Abstract
Surrogate-Assisted Evolutionary Optimisation algorithms are a specialized brand of optimisers developed to undertake problems with computationally expensive fitness functions. These algorithms work by building a cheap approximation or model of the exact function and using it in the evaluation of solutions within the optimisation process. This use of modelling techniques within optimisation, while offers a practical reduction in function calls, brings along with it some additional questions. This paper starts with a description of the key elements of surrogate-assisted evolutionary optimisation algorithms as they are outlined throughout the literature, and then, proceeds to rearrange these elements using a novel blueprint of the field. The proposed blueprint can be used to represent any surrogate-assisted evolutionary algorithm in a way that illustrates its principles and components in a non-vague manner. In addition, a survey of the most prominent works in the field is conducted using this novel blueprint. Finally, a number of challenges and perspectives are listed before the paper is concluded.
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The purpose given here is just an example, the approximation action can have other purposes which will be discussed later.
We include in our denotation of evolutionary algorithms here swarm intelligence algorithms.
PFoM refers to methods that combine predicted fitness and uncertainty estimates in a different manner than the three first criteria.
The selection of sample points is not to be confused with the evolutionary selection operator of the EA.
This question works better if we say what to optimise?
References
Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput. 9:3–12. https://doi.org/10.1007/s00500-003-0328-5
Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1(2):61–70. https://doi.org/10.1016/j.swevo.2011.05.001
Shi L, Rasheed K (2010) Computational intelligence in expensive optimization problems, adaptation learning and optimization, vol 2, Springer, Berlin, Heidelberg, chap A survey of fitness approximation methods applied in evolutionary algorithms, pp 3–28. https://doi.org/10.1007/978-3-642-10701-6_1
Giannakoglou K (2002) Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress Aerosp Sci 38(1):43–76. https://doi.org/10.1016/S0376-0421(01)00019-7
Stork J, Eiben AE, Bartz-Beielstein T (2020) A new taxonomy of global optimization algorithms. Nat Comput. https://doi.org/10.1007/s11047-020-09820-4
Diaz-Manriquez A, Pulido GT, Barron-Zambrano JH, Tello-Leal E (2016) A review of surrogate assisted multiobjective evolutionary algorithms. Comput Intell Neurosci 2016:1–14. https://doi.org/10.1155/2016/9420460
Knowles J, Nakayama H (2008) Meta-modeling in multiobjective optimization. In: Branke J, Deb K, Miettinen K, Słowiński R (eds) Multiobjective optimization interactive and evolutionary approaches, Springer, Berlin, Heidelberg., Lecture Notes in Computer Science, vol 5252, pp 245–284. https://doi.org/10.1007/978-3-540-88908-3_10
Santana-Quintero LV, Montano AA, Coello CAC (2010) Computational intelligence in expensive optimization problems, adaptation learning and optimization, vol 2, Springer, Berlin, Heidelberg, chap A Review of techniques for handling expensive functions in evolutionary multi-objective optimization, pp 29–59. https://doi.org/10.1007/978-3-642-10701-6_2
Allmendinger R, Emmerich M, Hakanen J, Jin Y, Rigoni E (2016) Surrogate-assisted multicriteria optimization: complexities, prospective solutions, and business case. J Multi-Criteria Decis Anal 24:5–24. https://doi.org/10.1002/mcda.1605
Horn D, Wagner T, Biermann D, Weihs C, Bischl B (2015) Model-based multi-objective optimization: taxonomy, multi-point proposal, toolbox and benchmark. In: Gaspar-Cunha A, Henggeler Antunes C, Coello CC (eds) Evol Multi-Criterion Optim. Springer International Publishing, Cham, pp 64–78
