Surrogate-Model-Based Design and Optimization

  • Ping JiangEmail author
  • Qi Zhou
  • Xinyu Shao
Part of the Springer Tracts in Mechanical Engineering book series (STME)


Since most engineering design problems involve time-consuming simulations and analysis, surrogate models are often used for fast calculations, sensitivity analysis, exploring the design space and supporting optimal design.


  1. Akhtar T, Shoemaker CA (2016) Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection. J Global Optim 64:17–32MathSciNetzbMATHCrossRefGoogle Scholar
  2. Alexandrov NM, Dennis J, Lewis RM, Torczon V (1998) A trust-region framework for managing the use of approximation models in optimization. Struct Optim 15:16–23CrossRefGoogle Scholar
  3. Andrés E, Salcedo-Sanz S, Monge F, Pérez-Bellido AM (2012) Efficient aerodynamic design through evolutionary programming and support vector regression algorithms. Expert Syst Appl 39:10700–10708CrossRefGoogle Scholar
  4. Apley DW, Liu J, Chen W (2006) Understanding the effects of model uncertainty in robust design with computer experiments. J Mech Des 128:945–958CrossRefGoogle Scholar
  5. Arendt PD, Apley DW, Chen W (2013) Objective-oriented sequential sampling for simulation based robust design considering multiple sources of uncertainty. J Mech Des 135:051005CrossRefGoogle Scholar
  6. Audet C, Denni J, Moore D, Booker A, Frank P (2000) A surrogate-model-based method for constrained optimization. In: 8th symposium on multidisciplinary analysis and optimization, p 4891Google Scholar
  7. Bahrami S, Tribes C, Devals C, Vu T, Guibault F (2016) Multi-fidelity shape optimization of hydraulic turbine runner blades using a multi-objective mesh adaptive direct search algorithm. Appl Math Model 40:1650–1668MathSciNetCrossRefGoogle Scholar
  8. Basudhar A, Dribusch C, Lacaze S, Missoum S (2012) Constrained efficient global optimization with support vector machines. Struct Multidiscip Optim 46:201–221zbMATHCrossRefGoogle Scholar
  9. Branke J, Schmidt C (2005) Faster convergence by means of fitness estimation. Soft Comput 9:13–20CrossRefGoogle Scholar
  10. Bui LT, Abbass HA, Essam D (2005) Fitness inheritance for noisy evolutionary multi-objective optimization. In: Proceedings of the 7th annual conference on Genetic and evolutionary computation: ACM, pp 779–785Google Scholar
  11. Chaudhuri A, Haftka RT (2014) Efficient global optimization with adaptive target setting. AIAA J 52:1573–1578CrossRefGoogle Scholar
  12. Chen T-Y, Cheng Y-L (2010) Data-mining assisted structural optimization using the evolutionary algorithm and neural network. Eng Optim 42:205–222CrossRefGoogle Scholar
  13. Chen J-H, Goldberg DE, Ho S-Y, Sastry K (2002) Fitness inheritance in multi-objective optimization. In: GECCO, pp 319–326Google Scholar
  14. Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des 127:875–886CrossRefGoogle Scholar
  15. Chen G, Han X, Liu G, Jiang C, Zhao Z (2012) An efficient multi-objective optimization method for black-box functions using sequential approximate technique. Appl Soft Comput 12:14–27CrossRefGoogle Scholar
  16. Chen Z, Qiu H, Gao L, Li X, Li P (2014) A local adaptive sampling method for reliability-based design optimization using Kriging model. Struct Multidiscip Optim 49:401–416MathSciNetCrossRefGoogle Scholar
  17. Chen S, Jiang Z, Yang S, Apley DW, Chen W (2016) Nonhierarchical multi-model fusion using spatial random processes. Int J Numer Meth Eng 106:503–526MathSciNetzbMATHCrossRefGoogle Scholar
  18. Cheng J, Liu Z, Wu Z, Li X, Tan J (2015a) Robust optimization of structural dynamic characteristics based on adaptive Kriging model and CNSGA. Struct Multidiscip Optim 51:423–437CrossRefGoogle Scholar
  19. Cheng R, Jin Y, Narukawa K, Sendhoff B (2015b) A multiobjective evolutionary algorithm using gaussian process-based inverse modeling. IEEE Trans Evol Comput 19:838–856CrossRefGoogle Scholar
