example, a first-order polynomial metamodel requires a "resolution-III" design, whereas Kriging may use Latin hypercube sampling. Polynomials of first or second order require resolution III, IV, V, or "central composite" designs. Before applying either regression or Kriging, sequential bifurcation may be applied to screen a great many inputs. Optimization of the simulated system may use either a sequence of low-order polynomials known as response surface methodology (RSM) or Kriging models fitted through sequential designs including efficient global optimization (EGO). The review includes robust optimization, which accounts for uncertain simulation inputs.

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Regression and Kriging Metamodels with Their Experimental Designs in Simulation: Review

An exploratory approach for adaptive policymaking by using multi-objective robust optimization

The growing power of computers enabled techniques created for design and analysis of simulations to be applied to a large spectrum of problems and to reach high level of acceptance among practitioners. Generally, when simulations are time consuming, a surrogate model replaces the computer code in further studies (e.g., optimization, sensitivity analysis, etc.). The first step for a successful surrogate modeling and statistical analysis is the planning of the input configuration that is used to exercise the simulation code. Among the strategies devised for computer experiments, Latin hypercube designs have become particularly popular. This paper provides a tutorial on Latin hypercube design of experiments, highlighting potential reasons of its widespread use. The discussion starts with the early developments in optimization of the point selection and goes all the way to the pitfalls of the indiscriminate use of Latin hypercube designs. Final thoughts are given on opportunities for future research. Copyright © 2015 John Wiley & Sons, Ltd.

A Tutorial on Latin Hypercube Design of Experiments

Estimating quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res.57 118--130) derived a batched infinitesimal perturbation analysis estimator for quantile sensitivities, and Liu and Hong (Liu, G., L. J. Hong. 2009. Kernel estimation of quantile sensitivities. Naval Res. Logist.56 511--525) derived a kernel estimator. Both of these estimators are consistent with convergence rates bounded by n-1/3 and n-2/5, respectively. In this paper, we use conditional Monte Carlo to derive a consistent quantile sensitivity estimator that improves upon these convergence rates and requires no batching or binning. We illustrate the new estimator using a simple but realistic portfolio credit risk example, for which the previous work is inapplicable.

https://www.jstor.org/stable/pdfplus/40539262.pdf

Jin Zhang

Papers

Methodology for determining the acceptability of system designs in uncertain environments