Chugh T, Sindhya K, Hakanen J, Miettinen K (2019) A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms. Soft Comput 23(9):3137–3166. https://doi.org/10.1007/s00500-017-2965-0
Cheng R, He C, Jin Y, Yao X (2018) Model-based evolutionary algorithms: a short survey. Complex Intell Syst 4(4):283–292. https://doi.org/10.1007/s40747-018-0080-1
Floreano D, Mattiussi C (2008) Bio-inspired artificial intelligence: theories, methods, and technologies, 1st edn. Intelligent robotics and autonomous agents, MIT Press, http://gen.lib.rus.ec/book/index.php?md5=231C7BABF8E623557C3B0C72307E2BB4
Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73
Fogel G, Fogel D, Fogel L (2011) Evolutionary programming. Scholarpedia 6(4):1818. https://doi.org/10.4249/scholarpedia.1818
Beyer HG, Schwefel HP (2002) Evolution strategies – a comprehensive introduction. Natural Comput 1(1):3–52. https://doi.org/10.1023/A:1015059928466
Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359. https://doi.org/10.1023/A:1008202821328
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95 - International conference on neural networks, vol 4, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
Dorigo M, Di Caro G (1999) Ant colony optimization: a new meta-heuristic. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), vol 2, pp 1470–1477. https://doi.org/10.1109/CEC.1999.782657
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J Glob Optim 39(3):459–471. https://doi.org/10.1007/s10898-007-9149-x
Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195. https://doi.org/10.1162/106365601750190398
Schmit LA, Miura H (1976) Approximation concepts for efficient structural synthesis. techreport, NASA
Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409–423
Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266
Elanayar VTS, Shin YC (1994) Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans Neural Netw 5(4):594–603. https://doi.org/10.1109/72.298229
Box GEP, Wilson KB (1951) On the experimental attainment of optimum conditions. J R Stat Soc Ser B (Methodological) 13(1):1–38. https://doi.org/10.1111/j.2517-6161.1951.tb00067.x
Basheer I, Hajmeer M (2000) Artificial neural networks: fundamentals, computing, design, and application. J Microbiol Methods 43(1):3–31. https://doi.org/10.1016/S0167-7012(00)00201-3
Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297. https://doi.org/10.1007/BF00994018
Simpson T, Toropov V, Balabanov V, Viana F (2008) Design and analysis of computer experiments in multidisciplinary design optimization: A review of how far we have come - or not. In: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, British Columbia, Canada, https://doi.org/10.2514/6.2008-5802
Rasmussen CE, Williams CKI (2005) Gaussian processes for machine learning. The MIT Press. https://doi.org/10.7551/mitpress/3206.001.0001
Simpson T, Mistree F, Korte J, Mauery T (1998) Comparison of response surface and kriging models for multidisciplinary design optimization. In: 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, American Institute of Aeronautics and Astronautics AIAA, St. Louis, MO, USA, https://doi.org/10.2514/6.1998-4755
Elanayar VTS, Shin YC (1994) Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans Neural Netw 5(4):594–603. https://doi.org/10.1109/72.298229
Regis RG (2014) Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions. IEEE Trans Evol Comput 18(3):326–347. https://doi.org/10.1109/TEVC.2013.2262111
Díaz-Manríquez A, Toscano-Pulido G, Gómez-Flores W (2011) On the selection of surrogate models in evolutionary optimization algorithms. In: 2011 IEEE congress of evolutionary computation (CEC), pp 2155–2162. https://doi.org/10.1109/CEC.2011.5949881