  20. Cheng S, Zhou J, Li M (2015c) A new hybrid algorithm for multi-objective robust optimization with interval uncertainty. J Mech Des 137:021401CrossRefGoogle Scholar
  21. Chung H-S, Alonso JJ (2004) Multiobjective optimization using approximation model-based genetic algorithms. AIAA paper 4325Google Scholar
  22. Clarke SM, Griebsch JH, Simpson TW (2005) Analysis of support vector regression for approximation of complex engineering analyses. J Mech Des 127:1077–1087CrossRefGoogle Scholar
  23. Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41:113–127CrossRefGoogle Scholar
  24. Couckuyt I, Deschrijver D, Dhaene T (2014) Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization. J Glob Optim 60:575–594MathSciNetzbMATHCrossRefGoogle Scholar
  25. Datta R, Regis RG (2016) A surrogate-assisted evolution strategy for constrained multi-objective optimization. Expert Syst Appl 57:270–284CrossRefGoogle Scholar
  26. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  27. Desautels T, Krause A, Burdick JW (2014) Parallelizing exploration-exploitation tradeoffs in gaussian process bandit optimization. J Mach Learn Res 15:3873–3923MathSciNetzbMATHGoogle Scholar
  28. Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126:225–233CrossRefGoogle Scholar
  29. Du X, Guo J, Beeram H (2008) Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip Optim 35:117–130MathSciNetzbMATHCrossRefGoogle Scholar
  30. Eldred M, Giunta A, Wojtkiewicz S, Trucano T (2002) Formulations for surrogate-based optimization under uncertainty. In: 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, p 5585Google Scholar
  31. Forrester AIJ, Keane AJ, Bressloff NW (2006) Design and analysis of “Noisy” computer experiments. AIAA J 44:2331–2339CrossRefGoogle Scholar
  32. Forrester AIJ, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45:50–79CrossRefGoogle Scholar
  33. Forrester A, Sobester A, Keane A (2008) Engineering design via surrogate modelling: a practical guide. WileyGoogle Scholar
  34. Gano SE, Renaud JE, Agarwal H, Tovar A (2006a) Reliability-based design using variable-fidelity optimization. Struct Infrastruct Eng 2:247–260CrossRefGoogle Scholar
  35. Gano SE, Renaud JE, Martin JD, Simpson TW (2006b) Update strategies for kriging models used in variable fidelity optimization. Struct Multidiscip Optim 32:287–298CrossRefGoogle Scholar
  36. Gary Wang G, Dong Z, Aitchison P (2001) Adaptive response surface method-a global optimization scheme for approximation-based design problems. Eng Optim 33:707–733CrossRefGoogle Scholar
  37. Ghisu T, Parks GT, Jarrett JP, Clarkson PJ (2011) Robust design optimization of gas turbine compression systems. J Propul Power 27:282–295CrossRefGoogle Scholar
  38. Gluzman S, Yukalov V (2006) Self-similar power transforms in extrapolation problems. J Math Chem 39:47–56MathSciNetzbMATHCrossRefGoogle Scholar
  39. Goel T, Vaidyanathan R, Haftka RT, Shyy W, Queipo NV, Tucker K (2007) Response surface approximation of Pareto optimal front in multi-objective optimization. Comput Methods Appl Mech Eng 196:879–893zbMATHCrossRefGoogle Scholar
  40. Gu L (2001) A comparison of polynomial based regression models in vehicle safety analysis. In: ASME design engineering technical conferences, ASME paper no.: DETC/DAC-21083Google Scholar
  41. Gu X, Renaud JE, Batill SM, Brach RM, Budhiraja AS (2000) Worst case propagated uncertainty of multidisciplinary systems in robust design optimization. Struct Multidiscip Optim 20:190–213CrossRefGoogle Scholar
  42. Gunawan S (2004) Parameter sensitivity measures for single objective, multi-objective, and feasibility robust design optimizationGoogle Scholar
  43. Gunawan S, Azarm S (2004) Non-gradient based parameter sensitivity estimation for single objective robust design optimization. J Mech Des 126:395–402CrossRefGoogle Scholar
