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

Listed author(s):
  • Bettonvil, B.W.M.

    (Tilburg University, Center For Economic Research)

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

    (Tilburg University, Center For Economic Research)

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.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-45.

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Date of creation: 2007
Handle: RePEc:tiu:tiucen:3e563d88-0029-47f6-a66b-ed001f03a5fb
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  1. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
  2. 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, vol. 51(12), pages 6321-6342, August.
  3. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
  4. 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.
  5. 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.
  6. Acácio M. De O. Porta Nova & James R. Wilson, 1989. "Estimation of Multiresponse Simulation Metamodels Using Control Variates," Management Science, INFORMS, vol. 35(11), pages 1316-1333, November.
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