Hajela P (1997) Non-gradient methods in mdo—status and future directions. In: 38th Structures, structural dynamics, and materials conference, American Institute of Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, Kissimmee, FL, U.S.A. https://doi.org/10.2514/6.1997-1570
Hajela P, Lee J (1995) Genetic algorithms in multidisciplinary rotor blade design. In: 36th Structures, structural dynamics and materials conference, American Institute of Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, New Orleans, LA, USA. https://doi.org/10.2514/6.1995-1144
Szewczyk Z, Hajela P (1993) Neural network approximations in a simulated annealing based optimal structural design. Struct optim 5(3):159–165. https://doi.org/10.1007/BF01743352
Rosales-Pérez A, Coello CAC, Gonzalez JA, Reyes-Garcia CA, Escalante HJ (2013) A hybrid surrogate-based approach for evolutionary multi-objective optimization. In: 2013 IEEE congress on evolutionary computation, IEEE, pp 2548–2555. https://doi.org/10.1109/CEC.2013.6557876
Bhattacharjee KS, Singh HK, Ray T, Branke J (2016) Multiple surrogate assisted multiobjective optimization using improved pre-selection. In: 2016 IEEE congress on evolutionary computation (CEC), IEEE, Vancouver, BC, Canada, pp 4328–4335. https://doi.org/10.1109/CEC.2016.7744340
Ratle A (1999) Optimal sampling strategies for learning a fitness model. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), vol 3, pp 2078–2085. https://doi.org/10.1109/CEC.1999.785531
Dietterich TG (2000) Ensemble methods in machine learning. In: Proceedings of the First international workshop on multiple classifier systems, Springer-Verlag, Berlin, Heidelberg, MCS ’00. pp 1–15
Hamza K, Saitou K (2012) A co-evolutionary approach for design optimization via ensembles of surrogates with application to vehicle crashworthiness. J Mech Des 134(1):011001-1–011001-10. https://doi.org/10.1115/1.4005439
Gorissen D, Dhaene T, Turck FD (2009) Evolutionary model type selection for global surrogate modeling. J Mach Learn Res 10:2039–2078
Jin Y, Husken M, Sendhoff B (2003) Quality measures for approximate models in evolutionary computation. In: GECCO 2003: Proceedings of the bird of a feather workshop, genetic and evolutionary computation conference, AAAI, pp 170–173
Gräning L, Jin Y, Sendhoff B (2007) Individual-based management of meta-models for evolutionary optimization with application to three-dimensional blade optimization. In: Yang S, Ong YS, Jin Y (eds) Evolutionary computation in dynamic and uncertain environments, studies in computational intelligence, vol 51, Springer Berlin Heidelberg, chap 10, pp 225–250. https://doi.org/10.1007/978-3-540-49774-5_10
Le MN, Ong YS, Menzel S, Jin Y, Sendhoff B (2013) Evolution by adapting surrogates. Evol Comput 21(2):313–340. https://doi.org/10.1162/EVCO_a_00079
Bischl B, Mersmann O, Trautmann H, Weihs C (2012) Resampling methods for meta-model validation with recommendations for evolutionary computation. Evol Comput 20(2):249–275. https://doi.org/10.1162/evco_a_00069
Lu J, Li B, Jin Y (2013) An evolution strategy assisted by an ensemble of local gaussian process models. In: Blum C (ed) GECCO 2013—Proceedings of the 2013 genetic and evolutionary computation conference, Association for Computing Machinery New York NY United States, Amsterdam The Netherlands, pp 447–454. https://doi.org/10.1145/2463372.2463425
Zongzhao Zhou, Yew Soon Ong, My Hanh Nguyen, Dudy Lim (2005) A study on polynomial regression and gaussian process global surrogate model in hierarchical surrogate-assisted evolutionary algorithm. In: 2005 IEEE Congress on Evolutionary Computation, IEEE, Edinburgh, Scotland, UK, vol 3, pp 2832–2839 Vol. 3, https://doi.org/10.1109/CEC.2005.1555050
Wang H, Jin Y, Jansen JO (2016) Data-driven surrogate-assisted multiobjective evolutionary optimization of a trauma system. IEEE Trans Evol Comput 20(6):939–952. https://doi.org/10.1109/TEVC.2016.2555315
