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

Author

Listed:
  • Bettonvil, B.W.M.

    (Tilburg University, Center For Economic Research)

  • Del Castillo, E.
  • Kleijnen, J.P.C.

    (Tilburg University, Center For Economic Research)

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.

Suggested Citation

  • 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)," Discussion Paper 2007-45, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:3e563d88-0029-47f6-a66b-ed001f03a5fb
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    File URL: https://pure.uvt.nl/portal/files/844392/dp2007-45.pdf
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    References listed on IDEAS

    as
    1. Acácio M. De O. Porta Nova & James R. Wilson, 1989. "Estimation of Multiresponse Simulation Metamodels Using Control Variates," Management Science, INFORMS, pages 1316-1333.
    2. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    3. Martin, Michael A., 2007. "Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties," Computational Statistics & Data Analysis, Elsevier, pages 6321-6342.
    4. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, pages 243-256.
    5. Kleijnen, Jack P. C. & van Beers, Wim C. M., 2005. "Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments," European Journal of Operational Research, Elsevier, vol. 165(3), pages 826-834, September.
    6. Kao, Chiang & Chen, Shih-Pin, 2006. "A stochastic quasi-Newton method for simulation response optimization," European Journal of Operational Research, Elsevier, vol. 173(1), pages 30-46, August.
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    More about this item

    Keywords

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

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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