{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T02:50:38Z","timestamp":1781232638021,"version":"3.54.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,3,24]],"date-time":"2012-03-24T00:00:00Z","timestamp":1332547200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2013,6]]},"DOI":"10.1007\/s10898-012-9892-5","type":"journal-article","created":{"date-parts":[[2012,3,23]],"date-time":"2012-03-23T18:21:05Z","timestamp":1332526865000},"page":"669-689","source":"Crossref","is-referenced-by-count":231,"title":["Efficient global optimization algorithm assisted by multiple surrogate techniques"],"prefix":"10.1007","volume":"56","author":[{"given":"Felipe A. C.","family":"Viana","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raphael T.","family":"Haftka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Layne T.","family":"Watson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2012,3,24]]},"reference":[{"issue":"4","key":"9892_CR1","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1080\/03052150410001686486","volume":"36","author":"L. Wang","year":"2004","unstructured":"Wang L., Shan S., Wang G.G.: Mode-pursuing sampling method for global optimization on expensive black-box functions. Eng. Optim. 36(4), 419\u2013438 (2004)","journal-title":"Eng. Optim."},{"issue":"3","key":"9892_CR2","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1287\/ijoc.1050.0136","volume":"17","author":"J.P.C. Kleijnen","year":"2005","unstructured":"Kleijnen J.P.C., Sanchez S.M., Lucas T.W., Cioppa T.M.: A user\u2019s guide to the brave new world of designing simulation experiments. INFORMS J. Comput. 17(3), 263\u2013289 (2005)","journal-title":"INFORMS J. Comput."},{"issue":"1","key":"9892_CR3","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10898-004-6733-1","volume":"33","author":"A. S\u00f3bester","year":"2005","unstructured":"S\u00f3bester A., Leary S., Keane A.: On the design of optimization strategies based on global response surface approximation models. J. Glob. Optim. 33(1), 31\u201359 (2005)","journal-title":"J. Glob. Optim."},{"key":"9892_CR4","doi-asserted-by":"crossref","unstructured":"Simpson, T.W., Toropov, V., Balabanov, V., Viana, F.A.C.: Design and analysis of computer experiments in multidisciplinary design optimization: a review of how far we have come\u2014or not. In: 12th AIAA\/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA\u20132008\u20135802. AIAA, Victoria, BC, Canada (2008)","DOI":"10.2514\/6.2008-5802"},{"issue":"1\u20133","key":"9892_CR5","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.paerosci.2008.11.001","volume":"45","author":"A.I.J. Forrester","year":"2009","unstructured":"Forrester A.I.J., Keane A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1\u20133), 50\u201379 (2009)","journal-title":"Prog. Aerosp. Sci."},{"key":"9892_CR6","doi-asserted-by":"crossref","unstructured":"Viana, F.A.C., Gogu, C., Haftka, R.T.: Making the most out of surrogate models: tricks of the trade. In: ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, DETC2010\u201328813, ASME, Montreal, QC, Canada (2009)","DOI":"10.1115\/DETC2010-28813"},{"issue":"4","key":"9892_CR7","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1023\/A:1008306431147","volume":"13","author":"D.R. Jones","year":"1998","unstructured":"Jones D.R., Schonlau M., Welch W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455\u2013492 (1998)","journal-title":"J. Glob. Optim."},{"key":"9892_CR8","doi-asserted-by":"crossref","unstructured":"Jin, R., Chen, W., Sudjianto, A.: On sequential sampling for global metamodeling for in engineering design. In: ASME 2002 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, DETC2002\u201334092. ASME, Montreal, QC, Canada (2002)","DOI":"10.1115\/DETC2002\/DAC-34092"},{"issue":"3","key":"9892_CR9","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s10898-005-2454-3","volume":"34","author":"D. Huang","year":"2006","unstructured":"Huang D., Allen T., Notz W., Zeng N.: Global optimization of stochastic black-box systems via sequential kriging meta-models. J. Glob. Optim. 34(3), 441\u2013466 (2006)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"9892_CR10","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1080\/08982110701621312","volume":"19","author":"N. Henkenjohann","year":"2007","unstructured":"Henkenjohann N., Kunert J.: An efficient sequential optimization approach based on the multivariate expected improvement criterion. Qual. Eng. 19(4), 267\u2013280 (2007)","journal-title":"Qual. Eng."