Gräning L, Jin Y, Sendhoff B (2005) Efficient evolutionary optimization using individual-based evolution control and neural networks: A comparative study. ESANN 2005, 13th European symposium on artificial neural networks. Bruges, Belgium, pp 273–278
Alexandrov NM, Dennis JE, Lewis RM, Torczon V (1998) A trust-region framework for managing the use of approximation models in optimization. Struct Optim 15(1):16–23. https://doi.org/10.1007/BF01197433
Ong YS, Nair PB, Keane AJ (2003) Evolutionary optimization of computationally expensive problems via surrogate modeling. AIAA J 41(4):687–696. https://doi.org/10.2514/2.1999
Lim D, Jin Y, Ong Y, Sendhoff B (2010) Generalizing surrogate-assisted evolutionary computation. IEEE Trans Evol Comput 14(3):329–355. https://doi.org/10.1109/TEVC.2009.2027359
Coello Coello CA (1999) A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowl Inf Syst 1(3):269–308. https://doi.org/10.1007/BF03325101
Wu M, Li K, Kwong S, Zhang Q, Zhang J (2019) Learning to decompose: a paradigm for decomposition-based multiobjective optimization. IEEE Trans Evol Comput 23(3):376–390. https://doi.org/10.1109/TEVC.2018.2865931
Audet C, Bigeon J, Cartier D, Le Digabel S, Salomon L (2021) Performance indicators in multiobjective optimization. Eur J Oper Res 292(2):397–422. https://doi.org/10.1016/j.ejor.2020.11.016
Tabatabaei M, Hakanen J, Hartikainen M, Miettinen K, Sindhya K (2015) A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods. Struct Multidiscip Optim 52(1):1–25. https://doi.org/10.1007/s00158-015-1226-z
Brownlee A, Mccall J, Zhang Q (2013) Fitness modeling with Markov networks. IEEE Trans Evol Comput 17(6):862–879. https://doi.org/10.1109/TEVC.2013.2281538
Pelikan M, Goldberg DE, Cantú-Paz E (2000) Linkage problem, distribution estimation, and bayesian networks. Evol Comput 8(3):311–340. https://doi.org/10.1162/106365600750078808
Hauschild M, Pelikan M (2011) An introduction and survey of estimation of distribution algorithms. Swarm Evol Comput 1(3):111–128. https://doi.org/10.1016/j.swevo.2011.08.003
Gibson PM, Byrne JA (1991) Neurogen, musical composition using genetic algorithms and cooperating neural networks. In: 1991 Second international conference on artificial neural networks, IEEE, pp 309–313
Spector L, Alpern A (1995) Induction and recapitulation of deep musical structure. In: In Proceedings of the IJCAI-95 workshop on artificial intelligence and music, pp 41–48
Baluja S, Pomerleau D, Jochem T (1994) Towards automated artificial evolution for computer-generated images. Connect Sci 6(2–3):325–354. https://doi.org/10.1080/09540099408915729
Jin Y, Wang H, Chugh T, Guo D, Miettinen K (2019) Data-driven evolutionary optimization: an overview and case studies. IEEE Trans Evol Comput 23(3):442–458. https://doi.org/10.1109/TEVC.2018.2869001
Zhou Z, Ong YS, Nair PB, Keane AJ, Lum KY (2007) Combining global and local surrogate models to accelerate evolutionary optimization. IEEE Trans Syst Man Cybern Part C 37(1):66–76. https://doi.org/10.1109/TSMCC.2005.855506
Lim D, Ong Y, Jin Y, Sendhoff B (2007) A study on metamodeling techniques, ensembles, and multi-surrogates in evolutionary computation. In: GECCO ’07: Proceedings of the 9th annual conference on Genetic and evolutionary computation, association for computing machinery, New York, NY, USA, pp 1288–1295. https://doi.org/10.1145/1276958.1277203
Bajer L, Holeňa M (2010) Surrogate model for continuous and discrete genetic optimization based on rbf networks. In: Fyfe C, Tino P, Charles D, Garcia-Osorio C, Yin H (eds) Intelligent data engineering and automated learning—IDEAL 2010, Springer Berlin Heidelberg, Paisley, UK, Lecture Notes in Computer Science, vol 6283, pp 251–258
Kim HS, Cho SB (2001) An efficient genetic algorithm with less fitness evaluation by clustering. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No.01TH8546), vol 2, pp 887–894. https://doi.org/10.1109/CEC.2001.934284