  44. Gunawan S, Azarm S (2005a) A feasibility robust optimization method using sensitivity region concept. J Mech Des 127:858–865CrossRefGoogle Scholar
  45. Gunawan S, Azarm S (2005b) Multi-objective robust optimization using a sensitivity region concept. Struct Multidiscip Optim 29:50–60CrossRefGoogle Scholar
  46. Gutmann HM (2001) A radial basis function method for global optimization. J Global Optim 19:201–227MathSciNetzbMATHCrossRefGoogle Scholar
  47. Haftka RT (1991) Combining global and local approximations. AIAA J 29:1523–1525CrossRefGoogle Scholar
  48. Hamdaoui M, Oujebbour F-Z, Habbal A, Breitkopf P, Villon P (2015) Kriging surrogates for evolutionary multi-objective optimization of CPU intensive sheet metal forming applications. IntJ Mater Form 8:469–480CrossRefGoogle Scholar
  49. Han Z-H, Zimmermann R, Goretz S (2010) A new cokriging method for variable-fidelity surrogate modeling of aerodynamic dataGoogle Scholar
  50. Han Z, Zimmerman R, Görtz S (2012) Alternative cokriging method for variable-fidelity surrogate modeling. AIAA J 50:1205–1210CrossRefGoogle Scholar
  51. Hsu YL, Wang SG, Yu CC (2003) A sequential approximation method using neural networks for engineering design optimization problems. Eng Optim 35:489–511MathSciNetCrossRefGoogle Scholar
  52. Hu Z, Mahadevan S (2017) Uncertainty quantification in prediction of material properties during additive manufacturing. Scripta Mater 135:135–140CrossRefGoogle Scholar
  53. Hu W, Enying L, Yao LG (2008) Optimization of drawbead design in sheet metal forming based on intelligent sampling by using response surface methodology. J Mater Process Technol 206:45–55CrossRefGoogle Scholar
  54. Hu W, Li M, Azarm S, Almansoori A (2011) Multi-objective robust optimization under interval uncertainty using online approximation and constraint cuts. J Mech Des 133:061002CrossRefGoogle Scholar
  55. Huang D, Allen TT, Notz WI, Miller RA (2006a) Sequential kriging optimization using multiple-fidelity evaluations. Struct Multidiscip Optim 32:369–382CrossRefGoogle Scholar
  56. Huang D, Allen TT, Notz WI, Zeng N (2006b) Global optimization of stochastic black-box systems via sequential kriging meta-models. J Global Optim 34:441–466MathSciNetzbMATHCrossRefGoogle Scholar
  57. Jeong S, Minemura Y, Obayashi S (2006) Optimization of combustion chamber for diesel engine using kriging model. J Fluid Sci Technol 1:138–146CrossRefGoogle Scholar
  58. Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9:3–12CrossRefGoogle Scholar
  59. Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1:61–70CrossRefGoogle Scholar
  60. Jin Y, Olhofer M, Sendhoff B (2000) On evolutionary optimization with approximate fitness functions. In: GECCO, pp 786–793Google Scholar
  61. Jin Y, Olhofer M, Sendhoff B (2002) A framework for evolutionary optimization with approximate fitness functions. IEEE Trans Evol Comput 6:481–494CrossRefGoogle Scholar
  62. Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. J Glob Optim 21:345–383MathSciNetzbMATHCrossRefGoogle Scholar
  63. Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492MathSciNetzbMATHCrossRefGoogle Scholar
  64. Kalyanmoy D (2001) Multi objective optimization using evolutionary algorithms: John Wiley and SonsGoogle Scholar
  65. Kannan B, Kramer SN (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des 116:405–411CrossRefGoogle Scholar
  66. Keane AJ (2006) Statistical improvement criteria for use in multiobjective design optimization. AIAA J 44:879–891CrossRefGoogle Scholar
  67. Kerschen G, Worden K, Vakakis AF, Golinval J-C (2006) Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Signal Process 20:505–592CrossRefGoogle Scholar
  68. Kim N-K, Kim D-H, Kim D-W, Kim H-G, Lowther D, Sykulski JK (2010) Robust optimization utilizing the second-order design sensitivity information. IEEE Trans Magn 46:3117–3120CrossRefGoogle Scholar