},{"key":"9892_CR11","doi-asserted-by":"crossref","unstructured":"Ponweiser, W., Wagner, T., Vincze, M.: Clustered multiple generalized expected improvement: a novel infill sampling criterion for surrogate models. In: IEEE Congress on Evolutionary Computation, pp. 3514\u20133521. IEEE, Hong Kong (2008)","DOI":"10.1109\/CEC.2008.4631273"},{"issue":"4","key":"9892_CR12","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1023\/A:1012771025575","volume":"21","author":"D.R. Jones","year":"2001","unstructured":"Jones D.R.: A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim. 21(4), 345\u2013383 (2001)","journal-title":"J. Glob. Optim."},{"key":"9892_CR13","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/978-3-642-10701-6_6","volume-title":"Computational Intelligence in Expensive Optimization Problems, vol. 2","author":"D. Ginsbourger","year":"2010","unstructured":"Ginsbourger D., Le Riche R., Carraro L.: Kriging is well-suited to parallelize optimization. In: Tenne, Y., Goh, C. (eds) Computational Intelligence in Expensive Optimization Problems, vol. 2, pp. 131\u2013162. Springer, Heidelberg (2010)"},{"issue":"2","key":"9892_CR14","doi-asserted-by":"crossref","first-page":"302","DOI":"10.2514\/1.28999","volume":"24","author":"A. Samad","year":"2008","unstructured":"Samad A., Kim K.Y., Goel T., Haftka R.T., Shyy W.: Multiple surrogate modeling for axial compressor blade shape optimization. J. Propuls. Power 24(2), 302\u2013310 (2008)","journal-title":"J. Propuls. Power"},{"key":"9892_CR15","unstructured":"Viana, F.A.C., Haftka, R.T.: Using multiple surrogates for metamodeling. In: 7th ASMO-UK ISSMO International Conference on Engineering Design Optimization, pp. 1\u201318. ISSMO, Bath, UK (2008)"},{"issue":"1","key":"9892_CR16","first-page":"2039","volume":"10","author":"D. Gorissen","year":"2009","unstructured":"Gorissen D., Dhaene T., de Turck F.: Evolutionary model type selection for global surrogate modeling. J. Mach. Learn. Res. 10(1), 2039\u20132078 (2009)","journal-title":"J. Mach. Learn. Res."},{"issue":"7","key":"9892_CR17","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1080\/10618562.2010.521129","volume":"24","author":"Y.C. Cho","year":"2010","unstructured":"Cho Y.C., Jayaraman B., Viana F.A.C., Haftka R.T., Shyy W.: Surrogate modeling for characterizing the performance of dielectric barrier discharge plasma actuator. Int. J. Comput. Fluid Dyn. 24(7), 281\u2013301 (2010)","journal-title":"Int. J. Comput. Fluid Dyn."},{"issue":"3","key":"9892_CR18","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1023\/A:1011255519438","volume":"19","author":"H.M. Gutmann","year":"2001","unstructured":"Gutmann H.M.: A radial basis function method for global optimization. J. Glob. Optim. 19(3), 201\u2013227 (2001)","journal-title":"J. Glob. Optim."},{"key":"9892_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1494-6","volume-title":"Interpolation of Spatial Data: Some Theory for Kriging","author":"M.L. Stein","year":"1999","unstructured":"Stein M.L.: Interpolation of Spatial Data: Some Theory for Kriging. Springer, Berlin (1999)"},{"issue":"4","key":"9892_CR20","doi-asserted-by":"crossref","first-page":"853","DOI":"10.2514\/1.8650","volume":"43","author":"J.D. Martin","year":"2005","unstructured":"Martin J.D., Simpson T.W.: Use of kriging models to approximate deterministic computer models. AIAA J. 43(4), 853\u2013863 (2005)","journal-title":"AIAA J."},{"issue":"4","key":"9892_CR21","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1023\/A:1007577916868","volume":"32","author":"J.K. Yamamoto","year":"2000","unstructured":"Yamamoto J.K.: An alternative measure of the reliability of ordinary kriging estimates. Math. Geol. 32(4), 489\u2013509 (2000)","journal-title":"Math. Geol."},{"issue":"4","key":"9892_CR22","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1057\/palgrave.jors.2601997","volume":"57","author":"D. den Hertog","year":"2006","unstructured":"den Hertog D., Kleijnen J.P.C., Siem A.Y.D.: The correct kriging variance estimated by bootstrapping. J. Oper. Res. Soc. 57(4), 400\u2013409 (2006)","journal-title":"J. Oper. Res. Soc."