Statistical testing of optimality conditions in multiresponse simulation-based optimization

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

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.
Original languageEnglish
Pages (from-to)448-458
JournalEuropean Journal of Operational Research
Volume199
Issue number2
Publication statusPublished - 2009

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Simulation-based Optimization
Optimality Conditions
First-order Optimality Conditions
Heuristic Optimization
Testing
t-test
Output
Random Function
Bootstrapping
Small Sample Size
Resampling
Simulation Model
Objective function
Gradient
Methodology
Simulation
Statistical testing
Optimality conditions
Sample size
Empirical results

Cite this

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title = "Statistical testing of optimality conditions in multiresponse simulation-based optimization",
abstract = "This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.",
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Statistical testing of optimality conditions in multiresponse simulation-based optimization. / Bettonvil, B.W.M.; Del Castillo, E.; Kleijnen, J.P.C.

In: European Journal of Operational Research, Vol. 199, No. 2, 2009, p. 448-458.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Statistical testing of optimality conditions in multiresponse simulation-based optimization

AU - Bettonvil, B.W.M.

AU - Del Castillo, E.

AU - Kleijnen, J.P.C.

N1 - Appeared earlier as CentER DP 2007-45

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N2 - This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.

AB - This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.

M3 - Article

VL - 199

SP - 448

EP - 458

JO - European Journal of Operational Research

JF - European Journal of Operational Research

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