  69. Kitayama S, Srirat J, Arakawa M, Yamazaki K (2013) Sequential approximate multi-objective optimization using radial basis function network. Struct Multidiscip Optim 48:501–515MathSciNetCrossRefGoogle Scholar
  70. Kleijnen JP, Van Beers W, Van Nieuwenhuyse I (2012) Expected improvement in efficient global optimization through bootstrapped kriging. J Glob Optim 54:59–73MathSciNetzbMATHCrossRefGoogle Scholar
  71. Koch P, Yang R-J, Gu L (2004) Design for six sigma through robust optimization. Struct Multidiscip Optim 26:235–248CrossRefGoogle Scholar
  72. Kodiyalam S, Nagendra S, DeStefano J (1996) Composite sandwich structure optimization with application to satellite components. AIAA J 34:614–621zbMATHCrossRefGoogle Scholar
  73. Laurenceau J, Meaux M, Montagnac M, Sagaut P (2010) Comparison of gradient-based and gradient-enhanced response-surface-based optimizers. AIAA J 48:981–994CrossRefGoogle Scholar
  74. Le MN, Ong YS, Menzel S, Jin Y, Sendhoff B (2013) Evolution by adapting surrogates. Evol Comput 21:313–340CrossRefGoogle Scholar
  75. Lee K-H, Park G-J (2001) Robust optimization considering tolerances of design variables. Comput Struct 79:77–86CrossRefGoogle Scholar
  76. Li G (2007) Online and offline approximations for population based multi-objective optimization. ProQuestGoogle Scholar
  77. Li M (2011) An improved kriging-assisted multi-objective genetic algorithm. J Mech Des 133:071008-071008-071011Google Scholar
  78. Li M, Azarm S, Boyars A (2006) A new deterministic approach using sensitivity region measures for multi-objective robust and feasibility robust design optimization. J Mech Des 128:874–883CrossRefGoogle Scholar
  79. Li G, Li M, Azarm S, Rambo J, Joshi Y (2007) Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm. Distrib Parallel Databases 21:167–192CrossRefGoogle Scholar
  80. Li G, Li M, Azarm S, Al Hashimi S, Al Ameri T, Al Qasas N (2009a) Improving multi-objective genetic algorithms with adaptive design of experiments and online metamodeling. Struct Multidiscip Optim 37:447–461CrossRefGoogle Scholar
  81. Li M, Williams N, Azarm S (2009b) Interval uncertainty reduction and single-disciplinary sensitivity analysis with multi-objective optimization. J Mech Des 131:031007CrossRefGoogle Scholar
  82. Li M, Hamel J, Azarm S (2010) Optimal uncertainty reduction for multi-disciplinary multi-output systems using sensitivity analysis. Struct Multidiscip Optim 40:77–96CrossRefGoogle Scholar
  83. Li X, Qiu H, Chen Z, Gao L, Shao X (2016) A local Kriging approximation method using MPP for reliability-based design optimization. Comput Struct 162:102–115CrossRefGoogle Scholar
  84. Lian Y, Liou M-S (2005) Multiobjective optimization using coupled response surface model and evolutionary algorithm. AIAA J 43:1316–1325CrossRefGoogle Scholar
  85. Lim J, Lee B, Lee I (2014) Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization. Int J Numer Meth Eng 100:773–792MathSciNetzbMATHCrossRefGoogle Scholar
  86. Liu Y, Collette M (2014) Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm. Appl Soft Comput 24:482–493CrossRefGoogle Scholar
  87. Liu J, Han Z, Song W (2012) Comparison of infill sampling criteria in kriging-based aerodynamic optimization. In: 28th congress of the international council of the aeronautical sciences, pp 23–28Google Scholar
  88. Long T, Wu D, Guo XS, Wang GG, Liu L (2015) Efficient adaptive response surface method using intelligent space exploration strategy. Struct Multidiscip Optim 51:1335–1362CrossRefGoogle Scholar
  89. Madsen HO, Krenk S, Lind NC (2006) Methods of structural safety. Courier CorporationGoogle Scholar
  90. Martin JD, Simpson TW (2005) Use of kriging models to approximate deterministic computer models. AIAA J 43:853–863CrossRefGoogle Scholar
  91. McKay MD, Beckman RJ, Conover WJ (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42:55–61zbMATHCrossRefGoogle Scholar