},{"key":"9892_CR23","doi-asserted-by":"crossref","unstructured":"Kleijnen, J.P.C., van Beers, W.C.M., van Nieuwenhuyse, I.: Expected improvement in efficient global optimization through bootstrapped kriging. J. Glob. Optim. (available online), pp. 1\u201315 (2011)","DOI":"10.2139\/ssrn.1763726"},{"key":"9892_CR24","doi-asserted-by":"crossref","DOI":"10.1002\/9780470770801","volume-title":"Engineering Design Via Surrogate Modelling: A Practical Guide","author":"A.I.J. Forrester","year":"2008","unstructured":"Forrester A.I.J., S\u00f3bester A., Keane A.J.: Engineering Design Via Surrogate Modelling: A Practical Guide. Wiley, New York (2008)"},{"issue":"2088","key":"9892_CR25","doi-asserted-by":"crossref","first-page":"3251","DOI":"10.1098\/rspa.2007.1900","volume":"463","author":"A.I.J. Forrester","year":"2007","unstructured":"Forrester A.I.J., S\u00f3bester A., Keane A.J.: Multi-fidelity optimization via surrogate modeling. Proc. R. Soc. A Math. Phys. Eng. Sci. 463(2088), 3251\u20133269 (2007)","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"issue":"4","key":"9892_CR26","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1080\/03052150500422294","volume":"38","author":"H. Fang","year":"2006","unstructured":"Fang H., Horstemeyer M.F.: Global response approximation with radial basis functions. Eng. Optim. 38(4), 407\u2013424 (2006)","journal-title":"Eng. Optim."},{"issue":"27\u201329","key":"9892_CR27","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.1016\/j.cma.2009.02.016","volume":"198","author":"T. Goel","year":"2009","unstructured":"Goel T., Stander N.: Comparing three error criteria for selecting radial basis function network topology. Comput. Methods Appl. Mech. Eng. 198(27\u201329), 2137\u20132150 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"9892_CR28","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1145\/326147.326154","volume":"25","author":"M.W. Berry","year":"1999","unstructured":"Berry M.W., Minser K.S.: Algorithm 798: high-dimensional interpolation using the modified Shepard method. ACM Trans. Math. Softw. 25(3), 353\u2013366 (1999)","journal-title":"ACM Trans. Math. Softw."},{"issue":"3","key":"9892_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1824801.1824812","volume":"37","author":"W.I. Thacker","year":"2010","unstructured":"Thacker W.I., Zhang J., Watson L.T., Birch J.B., Iyer M.A., Berry M.W.: Algorithm 905: Sheppack: modified Shepard algorithm for interpolation of scattered multivariate data. ACM Trans. Math. Softw. 37(3), 1\u201320 (2010)","journal-title":"ACM Trans. Math. Softw."},{"key":"9892_CR30","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511801389","volume-title":"An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods","author":"N. Cristianini","year":"2000","unstructured":"Cristianini N., Shawe-Taylor J.: An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, Cambridge (2000)"},{"issue":"3","key":"9892_CR31","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","volume":"14","author":"A.J. Smola","year":"2004","unstructured":"Smola A.J., Sch\u00f6lkopf B.: A tutorial on support vector regression. Stat. Comput. 14(3), 199\u2013222 (2004)","journal-title":"Stat. Comput."},{"key":"9892_CR32","doi-asserted-by":"crossref","unstructured":"Viana, F.A.C., Haftka, R.T.: Importing uncertainty estimates from one surrogate to another. In: 50th AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics, and Materials Conference, pp. AIAA\u20132009\u20132237. AIAA, Palm Springs, CA, USA (2009)","DOI":"10.2514\/6.2009-2237"},{"issue":"4","key":"9892_CR33","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/s00158-008-0338-0","volume":"39","author":"F.A.C. Viana","year":"2009","unstructured":"Viana F.A.C., Haftka R.T., Steffen V. Jr: Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct. Multidiscip. Optim. 39(4), 439\u2013457 (2009)","journal-title":"Struct. Multidiscip. Optim."},{"key":"9892_CR34","unstructured":"Lophaven, S.N., Nielsen, H.B., S\u00f8ndergaard, J.: Dace\u2014a matlab kriging toolbox. Tech. Rep. IMM\u2013TR\u20132002\u201312, Technical University of Denmark, Denmark (2002). Available at http:\/\/www2.imm.dtu.dk\/~hbn\/dace\/"},{"key":"9892_CR35","unstructured":"MathWorks contributors: MATLAB The language of technical computing. The MathWorks, Inc, Natick, MA, USA, version 7.0 release 14 edn. (2004)"},{"key":"9892_CR36","unstructured":"Jekabsons, G.: RBF: Radial Basis Function interpolation for MATLAB\/OCTAVE. Riga Technical University, Latvia, version 1.1 edn. (2009). Available at http:\/\/www.cs.rtu.lv\/jekabsons\/regression.html"},{"key":"9892_CR37","unstructured":"Viana, F.A.C.: SURROGATES Toolbox User\u2019s Guide. Gainesville, FL, USA, version 3.0 edn. (2011). Available at http:\/\/sites.google.com\/site\/felipeacviana\/surrogatestoolbox"},{"key":"9892_CR38","unstructured":"Gunn, S.R.: Support vector machines for classification and regression. Tech. rep., University of Southampton, UK (1997). Available at