Ratle A (1998) Accelerating the convergence of evolutionary algorithms by fitness landscape approximation. In: Eiben AE, Bäck T, Schoenauer M, Schwefel HP (eds) Parallel problem solving from nature—PPSN V, Springer Berlin Heidelberg, Amsterdam, The Netherlands, Lecture Notes in Computer Science, vol 1498, pp 87–96
Handoko SD, Kwoh CK, Ong Y (2010) Feasibility structure modeling: an effective chaperone for constrained memetic algorithms. IEEE Trans Evol Comput 14(5):740–758. https://doi.org/10.1109/TEVC.2009.2039141
Rasheed K (2000) An incremental-approximate-clustering approach for developing dynamic reduced models for design optimization. In: Proceedings of the 2000 congress on evolutionary computation. CEC00 (Cat. No.00TH8512), IEEE, La Jolla, CA, USA, vol 2, pp 986–993. https://doi.org/10.1109/CEC.2000.870752
Zhou Z, Ong YS, Lim MH, Lee BS (2007) Memetic algorithm using multi-surrogates for computationally expensive optimization problems. Soft Comput 11(10):957–971. https://doi.org/10.1007/s00500-006-0145-8
Lian Y, Liou MS (2005) Multiobjective optimization using coupled response surface model and evolutionary algorithm. AIAA J 43(6):1316–1325. https://doi.org/10.2514/1.12994
Kattan A, Galvan E (2012) Evolving radial basis function networks via gp for estimating fitness values using surrogate models. In: 2012 IEEE Congress on Evolutionary Computation, pp 1–7, https://doi.org/10.1109/CEC.2012.6256108
Ong YS, Lum KY, Nair PB (2008) Hybrid evolutionary algorithm with hermite radial basis function interpolants for computationally expensive adjoint solvers. Comput Optim Appl 39(1):97–119. https://doi.org/10.1007/s10589-007-9065-5
Fan M, Li J (2020) Surrogate-assisted genetic algorithms for the travelling salesman problem and vehicle routing problem. In: 2020 IEEE congress on evolutionary computation (CEC), pp 1–7. https://doi.org/10.1109/CEC48606.2020.9185817
Li JY, Zhan ZH, Wang H, Zhang J (2020) Data-driven evolutionary algorithm with perturbation-based ensemble surrogates. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3008280
Liang Kh, Yao X, Newton C (2000) Evolutionary search of approximated n-dimensional landscapes. Int J Knowl Based Intell Eng Syst 4:172–183
Jin Y, Sendhoff B (2004) Reducing fitness evaluations using clustering techniques and neural network ensembles. In: Deb K (ed) Genetic and evolutionary computation—GECCO 2004, Springer Berlin Heidelberg, Seattle, WA, USA, Lecture Notes in Computer Science, vol 3102, pp 688–699
Bhattacharjee K, Singh H, Ray T (2018) Multiple surrogate-assisted many-objective optimization for computationally expensive engineering design. J Mech Des 140(5):051403-1–051403-10. https://doi.org/10.1115/1.4039450
Branke J, Schmidt C (2005) Faster convergence by means of fitness estimation. Soft Comput 9(1):13–20. https://doi.org/10.1007/s00500-003-0329-4
Emmerich MTM, Giannakoglou KC, Naujoks B (2006) Single- and multiobjective evolutionary optimization assisted by gaussian random field metamodels. IEEE Trans Evol Comput 10(4):421–439. https://doi.org/10.1109/TEVC.2005.859463
Ulmer H, Streichert F, Zell A (2004) Evolution strategies assisted by gaussian processes with improved pre-selection criterion. In: Proceedings of The IEEE Congress on Evolutionary Computation, 2003 Cec ’03 1:692–699. https://doi.org/10.1109/CEC.2003.1299643
Georgopoulou CA, Giannakoglou KC (2009) A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement. Eng Optim 41(10):909–923. https://doi.org/10.1080/03052150902866577
Dudy Lim, Yew-Soon Ong, Yaochu Jin, Sendhoff B (2006) Trusted evolutionary algorithm. In: 2006 IEEE international conference on evolutionary computation, pp 149–156. https://doi.org/10.1109/CEC.2006.1688302