  92. Mlakar M, Petelin D, Tušar T, Filipič B (2015) GP-DEMO: differential evolution for multiobjective optimization based on Gaussian process models. Eur J Oper Res 243:347–361MathSciNetzbMATHCrossRefGoogle Scholar
  93. Mogilicharla A, Mittal P, Majumdar S, Mitra K (2015) Kriging surrogate based multi-objective optimization of bulk vinyl acetate polymerization with branching. Mater Manuf Processes 30:394–402CrossRefGoogle Scholar
  94. Oberkampf W, Helton J, Sentz K (2001) Mathematical representation of uncertainty. In: 19th AIAA applied aerodynamics conference, p 1645Google Scholar
  95. Papadimitriou D, Giannakoglou K (2013) Third-order sensitivity analysis for robust aerodynamic design using continuous adjoint. Int J Numer Meth Fluids 71:652–670MathSciNetCrossRefGoogle Scholar
  96. Park H-S, Dang X-P (2010) Structural optimization based on CAD–CAE integration and metamodeling techniques. Comput Aided Des 42:889–902CrossRefGoogle Scholar
  97. Parr J, Keane A, Forrester AI, Holden C (2012) Infill sampling criteria for surrogate-based optimization with constraint handling. Eng Optim 44:1147–1166zbMATHCrossRefGoogle Scholar
  98. Ponweiser W, Wagner T, Vincze M (2008) Clustered multiple generalized expected improvement: a novel infill sampling criterion for surrogate models. In: IEEE world congress on computational intelligence evolutionary computation, 2008. CEC 2008, pp 3515–3522. IEEEGoogle Scholar
  99. Ratle A (1998) Accelerating the convergence of evolutionary algorithms by fitness landscape approximation. Parallel problem solving from nature—PPSN V. Springer, pp 87–96Google Scholar
  100. Regis RG (2013) Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions. IEEE Trans Evol Comput 18:326–347CrossRefGoogle Scholar
  101. Regis RG, Shoemaker CA (2005) Constrained global optimization of expensive black box functions using radial basis functions. J Glob Optim 31:153–171MathSciNetzbMATHCrossRefGoogle Scholar
  102. Regis RG, Shoemaker CA (2007) Improved strategies for radial basis function methods for global optimization. J Glob Optim 37:113–135MathSciNetzbMATHCrossRefGoogle Scholar
  103. Regis RG, Shoemaker CA (2013) Combining radial basis function surrogates and dynamic coordinate search in high-dimensional expensive black-box optimization. Eng Optim 45:529–555MathSciNetCrossRefGoogle Scholar
  104. Renaud J (1997) Automatic differentiation in robust optimization. AIAA J 35:1072–1079zbMATHCrossRefGoogle Scholar
  105. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 409–423MathSciNetzbMATHCrossRefGoogle Scholar
  106. Sasena MJ (2002) Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. CiteseerGoogle Scholar
  107. Sasena MJ, Papalambros P, Goovaerts P (2002) Exploration of metamodeling sampling criteria for constrained global optimization. Eng Optim 34:263–278CrossRefGoogle Scholar
  108. Schonlau M (1997) Computer experiments and global optimizationGoogle Scholar
  109. Shan S, Wang GG (2005) An efficient Pareto set identification approach for multiobjective optimization on black-box functions. J Mech Des 127:866–874CrossRefGoogle Scholar
  110. Sharif B, Wang GG, ElMekkawy TY (2008) Mode pursuing sampling method for discrete variable optimization on expensive black-box functions. J Mech Des 130:021402CrossRefGoogle Scholar
  111. Shimoyama K, Sato K, Jeong S, Obayashi S (2013) Updating kriging surrogate models based on the hypervolume indicator in multi-objective optimization. J Mech Des 135:094503CrossRefGoogle Scholar
  112. Shu L, Jiang P, Zhou Q, Shao X, Hu J, Meng X (2018) An on-line variable fidelity metamodel assisted multi-objective genetic algorithm for engineering design optimization. Appl Soft Comput 66:438–448CrossRefGoogle Scholar
  113. Simpson TW, Mauery TM, Korte JJ, Mistree F (2001) Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J 39:2233–2241CrossRefGoogle Scholar
