Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45)

B.W.M. Bettonvil, E. Del Castillo, Jack P.C. Kleijnen

Research output: Working paperDiscussion paperOther research output

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Abstract

This paper derives a novel procedure for testing the Karush-Kuhn-Tucker (KKT) first-order optimality conditions in models with multiple random responses.Such models arise in simulation-based optimization with multivariate outputs.This paper focuses on expensive simulations, which have small sample sizes.The paper estimates the gradients (in the KKT conditions) through low-order polynomials, fitted locally.These polynomials are estimated using Ordinary Least Squares (OLS), which also enables estimation of the variability of the estimated gradients.Using these OLS results, the paper applies the bootstrap (resampling) method to test the KKT conditions.Furthermore, it applies the classic Student t test to check whether the simulation outputs are feasible, and whether any constraints are binding.The paper applies the new procedure to both a synthetic example and an inventory simulation; the empirical results are encouraging.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages40
Volume2005-81
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-81

Fingerprint

Simulation
Statistical testing
Optimality conditions
Gradient
Ordinary least squares
Polynomials
Sample size
Empirical results
T-test
Resampling methods
Small sample
Testing
Bootstrap

Keywords

  • stopping rule
  • metaheuristics
  • RSM
  • design of experiments

Cite this

Bettonvil, B. W. M., Del Castillo, E., & Kleijnen, J. P. C. (2005). Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45). (CentER Discussion Paper; Vol. 2005-81). Tilburg: Operations research.
Bettonvil, B.W.M. ; Del Castillo, E. ; Kleijnen, Jack P.C. / Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45). Tilburg : Operations research, 2005. (CentER Discussion Paper).
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abstract = "This paper derives a novel procedure for testing the Karush-Kuhn-Tucker (KKT) first-order optimality conditions in models with multiple random responses.Such models arise in simulation-based optimization with multivariate outputs.This paper focuses on expensive simulations, which have small sample sizes.The paper estimates the gradients (in the KKT conditions) through low-order polynomials, fitted locally.These polynomials are estimated using Ordinary Least Squares (OLS), which also enables estimation of the variability of the estimated gradients.Using these OLS results, the paper applies the bootstrap (resampling) method to test the KKT conditions.Furthermore, it applies the classic Student t test to check whether the simulation outputs are feasible, and whether any constraints are binding.The paper applies the new procedure to both a synthetic example and an inventory simulation; the empirical results are encouraging.",
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Bettonvil, BWM, Del Castillo, E & Kleijnen, JPC 2005 'Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45)' CentER Discussion Paper, vol. 2005-81, Operations research, Tilburg.

Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45). / Bettonvil, B.W.M.; Del Castillo, E.; Kleijnen, Jack P.C.

Tilburg : Operations research, 2005. (CentER Discussion Paper; Vol. 2005-81).

Research output: Working paperDiscussion paperOther research output

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T1 - Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45)

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AB - This paper derives a novel procedure for testing the Karush-Kuhn-Tucker (KKT) first-order optimality conditions in models with multiple random responses.Such models arise in simulation-based optimization with multivariate outputs.This paper focuses on expensive simulations, which have small sample sizes.The paper estimates the gradients (in the KKT conditions) through low-order polynomials, fitted locally.These polynomials are estimated using Ordinary Least Squares (OLS), which also enables estimation of the variability of the estimated gradients.Using these OLS results, the paper applies the bootstrap (resampling) method to test the KKT conditions.Furthermore, it applies the classic Student t test to check whether the simulation outputs are feasible, and whether any constraints are binding.The paper applies the new procedure to both a synthetic example and an inventory simulation; the empirical results are encouraging.

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PB - Operations research

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