Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations

Abstract

Monotonicity-preserving bootstrapped kriging metamodels for expensive simulationsKleijnen, J.P.C.; van Beers, W.C.M. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Kriging metamodels (also called Gaussian process or spatial correlation models) approximate the Input/ Output functions implied by the underlying simulation models. Such metamodels serve sensitivity analysis, especially for computationally expensive simulations. In practice, simulation analysts often know that this Input/Output function is monotonic. To obtain a Kriging metamodel that preserves this characteristic, this article uses distribution-free bootstrapping assuming each input combination is simulated several times to obtain more reliable averaged outputs. Nevertheless, these averages still show sampling variation, so the Kriging metamodel does not need to be an exact interpolator; bootstrapping gives a noninterpolating Kriging metamodel. Bootstrapping may use standard Kriging software. The method is illustrated through the popular M/M/1 model with either the mean or the 90% quantile as output; these outputs are monotonic functions of the traffic rate. The empirical results demonstrate that monotonicity-preserving bootstrapped Kriging gives higher probability of covering the true outputs, without lengthening the confidence interval.

Gaussian Process Emulators for Computer Experiments with Inequality Constraints

“…In this framework, constrained Kriging has been studied in the domain of geostatistics (see e.g. [13] and [21]). In previous work, some methodologies have been based on the knowledge of the derivatives of the GP at some input locations (see e.g.…”

An interactive surrogate-based method for computationally expensive multiobjective optimisation

“…See Miettinen (2008), Miettinen, Ruiz, and Wierzbicki (2008) for details of non-interactive and interactive methods. Surrogate-based methods are commonly used in the literature to alleviate computational cost (Jones, 2001;Regis & Shoemaker, 2012;Audet, 2014;Tan, 2015;Dengiz et al, 2009;Chih, 2013;Reis dos Santos & Reis dos Santos, 2011;Hurrion, 2000;Kleijnen & van Beers, 2013;Van Beers & Kleijnen, 2003;Yang & Tseng, 2002;Mehdad & Kleijnen, 2015;Park, Yum, Hung, Jeong, & Jeong, 2016). The basic idea in such methods is to introduce a computationally less expensive problem called a surrogate problem and to replace the original problem with the surrogate one.…”

Kriging of financial term-structures

“…Recently, some authors have studied the integration of monotonicity constraints into Gaussian process emulators, see e.g. Golchi et al (2015) and Kleijnen and Van Beers (2012). However, these methods do not guaranty monotonicity constraints in the entire domain.…”