  114. Simpson TW, Booker AJ, Ghosh D, Giunta AA, Koch PN, Yang RJ (2004) Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct Multidiscip Optim 27:302–313CrossRefGoogle Scholar
  115. Sóbester A, Leary SJ, Keane AJ (2005) On the design of optimization strategies based on global response surface approximation models. J Global Optim 33:31–59MathSciNetzbMATHCrossRefGoogle Scholar
  116. Song Z, Murray BT, Sammakia B, Lu S (2012) Multi-objective optimization of temperature distributions using Artificial Neural Networks. In: 2012 13th IEEE intersociety conference on thermal and thermomechanical phenomena in electronic systems (ITherm), pp 1209–1218. IEEEGoogle Scholar
  117. Srinivas N, Krause A, Kakade SM, Seeger MW (2012) Information-theoretic regret bounds for gaussian process optimization in the bandit setting. IEEE Trans Inf Theory 58:3250–3265MathSciNetzbMATHCrossRefGoogle Scholar
  118. Steuben JC, Turner CJ (2015) Graph analysis of non-uniform rational B-spline-based metamodels. Eng Optim 47:1157–1176MathSciNetCrossRefGoogle Scholar
  119. Sun GY, Li GY, Gong ZH, He GQ, Li Q (2011) Radial basis functional model for multi-objective sheet metal forming optimization. Eng Optim 43:1351–1366MathSciNetCrossRefGoogle Scholar
  120. Sun X, Gong D, Jin Y, Chen S (2013) A new surrogate-assisted interactive genetic algorithm with weighted semisupervised learning. IEEE Trans Cybern 43:685–698CrossRefGoogle Scholar
  121. Sun C, Jin Y, Cheng R, Ding J, Zeng J (2017) Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems. IEEE Trans Evol ComputGoogle Scholar
  122. Taguchi G (1978) Performance analysis design. Int J Prod Res 16:521–530CrossRefGoogle Scholar
  123. Tan MHY (2015a) Robust parameter design with computer experiments using orthonormal polynomials. Technometrics 57:468–478MathSciNetCrossRefGoogle Scholar
  124. Tan MHY (2015b) Stochastic polynomial interpolation for uncertainty quantification with computer experiments. Technometrics 57:457–467MathSciNetCrossRefGoogle Scholar
  125. Tang Y, Chen J, Wei J (2013) A surrogate-based particle swarm optimization algorithm for solving optimization problems with expensive black box functions. Eng Optim 45:557–576MathSciNetCrossRefGoogle Scholar
  126. Törn A, Zilinskas A (1989) Global optimization. SpringerGoogle Scholar
  127. Viana F, Haftka R (2010) Surrogate-based optimization with parallel simulations using the probability of improvement. In: 13th AIAA/ISSMO multidisciplinary analysis optimization conference, p 9392Google Scholar
  128. Viana FA, Simpson TW, Balabanov V, Toropov V (2014) Special section on multidisciplinary design optimization: metamodeling in multidisciplinary design optimization: how far have we really come? AIAA J 52:670–690CrossRefGoogle Scholar
  129. Wang GG (2003) Adaptive response surface method using inherited latin hypercube design points. J Mech Des 125:210–220CrossRefGoogle Scholar
  130. Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129:370–380CrossRefGoogle Scholar
  131. Wang L, Shan S, Wang GG (2004) Mode-pursuing sampling method for global optimization on expensive black-box functions. Eng Optim 36:419–438CrossRefGoogle Scholar
  132. Wang H, Jin Y, Jansen JO (2016) Data-driven surrogate-assisted multiobjective evolutionary optimization of a trauma system. IEEE Trans Evol Comput 20:939–952CrossRefGoogle Scholar
  133. Wang H, Jin Y, Doherty J (2017) Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems. IEEE Trans CybernGoogle Scholar
  134. Wu J, Azarm S (2001) Metrics for quality assessment of a multiobjective design optimization solution set. J Mech Des 123:18–25CrossRefGoogle Scholar
  135. Xia T, Li M, Zhou J (2016) A sequential robust optimization approach for multidisciplinary design optimization with uncertainty. J Mech Des 138:111406CrossRefGoogle Scholar
