A kriging method for the solution of nonlinear programs with black-box functions

Eddie Davis, Marianthi Ierapetritou

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time.

Original languageEnglish (US)
Pages (from-to)2001-2012
Number of pages12
JournalAIChE Journal
Volume53
Issue number8
DOIs
StatePublished - Aug 1 2007

Fingerprint

Spatial Analysis
Costs and Cost Analysis
Sampling
Costs

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Environmental Engineering
  • Chemical Engineering(all)

Cite this

Davis, Eddie ; Ierapetritou, Marianthi. / A kriging method for the solution of nonlinear programs with black-box functions. In: AIChE Journal. 2007 ; Vol. 53, No. 8. pp. 2001-2012.
@article{255ecaeacb8140c5a879e39b35fd936f,
title = "A kriging method for the solution of nonlinear programs with black-box functions",
abstract = "In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time.",
author = "Eddie Davis and Marianthi Ierapetritou",
year = "2007",
month = "8",
day = "1",
doi = "10.1002/aic.11228",
language = "English (US)",
volume = "53",
pages = "2001--2012",
journal = "AICHE Journal",
issn = "0001-1541",
publisher = "American Institute of Chemical Engineers",
number = "8",

}

A kriging method for the solution of nonlinear programs with black-box functions. / Davis, Eddie; Ierapetritou, Marianthi.

In: AIChE Journal, Vol. 53, No. 8, 01.08.2007, p. 2001-2012.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A kriging method for the solution of nonlinear programs with black-box functions

AU - Davis, Eddie

AU - Ierapetritou, Marianthi

PY - 2007/8/1

Y1 - 2007/8/1

N2 - In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time.

AB - In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time.

UR - http://www.scopus.com/inward/record.url?scp=34547691033&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547691033&partnerID=8YFLogxK

U2 - 10.1002/aic.11228

DO - 10.1002/aic.11228

M3 - Article

AN - SCOPUS:34547691033

VL - 53

SP - 2001

EP - 2012

JO - AICHE Journal

JF - AICHE Journal

SN - 0001-1541

IS - 8

ER -