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Constrained optimization in expensive simulation: Novel approach

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  • Kleijnen, Jack P.C.
  • Beers, Wim van
  • Nieuwenhuyse, Inneke van

Abstract

This article presents a novel heuristic for constrained optimization of computationally expensive random simulation models. One output is selected as objective to be minimized, while other outputs must satisfy given threshold values. Moreover, the simulation inputs must be integer and satisfy linear or nonlinear constraints. The heuristic combines (i) sequentialized experimental designs to specify the simulation input combinations, (ii) Kriging (or Gaussian process or spatial correlation modeling) to analyze the global simulation input/output data resulting from these designs, and (iii) integer nonlinear programming to estimate the optimal solution from the Kriging metamodels. The heuristic is applied to an (s,S) inventory system and a call-center simulation, and compared with the popular commercial heuristic OptQuest embedded in the Arena versions 11 and 12. In these two applications the novel heuristic outperforms OptQuest in terms of number of simulated input combinations and quality of the estimated optimum.

Suggested Citation

  • Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.
  • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:164-174
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    References listed on IDEAS

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    1. Kleijnen, Jack P.C. & Deflandre, David, 2006. "Validation of regression metamodels in simulation: Bootstrap approach," European Journal of Operational Research, Elsevier, vol. 170(1), pages 120-131, April.
    2. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
    3. Mehmet Tolga Cezik & Pierre L'Ecuyer, 2008. "Staffing Multiskill Call Centers via Linear Programming and Simulation," Management Science, INFORMS, vol. 54(2), pages 310-323, February.
    4. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    5. Kleijnen, Jack P. C. & den Hertog, Dick & Angun, Ebru, 2004. "Response surface methodology's steepest ascent and step size revisited," European Journal of Operational Research, Elsevier, vol. 159(1), pages 121-131, November.
    6. van Beers, Wim C.M. & Kleijnen, Jack P.C., 2008. "Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1099-1113, May.
    7. 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.
    8. Angun, M.E. & Gürkan, G. & den Hertog, D. & Kleijnen, J.P.C., 2002. "Response surface methodology revisited," Other publications TiSEM 32c35a04-3de9-4dee-a242-6, Tilburg University, School of Economics and Management.
    9. Driessen, L. & Brekelmans, R.C.M. & Gerichhausen, M. & Hamers, H.J.M. & den Hertog, D., 2006. "Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models," Discussion Paper 2006-4, Tilburg University, Center for Economic Research.
    10. Jürgen Branke & Stephen E. Chick & Christian Schmidt, 2007. "Selecting a Selection Procedure," Management Science, INFORMS, vol. 53(12), pages 1916-1932, December.
    11. Júlíus Atlason & Marina A. Epelman & Shane G. Henderson, 2008. "Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods," Management Science, INFORMS, vol. 54(2), pages 295-309, February.
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    Citations

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    Cited by:

    1. Kleijnen, Jack P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2011. "Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging - Replaces CentER DP 2010-62," Discussion Paper 2011-015, Tilburg University, Center for Economic Research.
    2. Fani Boukouvala & M. M. Faruque Hasan & Christodoulos A. Floudas, 2017. "Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption," Journal of Global Optimization, Springer, vol. 67(1), pages 3-42, January.
    3. Kleijnen, Jack P.C. & Mehdad, E., 2012. "Kriging in Multi-response Simulation, including a Monte Carlo Laboratory (Replaced by 2014-012)," Discussion Paper 2012-039, Tilburg University, Center for Economic Research.
    4. Arreola-Risa, Antonio & Giménez-García, Víctor M. & Martínez-Parra, José Luis, 2011. "Optimizing stochastic production-inventory systems: A heuristic based on simulation and regression analysis," European Journal of Operational Research, Elsevier, vol. 213(1), pages 107-118, August.
    5. Hernandez, Andres F. & Grover, Martha A., 2013. "Error estimation properties of Gaussian process models in stochastic simulations," European Journal of Operational Research, Elsevier, vol. 228(1), pages 131-140.
    6. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Discussion Paper 2013-064, Tilburg University, Center for Economic Research.
    7. Tsai, Shing Chih & Fu, Sheng Yang, 2014. "Genetic-algorithm-based simulation optimization considering a single stochastic constraint," European Journal of Operational Research, Elsevier, vol. 236(1), pages 113-125.
    8. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.
    9. Kabirian, Alireza & Ólafsson, Sigurdur, 2011. "Continuous optimization via simulation using Golden Region search," European Journal of Operational Research, Elsevier, vol. 208(1), pages 19-27, January.
    10. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    11. repec:eee:ejores:v:262:y:2017:i:2:p:673-681 is not listed on IDEAS
    12. Kleijnen, Jack P.C. & Mehdad, E., 2014. "Multivariate Versus Univariate Kriging Metamodels for Multi-Response Simulation Models (Revision of 2012-039)," Discussion Paper 2014-012, Tilburg University, Center for Economic Research.
    13. Strang, Kenneth David, 2012. "Importance of verifying queue model assumptions before planning with simulation software," European Journal of Operational Research, Elsevier, vol. 218(2), pages 493-504.
    14. Kleijnen, Jack P.C. & Mehdad, Ehsan, 2014. "Multivariate versus univariate Kriging metamodels for multi-response simulation models," European Journal of Operational Research, Elsevier, vol. 236(2), pages 573-582.

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