Statistical Testing of Optimality Conditions in Multiresponse Simulation-based Optimization (Revision of 2005-81)

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

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Abstract

This paper 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 test- ing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush-Kuhn-Tucker (KKT) first-order optimality conditions. The pa- per focuses on "expensive" simulations, which have small sample sizes. The paper applies the classic t test to check whether the specific input combination is feasi- ble, and whether any constraints are binding; 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
Place of PublicationTilburg
PublisherOperations research
Number of pages31
Volume2007-45
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-45

Keywords

  • Stopping rule
  • metaheuristics
  • response surface methodology
  • design of experiments

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    Bettonvil, B. W. M., Del Castillo, E., & Kleijnen, J. P. C. (2007). Statistical Testing of Optimality Conditions in Multiresponse Simulation-based Optimization (Revision of 2005-81). (CentER Discussion Paper; Vol. 2007-45). Operations research.