http:\/\/www.isis.ecs.soton.ac.uk\/resources\/svminfo\/"},{"key":"9892_CR39","unstructured":"Roustant, O. Ginsbourger, D., Deville, Y.: DiceKriging, DiceOptim: two R packages for the analysis of computer experiments by kriging-based metamodeling and optimization. Ecole Nationale Sup\u00e9rieure des Mines de Saint-Etienne, France and University of Bern, Switzerland (2010). Available at http:\/\/hal.archives-ouvertes.fr\/hal-00495766\/"},{"issue":"1","key":"9892_CR40","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0893-6080(03)00169-2","volume":"17","author":"V. Cherkassky","year":"2004","unstructured":"Cherkassky V., Ma Y.: Practical selection of svm parameters and noise estimation for svm regression. Neural Netw. 17(1), 113\u2013126 (2004)","journal-title":"Neural Netw."},{"key":"9892_CR41","unstructured":"Sasena, M.J.: Optimization of computer simulations via smoothing splines and kriging metamodels. Master\u2019s thesis, University of Michigan, Ann Arbor, MI, USA (1998)"},{"key":"9892_CR42","unstructured":"Dixon, L.C.W., Szeg\u00f6, G.P.: Towards Global Optimization 2. North Holland, Amsterdam (1978)"},{"issue":"2","key":"9892_CR43","first-page":"239","volume":"21","author":"M.D. McKay","year":"1979","unstructured":"McKay M.D., Beckman R.J., Conover W.J.: A comparison of three methods for selecting values of input variables from a computer code. Technometrics 21(2), 239\u2013245 (1979)","journal-title":"Technometrics"},{"key":"9892_CR44","volume-title":"Differential Evolution: A Practical Approach to Global Optimization","author":"K.V. Price","year":"2005","unstructured":"Price K.V., Storn R.M., Lampinen J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, New York (2005)"},{"issue":"4","key":"9892_CR45","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R. Storn","year":"1997","unstructured":"Storn R., Price K.: Differential evolution\u2014a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341\u2013359 (1997)","journal-title":"J. Glob. Optim."},{"issue":"6","key":"9892_CR46","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1002\/nme.1960","volume":"71","author":"J.F. Schutte","year":"2007","unstructured":"Schutte J.F., Haftka R.T., Fregly B.J.: Improved global convergence probability using multiple independent optimizations. Int. J. Numer. Methods Eng. 71(6), 678\u2013702 (2007)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"9","key":"9892_CR47","doi-asserted-by":"crossref","first-page":"2266","DOI":"10.2514\/1.42162","volume":"47","author":"F.A.C. Viana","year":"2009","unstructured":"Viana F.A.C., Haftka R.T.: Cross validation can estimate how well prediction variance correlates with error. AIAA J. 47(9), 2266\u20132270 (2009)","journal-title":"AIAA J."},{"issue":"10","key":"9892_CR48","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.2514\/2.1538","volume":"40","author":"M. Meckesheimer","year":"2002","unstructured":"Meckesheimer M., Booker A.J., Barton R.R., Simpson T.W.: Computationally inexpensive metamodel assessment strategies. AIAA J. 40(10), 2053\u20132060 (2002)","journal-title":"AIAA J."},{"issue":"387","key":"9892_CR49","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1080\/01621459.1984.10478083","volume":"79","author":"R.R. Picard","year":"1984","unstructured":"Picard R.R., Cook R.D.: Cross-validation of regression models. J. Am. Stat. Assoc. 79(387), 575\u2013583 (1984)","journal-title":"J. Am. Stat. Assoc."},{"issue":"91","key":"9892_CR50","first-page":"1290","volume":"7","author":"S. Varma","year":"2006","unstructured":"Varma S., Simon R.: Bias in error estimation when using cross-validation for model selection. BMC Bioinf. 7(91), 1290\u20131300 (2006)","journal-title":"BMC Bioinf."},{"key":"9892_CR51","volume-title":"Classical and Modern Regression with Applications","author":"R.H. Myers","year":"2000","unstructured":"Myers R.H.: Classical and Modern Regression with Applications. Duxbury Press, Belmont (2000)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9892-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-012-9892-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9892-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,26]],"date-time":"2019-06-26T01:06:29Z","timestamp":1561511189000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-012-9892-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,24]]},"references-count":51,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["9892"],"URL":"https:\/\/doi.org\/10.1007\/s10898-012-9892-5","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,24]]}}}