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A Methodology for Fitting and Validating Metamodels in Simulation

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Author Info

  • Kleijnen, J.P.C.
  • Sargent, R.

    (Tilburg University, Center for Economic Research)

Abstract

This expository paper discusses the relationships among metamodels, simulation models, and problem entities. A metamodel or response surface is an approximation of the input/output function implied by the underlying simulation model. There are several types of metamodel: linear regression, splines, neural networks, etc. This paper distinguishes between fitting and validating a metamodel. Metamodels may have different goals: (i) understanding, (ii) prediction, (iii) optimization, and (iv) verification and validation. For this metamodeling, a process with thirteen steps is proposed. Classic design of experiments (DOE) is summarized, including standard measures of fit such as the R-square coefficient and cross-validation measures. This DOE is extended to sequential or stagewise DOE. Several validation criteria, measures, and estimators are discussed. Metamodels in general are covered, along with a procedure for developing linear regression (including polynomial) metamodels.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1997-116.

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Date of creation: 1997
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Handle: RePEc:dgr:kubcen:1997116

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Web page: http://center.uvt.nl

Related research

Keywords: Simulation; approximation; response surface; modelling; regression;

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References

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  1. Kleijnen, J.P.C., 1995. "Verification and validation of simulation models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-369797, Tilburg University.
  2. Kleijnen, J.P.C., 1992. "Regression metamodels for simulation with common random numbers: Comparison of validation tests and confidence intervals," Open Access publications from Tilburg University urn:nbn:nl:ui:12-369802, Tilburg University.
  3. Kleijnen, J.P.C., 1995. "Case study: Statistical validation of simulation models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-369796, Tilburg University.
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Citations

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Cited by:
  1. Vonk Noordegraaf, Antonie & Nielen, Mirjam & Kleijnen, Jack P. C., 2003. "Sensitivity analysis by experimental design and metamodelling: Case study on simulation in national animal disease control," European Journal of Operational Research, Elsevier, vol. 146(3), pages 433-443, May.
  2. Husslage, B.G.M. & Dam, E.R. van & Hertog, D. den & Stehouwer, H.P. & Stinstra, E., 2003. "Coordination of Coupled Black Box Simulations in the Construction of Metamodels," Discussion Paper 2003-2, Tilburg University, Center for Economic Research.
  3. Graham, Tennille, 2005. "On the Road to Better Management: An investigation into the benefits of managing the impacts of dryland salinity on roads," 2005 Conference (49th), February 9-11, 2005, Coff's Harbour, Australia 137921, Australian Agricultural and Resource Economics Society.
  4. Marrel, Amandine & Iooss, Bertrand & Van Dorpe, Fran├žois & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
  5. Galelli, S. & Gandolfi, C. & Soncini-Sessa, R. & Agostani, D., 2010. "Building a metamodel of an irrigation district distributed-parameter model," Agricultural Water Management, Elsevier, vol. 97(2), pages 187-200, February.
  6. Ekren, Orhan & Ekren, Banu Y. & Ozerdem, Baris, 2009. "Break-even analysis and size optimization of a PV/wind hybrid energy conversion system with battery storage - A case study," Applied Energy, Elsevier, vol. 86(7-8), pages 1043-1054, July.
  7. 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.
  8. Noguera, Jose H. & Watson, Edward F., 2006. "Response surface analysis of a multi-product batch processing facility using a simulation metamodel," International Journal of Production Economics, Elsevier, vol. 102(2), pages 333-343, August.
  9. Wise, Russell M. & Cacho, Oscar J., 2006. "Optimal Land-Use Decisions in the Presence of Carbon Payments and Fertilizer Subsidies: An Indonesian Case Study," 2006 Annual Meeting, August 12-18, 2006, Queensland, Australia 25356, International Association of Agricultural Economists.
  10. van der Gaag, Monique A. & Vos, Fred & Saatkamp, Helmut W. & van Boven, Michiel & van Beek, Paul & Huirne, Ruud B. M., 2004. "A state-transition simulation model for the spread of Salmonella in the pork supply chain," European Journal of Operational Research, Elsevier, vol. 156(3), pages 782-798, August.
  11. Marjolijn Haasnoot & Hans Middelkoop & Astrid Offermans & Eelco Beek & Willem Deursen, 2012. "Exploring pathways for sustainable water management in river deltas in a changing environment," Climatic Change, Springer, vol. 115(3), pages 795-819, December.
  12. Tunali, S. & Batmaz, I., 2003. "A metamodeling methodology involving both qualitative and quantitative input factors," European Journal of Operational Research, Elsevier, vol. 150(2), pages 437-450, October.
  13. 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.
  14. Batmaz, Inci & Tunali, Semra, 2003. "Small response surface designs for metamodel estimation," European Journal of Operational Research, Elsevier, vol. 145(2), pages 455-470, March.
  15. Shi, Wen & Shang, Jennifer & Liu, Zhixue & Zuo, Xiaolu, 2014. "Optimal design of the auto parts supply chain for JIT operations: Sequential bifurcation factor screening and multi-response surface methodology," European Journal of Operational Research, Elsevier, vol. 236(2), pages 664-676.
  16. Ekren, Orhan & Ekren, Banu Yetkin, 2008. "Size optimization of a PV/wind hybrid energy conversion system with battery storage using response surface methodology," Applied Energy, Elsevier, vol. 85(11), pages 1086-1101, November.
  17. Durieux, Severine & Pierreval, Henri, 2004. "Regression metamodeling for the design of automated manufacturing system composed of parallel machines sharing a material handling resource," International Journal of Production Economics, Elsevier, vol. 89(1), pages 21-30, May.
  18. Reis dos Santos, Pedro M. & Isabel Reis dos Santos, M., 2009. "Using subsystem linear regression metamodels in stochastic simulation," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1031-1040, August.
  19. Poropudas, Jirka & Virtanen, Kai, 2011. "Simulation metamodeling with dynamic Bayesian networks," European Journal of Operational Research, Elsevier, vol. 214(3), pages 644-655, November.

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