  136. Xiao S, Rotaru M, Sykulski JK (2012) Exploration versus exploitation using kriging surrogate modelling in electromagnetic design. COMPEL Int J Comput Math Electr Electron Eng 31:1541–1551CrossRefGoogle Scholar
  137. Xiao S, Rotaru M, Sykulski JK (2013) Adaptive weighted expected improvement with rewards approach in kriging assisted electromagnetic design. IEEE Trans Magn 49:2057–2060CrossRefGoogle Scholar
  138. Yondo R, Andrés E, Valero E (2018) A review on design of experiments and surrogate models in aircraft real-time and many-query aerodynamic analyses. Prog Aerosp Sci 96:23–61CrossRefGoogle Scholar
  139. Younis A, Dong Z (2010) Trends, features, and tests of common and recently introduced global optimization methods. Eng Optim 42:691–718MathSciNetCrossRefGoogle Scholar
  140. Zhang S, Zhu P, Chen W, Arendt P (2012) Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design. Struct Multidiscip Optim 47:63–76MathSciNetzbMATHCrossRefGoogle Scholar
  141. Zheng J, Li Z, Gao L, Jiang G (2016) A parameterized lower confidence bounding scheme for adaptive metamodel-based design optimization. Eng Comput 33:2165–2184CrossRefGoogle Scholar
  142. Zhou J, Li M (2014) Advanced robust optimization with interval uncertainty using a single-looped structure and sequential quadratic programming. J Mech Des 136:021008CrossRefGoogle Scholar
  143. Zhou J, Cheng S, Li M (2012) Sequential quadratic programming for robust optimization with interval uncertainty. J Mech Des 134:100913CrossRefGoogle Scholar
  144. Zhou Q, Shao X, Jiang P, Cao L, Zhou H, Shu L (2015a) Differing mapping using ensemble of metamodels for global variable-fidelity metamodeling. CMES Comput Model Eng Sci 106: 23–355Google Scholar
  145. Zhou Q, Shao X, Jiang P, Zhou H, Cao L, Zhang L (2015b) A deterministic robust optimisation method under interval uncertainty based on the reverse model. J Eng Des 26:416–444CrossRefGoogle Scholar
  146. Zhou Q, Shao X, Jiang P, Zhou H, Cao L, Zhang L (2015) A deterministic robust optimisation method under interval uncertainty based on the reverse model. J Eng Des 1–29Google Scholar
  147. Zhou Q, Shao X, Jiang P, Gao Z, Wang C, Shu L (2016a) An active learning metamodeling approach by sequentially exploiting difference information from variable-fidelity models. Adv Eng Inform 30:283–297CrossRefGoogle Scholar
  148. Zhou Q, Shao X, Jiang P, Gao Z, Zhou H, Shu L (2016b) An active learning variable-fidelity metamodelling approach based on ensemble of metamodels and objective-oriented sequential sampling. J Eng Des 27:205–231CrossRefGoogle Scholar
  149. Zhou Q, Wang Y, Jiang P, Shao X, Choi S-K, Hu J, Cao L, Meng X (2017) An active learning radial basis function modeling method based on self-organization maps for simulation-based design problems. Knowl Based Syst 131:10–27CrossRefGoogle Scholar
  150. Zhu P, Zhang Y, Chen G (2009) Metamodel-based lightweight design of an automotive front-body structure using robust optimization. Proc Inst Mech Eng Part D J Automob Eng 223:1133–1147CrossRefGoogle Scholar
  151. Zhu J, Wang Y-J, Collette M (2013) A multi-objective variable-fidelity optimization method for genetic algorithms. Eng Optim 46:521–542MathSciNetCrossRefGoogle Scholar
  152. Zhu J, Wang Y-J, Collette M (2014) A multi-objective variable-fidelity optimization method for genetic algorithms. Eng Optim 46:521–542MathSciNetCrossRefGoogle Scholar
  153. Zhu P, Zhang S, Chen W (2015) Multi-point objective-oriented sequential sampling strategy for constrained robust design. Eng Optim 47:287–307CrossRefGoogle Scholar
  154. Zimmermann R, Han Z (2010) Simplified cross-correlation estimation for multi-fidelity surrogate cokriging models. Adv Appl Math Sci 7:181–202MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.School of Aerospace EngineeringHuazhong University of Science and TechnologyWuhanChina
  3. 3.The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations