Advertisement

A Survey of Surrogate Approaches for Expensive Constrained Black-Box Optimization

  • Rommel G. RegisEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

Numerous practical optimization problems involve black-box functions whose values come from computationally expensive simulations. For these problems, one can use surrogates that approximate the expensive objective and constraint functions. This paper presents a survey of surrogate-based or surrogate-assisted methods for computationally expensive constrained global optimization problems. The methods can be classified by type of surrogate used (e.g., kriging or radial basis function) or by the type of infill strategy. This survey also mentions algorithms that can be parallelized and that can handle infeasible initial points and high-dimensional problems.

Keywords

Global optimization Black-box optimization Constraints Surrogates Kriging Radial basis functions 

References

  1. 1.
    Appel, M.J., LaBarre, R., Radulović, D.: On accelerated random search. SIAM J. Optim. 14(3), 708–731 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bagheri, S., Konen, W., Allmendinger, R., Branke, J., Deb, K., Fieldsend, J., Quagliarella, D., Sindhya, K.: Constraint handling in efficient global optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 673–680. GECCO 2017, ACM, New York (2017)Google Scholar
  3. 3.
    Bagheri, S., Konen, W., Emmerich, M., Bäck, T.: Self-adjusting parameter control for surrogate-assisted constrained optimization under limited budgets. Appl. Soft Comput. 61, 377–393 (2017)CrossRefGoogle Scholar
  4. 4.
    Basudhar, A., Dribusch, C., Lacaze, S., Missoum, S.: Constrained efficient global optimization with support vector machines. Struct. Multidiscip. Optim. 46(2), 201–221 (2012)CrossRefGoogle Scholar
  5. 5.
    Bouhlel, M.A., Bartoli, N., Otsmane, A., Morlier, J.: Improving kriging surrogates of high-dimensional design models by partial least squares dimension reduction. Struct. Multidiscip. Optim. 53(5), 935–952 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bouhlel, M.A., Bartoli, N., Regis, R.G., Otsmane, A., Morlier, J.: Efficient global optimization for high-dimensional constrained problems by using the kriging models combined with the partial least squares method. Eng. Optim. 50(12), 2038–2053 (2018)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Boukouvala, F., Hasan, M.M.F., Floudas, C.A.: Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption. J. Global Optim. 67(1), 3–42 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Conn, A.R., Le Digabel, S.: Use of quadratic models with mesh-adaptive direct search for constrained black box optimization. Optim. Methods Softw. 28(1), 139–158 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Forrester, A.I.J., Sobester, A., Keane, A.J.: Engineering Design Via Surrogate Modelling: A Practical Guide. Wiley (2008)Google Scholar
  10. 10.
    Ginsbourger, D., Le Riche, R., Carraro, L.: Kriging Is Well-Suited to Parallelize Optimization, pp. 131–162. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Jones, D.R.: Large-scale multi-disciplinary mass optimization in the auto industry. In: MOPTA 2008, Modeling and Optimization: Theory and Applications Conference. MOPTA, Ontario, Canada, August 2008Google Scholar
  12. 12.
    Jones, D.R.: A taxonomy of global optimization methods based on response surfaces. J. Global Optim. 21(4), 345–383 (2001)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Jones, D., Schonlau, M., Welch, W.: Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4), 455–492 (1998)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Koch, P., Bagheri, S., Konen, W., Foussette, C., Krause, P., Bäck, T.: A new repair method for constrained optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2015), pp. 273–280 (2015)Google Scholar
  15. 15.
    Nuñez, L., Regis, R.G., Varela, K.: Accelerated random search for constrained global optimization assisted by radial basis function surrogates. J. Comput. Appl. Math. 340, 276–295 (2018)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Parr, J.M., Keane, A.J., Forrester, A.I., Holden, C.M.: Infill sampling criteria for surrogate-based optimization with constraint handling. Eng. Optim. 44(10), 1147–1166 (2012)CrossRefGoogle Scholar
  17. 17.
    Powell, M.J.D.: The theory of radial basis function approximation in 1990. In: Light, W. (ed.) Advances in Numerical Analysis, Volume 2: Wavelets, Subdivision Algorithms and Radial Basis Functions, pp. 105–210. Oxford University Press, Oxford (1992)Google Scholar
  18. 18.
    Regis, R.G.: Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions. Comput. Oper. Res. 38(5), 837–853 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Regis, R.G.: Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points. Eng. Optim. 46(2), 218–243 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Regis, R.G.: Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions. IEEE Trans. Evol. Comput. 18(3), 326–347 (2014)CrossRefGoogle Scholar
  21. 21.
    Regis, R.G.: Surrogate-assisted particle swarm with local search for expensive constrained optimization. In: Korošec, P., Melab, N., Talbi, E.G. (eds.) Bioinspired Optimization Methods and Their Applications, pp. 246–257. Springer International Publishing, Cham (2018)Google Scholar
  22. 22.
    Regis, R.G., Shoemaker, C.A.: Parallel radial basis function methods for the global optimization of expensive functions. Eur. J. Oper. Res. 182(2), 514–535 (2007)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Regis, R.G., Wild, S.M.: CONORBIT: constrained optimization by radial basis function interpolation in trust regions. Optim. Methods Softw. 32(3), 552–580 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Sasena, M.J., Papalambros, P., Goovaerts, P.: Exploration of metamodeling sampling criteria for constrained global optimization. Eng. Optim. 34(3), 263–278 (2002)CrossRefGoogle Scholar
  25. 25.
    Schonlau, M.: Computer Experiments and Global Optimization. Ph.D. thesis, University of Waterloo, Canada (1997)Google Scholar
  26. 26.
    Sóbester, A., Leary, S.J., Keane, A.J.: On the design of optimization strategies based on global response surface approximation models. J. Global Optim. 33(1), 31–59 (2005)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Wild, S.M., Regis, R.G., Shoemaker, C.A.: ORBIT: optimization by radial basis function interpolation in trust-regions. SIAM J. Sci. Comput. 30(6), 3197–3219 (2008)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Zhan, D., Qian, J., Cheng, Y.: Pseudo expected improvement criterion for parallel EGO algorithm. J. Global Optim. 68(3), 641–662 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsSaint Joseph’s UniversityPhiladelphiaUSA

Personalised recommendations