Simulation Optimization Through Regression or Kriging Metamodels

  • Jack P. C. KleijnenEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 833)


This chapter surveys two methods for the optimization of real-world systems that are modelled through simulation. These methods use either linear regression or Kriging (Gaussian processes) metamodels. The metamodel guides the design of the experiment; this design fixes the input combinations of the simulation model. The linear-regression metamodel uses a sequence of local first-order and second-order polynomials—known as response surface methodology (RSM). Kriging models are global, but are re-estimated through sequential designs. “Robust” optimization may use RSM or Kriging, to account for uncertainty in simulation inputs.



I thank Thomas Bartz-Beielstein for his very useful comments on the first version of this chapter.


  1. 1.
    Ankenman, B., Nelson, B., Staum, J.: Stochastic Kriging for simulation metamodeling. Oper. Res. 58(2), 371–382 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bartz-Beielstein, T., Zaefferer, M.: Model-based methods for continuous and discrete global optimization. Appl. Soft Comput. 55, 154–167 (2017)CrossRefGoogle Scholar
  3. 3.
    Bertsimas, D., Mišić, V.V.: Robust product line design. Oper. Res. 65(1), 19–37 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Binois, M., Gramacy, R.B., Ludkovskiz, M.: Practical heteroskedastic Gaussian process modeling for large simulation experiments (2016). 17 Nov 2016Google Scholar
  5. 5.
    Chatterjee, T., Chakraborty, S., Chowdhury, R.: A critical review of surrogate assisted robust design optimization. Arch. Comput. Methods Eng. 26(1), 245–274 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cressie, N.A.C.: Statistics for Spatial Data, revised edn. Wiley, New York (1993)zbMATHGoogle Scholar
  7. 7.
    Dellino, G., Kleijnen, J.P.C., Meloni, C.: Robust optimization in simulation: Taguchi and response surface methodology. Int. J. Prod. Econ. 125(1), 52–59 (2010)CrossRefGoogle Scholar
  8. 8.
    Dellino, G., Kleijnen, J.P.C., Meloni, C.: Robust optimization in simulation: Taguchi and Krige combined. Informs J. Comput. 24(3), 471–484 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Erickson, C.B., Ankenman B.E., Sanchez, S.M.: Comparison of Gaussian process modeling software. European J. Operat. Res. 266, 179–192 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Friese, M., Bartz-Beielstein, T., Emmerich, M.: Building ensembles of surrogates by optimal convex combinations. In: Conference Paper (2016)Google Scholar
  11. 11.
    Gramacy, R.B.: LAGP: large-scale spatial modeling via local approximate Gaussian processes. J. Stat. Softw. (Available as a vignette in the LAGP package) (2015)Google Scholar
  12. 12.
    Hamdi, H., Couckuyt, I., Costa Sousa, M., Dhaene, T.: Gaussian processes for history-matching: application to an unconventional gas reservoir. Comput. Geosci. 21, 267–287 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Havinga, J., van den Boogaard, A.H., Klaseboer, G.: Sequential improvement for robust optimization using an uncertainty measure for radial basis functions. Struct. Multidiscip. Optim. 55, 1345–1363 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Jalali, H., Van Nieuwenhuyse, I.: Simulation optimization in inventory replenishment: a classification. IIE Trans. 47(11), 1217–1235 (2015)CrossRefGoogle Scholar
  15. 15.
    Jilu, F., Zhili, S., Hongzhe, S.: Optimization of structure parameters for angular contact ball bearings based on Kriging model and particle swarm optimization algorithm. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 231(23), 4298–4308 (2017)CrossRefGoogle Scholar
  16. 16.
    Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13, 455–492 (1998)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kajero, O.T., Thorpe, R., Yao, Y., Wong, D.S.H., Chen, T.: Meta-model based calibration and sensitivity studies of CFD simulation of jet pumps. Chem. Eng. Technol. 40(9), 1674–1684 (2017)CrossRefGoogle Scholar
  18. 18.
    Kleijnen, J.P.C.: Design and Analysis of Simulation Experiments, 2nd edn. Springer, Berlin (2015)CrossRefGoogle Scholar
  19. 19.
