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

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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

Keywords

  • stopping rule
  • metaheuristics
  • RSM
  • design of experiments

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    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). Operations research.