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Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems

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  • Juliane Müller
  • Christine Shoemaker

Abstract

This paper examines the influence of two major aspects on the solution quality of surrogate model algorithms for computationally expensive black-box global optimization problems, namely the surrogate model choice and the method of iteratively selecting sample points. A random sampling strategy (algorithm SO-M-c) and a strategy where the minimum point of the response surface is used as new sample point (algorithm SO-M-s) are compared in numerical experiments. Various surrogate models and their combinations have been used within the SO-M-c and SO-M-s sampling frameworks. The Dempster–Shafer Theory approach used in the algorithm by Müller and Piché (J Glob Optim 51:79–104, 2011 ) has been used for combining the surrogate models. The algorithms are numerically compared on 13 deterministic literature test problems with 2–30 dimensions, an application problem that deals with groundwater bioremediation, and an application that arises in energy generation using tethered kites. NOMAD and the particle swarm pattern search algorithm (PSWARM), which are derivative-free optimization methods, have been included in the comparison. The algorithms have also been compared to a kriging method that uses the expected improvement as sampling strategy (FEI), which is similar to the Efficient Global Optimization (EGO) algorithm. Data and performance profiles show that surrogate model combinations containing the cubic radial basis function (RBF) model work best regardless of the sampling strategy, whereas using only a polynomial regression model should be avoided. Kriging and combinations including kriging perform in general worse than when RBF models are used. NOMAD, PSWARM, and FEI perform for most problems worse than SO-M-s and SO-M-c. Within the scope of this study a Matlab toolbox has been developed that allows the user to choose, among others, between various sampling strategies and surrogate models and their combinations. The open source toolbox is available from the authors upon request. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Juliane Müller & Christine Shoemaker, 2014. "Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems," Journal of Global Optimization, Springer, vol. 60(2), pages 123-144, October.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:123-144
    DOI: 10.1007/s10898-014-0184-0
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    1. Felipe Viana & Raphael Haftka & Layne Watson, 2013. "Efficient global optimization algorithm assisted by multiple surrogate techniques," Journal of Global Optimization, Springer, vol. 56(2), pages 669-689, June.
    2. Regis, Rommel G. & Shoemaker, Christine A., 2007. "Parallel radial basis function methods for the global optimization of expensive functions," European Journal of Operational Research, Elsevier, vol. 182(2), pages 514-535, October.
    3. Rommel Regis & Christine Shoemaker, 2005. "Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions," Journal of Global Optimization, Springer, vol. 31(1), pages 153-171, January.
    4. Rommel G. Regis & Christine A. Shoemaker, 2009. "Parallel Stochastic Global Optimization Using Radial Basis Functions," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 411-426, August.
    5. X. B. Lam & Y. S. Kim & A. D. Hoang & C. W. Park, 2009. "Coupled Aerostructural Design Optimization Using the Kriging Model and Integrated Multiobjective Optimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 533-556, September.
    6. Argatov, I. & Rautakorpi, P. & Silvennoinen, R., 2009. "Estimation of the mechanical energy output of the kite wind generator," Renewable Energy, Elsevier, vol. 34(6), pages 1525-1532.
    7. Rommel G. Regis & Christine A. Shoemaker, 2007. "A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 497-509, November.
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    1. 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.
    2. Mehdad, E. & Kleijnen, Jack P.C., 2014. "Global Optimization for Black-box Simulation via Sequential Intrinsic Kriging," Discussion Paper 2014-063, Tilburg University, Center for Economic Research.
    3. Juliane Müller, 2017. "SOCEMO: Surrogate Optimization of Computationally Expensive Multiobjective Problems," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 581-596, November.
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    5. Mehdad, E., 2015. "Kriging metamodels and global opimization in simulation," Other publications TiSEM 5b5c276a-fe68-4ce9-b8a8-1, Tilburg University, School of Economics and Management.
    6. Lu, Zhaoyang & Li, Yanfeng & Zuo, Dajie, 2024. "Period-dependent pricing methods of multi-type vehicles for BOT highway projects with pavement rehabilitation effects," Transport Policy, Elsevier, vol. 150(C), pages 84-94.
    7. Tipaluck Krityakierne & Taimoor Akhtar & Christine A. Shoemaker, 2016. "SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems," Journal of Global Optimization, Springer, vol. 66(3), pages 417-437, November.
    8. Charles Audet & Michael Kokkolaras & Sébastien Le Digabel & Bastien Talgorn, 2018. "Order-based error for managing ensembles of surrogates in mesh adaptive direct search," Journal of Global Optimization, Springer, vol. 70(3), pages 645-675, March.
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    10. Nicolau Andrés-Thió & Mario Andrés Muñoz & Kate Smith-Miles, 2022. "Bifidelity Surrogate Modelling: Showcasing the Need for New Test Instances," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3007-3022, November.
    11. Juliane Müller & Marcus Day, 2019. "Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 689-702, October.
    12. Zan Yang & Haobo Qiu & Liang Gao & Chen Jiang & Jinhao Zhang, 2019. "Two-layer adaptive surrogate-assisted evolutionary algorithm for high-dimensional computationally expensive problems," Journal of Global Optimization, Springer, vol. 74(2), pages 327-359, June.
    13. Simpson, Michael C. & Chatzopoulou, Maria Anna & Oyewunmi, Oyeniyi A. & Le Brun, Niccolo & Sapin, Paul & Markides, Christos N., 2019. "Technoeconomic analysis of internal combustion engine – organic Rankine cycle systems for combined heat and power in energy-intensive buildings," Applied Energy, Elsevier, vol. 253(C), pages 1-1.
    14. 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.
    15. Miriyala, Srinivas Soumitri & Subramanian, Venkat & Mitra, Kishalay, 2018. "TRANSFORM-ANN for online optimization of complex industrial processes: Casting process as case study," European Journal of Operational Research, Elsevier, vol. 264(1), pages 294-309.
    16. Andrea Bacigalupo & Giorgio Gnecco & Marco Lepidi & Luigi Gambarotta, 2020. "Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials," Journal of Optimization Theory and Applications, Springer, vol. 187(3), pages 630-653, December.

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