    Kleijnen, J.P.C.: Design and analysis of simulation experiments: tutorial. In: Tolk, A., Fowler, J., Shao, G., Yucesan, E. (eds.) Advances in Modeling and Simulation: Seminal Research from 50 Years of Winter Simulation Conferences, pp. 135–158. Springer, Berlin (2017)Google Scholar
  20. 20.
    Kleijnen, J.P.C., Shi, W.: Sequential probability ratio tests: conservative and robust. CentER Discussion Paper; vol. 2017-001, Tilburg: CentER, Center for Economic Research (2017)Google Scholar
  21. 21.
    Kleijnen, J.P.C., van Beers, W.C.M.: Prediction for big data through Kriging. CentER Discussion Paper; Center for Economic Research (CentER), Tilburg University, forthcoming (2017)Google Scholar
  22. 22.
    Law, A.M.: Simulation Modeling and Analysis, 5th edn. McGraw-Hill, Boston (2015)Google Scholar
  23. 23.
    Liu, Z., Rexachs, D., Epelde, F., Luque, E.: A simulation and optimization based method for calibrating agent-based emergency department models under data scarcity. Comput. Ind. Eng. 103, 300–309 (2017)CrossRefGoogle Scholar
  24. 24.
    Lophaven, S.N., Nielsen, H.B., Sondergaard, J.: DACE: a Matlab Kriging toolbox, version 2.0. IMM Technical University of Denmark, Kongens Lyngby (2002)Google Scholar
  25. 25.
    Moghaddam, S., Mahlooji, H.: A new metamodel-based method for solving semi-expensive simulation optimization problems. Commun. Stat. Simul. Comput. 46(6), 4795–4811 (2017)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Montgomery, D.C.: Design and Analysis of Experiments, 7th edn. Wiley, Hoboken (2009)Google Scholar
  27. 27.
    Myers, R.H., Montgomery, D.C., Anderson-Cook, C.M.: Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd edn. Wiley, New York (2009)zbMATHGoogle Scholar
  28. 28.
    Pontes, F.J., Amorim, G.F., Balestrassi, P.P., Paiva, A.P., Ferreira, J.R.: Design of experiments and focused grid search for neural network parameter optimization. Neurocomputing 186, 22–34 (2016)CrossRefGoogle Scholar
  29. 29.
    Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT, Cambridge (2006)zbMATHGoogle Scholar
  30. 30.
    Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments (includes comments and rejoinder). Stat. Sci. 4(4), 409–435 (1989)CrossRefGoogle Scholar
  31. 31.
    Sanchez, S.M., Lucas, T.W., Sanchez, P.J., Nannini, C.J., Wan, H.: Designs for large-scale simulation experiments, with applications to defense and homeland security. In: Hinkelmann, K. (ed.) Design and Analysis of Experiments, Volume 3, Special Designs and Applications, pp. 413–442. Wiley, New York (2012)CrossRefGoogle Scholar
  32. 32.
    Shi, X., Tong, C., Wang, L.: Evolutionary optimization with adaptive surrogates and its application in crude oil distillation. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI), Athens Greece, pp. 1–8 (2016)Google Scholar
  33. 33.
    Simpson, T.W., Booker, A.J., Ghosh, D., Giunta, A.A., Koch, P.N., Yang, R.-J.: Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct. Multidiscip. Optim. 27(5), 302–313 (2004)CrossRefGoogle Scholar
  34. 34.
    Snoek, J., Larochelle, H., Adams, R.P.: Practical Bayesian optimization of machine learning algorithms. Adv. Neural Inf. Process. Syst. 2951–2959 (2012)Google Scholar
  35. 35.
    Yanikoğlu, I., den Hertog, D., Kleijnen, J.P.C.: Robust dual-response optimization. IIE Trans. Ind. Eng. Res. Dev. 48(3), 298–312 (2016)Google Scholar
  36. 36.
    Yousefi, M., Yousefi, M., Ferreira, R.P.M., Kim, J.H., Fogliatto, F.S.: Chaotic genetic algorithm and Adaboost ensemble metamodeling approach for optimum resource planning in emergency departments. Artif. Intell. Med. 84, 23–33 (2018)CrossRefGoogle Scholar
  37. 37.
    Yu, H., Tan, Y., Sun, C., Zeng, J., Jin, Y.: An adaptive model selection strategy for surrogate-assisted particle swarm optimization algorithm. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1–8 (2016)Google Scholar
  38. 38.
    Zeigler, B.P., Praehofer, H., Kim, T.G.: Theory of Modeling and Simulation, 2nd edn. Academic, San Diego (2000)zbMATHGoogle Scholar
  39. 39.
    Zhang, W., Xu, W.: Simulation-based robust optimization for the schedule of single-direction bus transit route: the design of experiment. Transp. Res. Part E 106, 203–230 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Tilburg UniversityTilburgThe Netherlands

Personalised recommendations