Yang J, Arnold DV (2019) A surrogate model assisted (1+1)-es with increased exploitation of the model. In: Proceedings of the genetic and evolutionary computation conference, Association for computing machinery, New York, NY, USA, GECCO ’19, p 727–735, https://doi.org/10.1145/3321707.3321728
Hansen N (2019) A Global Surrogate Assisted CMA-ES. In: GECCO 2019—the genetic and evolutionary computation conference, ACM, Prague, Czech Republic, pp 664–672. https://doi.org/10.1145/3321707.3321842, https://hal.inria.fr/hal-02143961
Jin Yaochu, Olhofer M, Sendhoff B (2002) A framework for evolutionary optimization with approximate fitness functions. IEEE Trans Evol Comput 6(5):481–494. https://doi.org/10.1109/TEVC.2002.800884
Husken M, Jin Y, Sendhoff B (2005) Structure optimization of neural networks for evolutionary design optimization. Soft Comput 9(1):21–28. https://doi.org/10.1007/s00500-003-0330-y
Willmes L, Back T, Yaochu Jin, Sendhoff B (2003) Comparing neural networks and kriging for fitness approximation in evolutionary optimization. In: The 2003 congress on evolutionary computation, 2003. CEC ’03., IEEE, vol 1, pp 663–670. https://doi.org/10.1109/CEC.2003.1299639
Buche D, Schraudolph NN, Koumoutsakos P (2005) Accelerating evolutionary algorithms with gaussian process fitness function models. IEEE Trans Syst Man Cybern Part C (Appl Rev) 35(2):183–194. https://doi.org/10.1109/TSMCC.2004.841917
Loshchilov I, Schoenauer M, Sebag M (2010) Comparison-based optimizers need comparison-based surrogates. In: Schaefer R, Cotta C, Kołodziej J, Rudolph G (eds) Parallel problem solving from nature XI (PPSN 2010), Springer, Berlin, Heidelberg, Kraków, Poland, Lecture Notes in computer science, vol 6238, pp 364–373. https://doi.org/10.1007/978-3-642-15844-5_37
Bajer L, Pitra Z, Repický J, Holeňa M (2019) Gaussian process surrogate models for the cma evolution strategy. Evol Comput 27(4):665–697. https://doi.org/10.1162/evco_a_00244
Pitra Z, Bajer L, Repický J, Holeňa M (2017) Overview of surrogate-model versions of covariance matrix adaptation evolution strategy. In: Proceedings of the genetic and evolutionary computation conference companion, Association for Computing Machinery, New York, NY, USA, GECCO ’17, p 1622–1629, https://doi.org/10.1145/3067695.3082539,
Rui Li, Emmerich MTM, Eggermont J, Bovenkamp EGP, Back T, Dijkstra J, Reiber JHC (2008) Metamodel-assisted mixed integer evolution strategies and their application to intravascular ultrasound image analysis. In: 2008 IEEE congress on evolutionary computation (IEEE World Congress on Computational Intelligence), IEEE, Hong Kong, China, pp 2764–2771, https://doi.org/10.1109/CEC.2008.4631169
Emmerich M, Grötzner M, Groß B, Schütz M (2000) Mixed-integer evolution strategy for chemical plant optimization with simulators. In: Parmee IC (ed) Evolutionary design and manufacture. Springer, London, London, pp 55–67
Fu G, Sun C, Tan Y, Zhang G, Jin Y (2020) A surrogate-assisted evolutionary algorithm with random feature selection for large-scale expensive problems. In: Bäck T, Preuss M, Deutz A, Wang H, Doerr C, Emmerich M, Trautmann H (eds) Parallel problem solving from nature—PPSN XVI, Springer International Publishing, Leiden, The Netherlands., Lecture Notes in Computer Science, vol 12269, pp 125–139
Liu B, Zhang Q, Gielen GGE (2014) A gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems. IEEE Trans Evol Comput 18(2):180–192. https://doi.org/10.1109/TEVC.2013.2248012
Liu B, Yang H, Lancaster MJ (2017) Global optimization of microwave filters based on a surrogate model-assisted evolutionary algorithm. IEEE Trans Microw Theory Tech 65(6):1976–1985. https://doi.org/10.1109/TMTT.2017.2661739
Mallipeddi R, Lee M (2015) An evolving surrogate model-based differential evolution algorithm. Appl Soft Comput 34:770–787. https://doi.org/10.1016/j.asoc.2015.06.010
Vincenzi L, Gambarelli P (2017) A proper infill sampling strategy for improving the speed performance of a surrogate-assisted evolutionary algorithm. Comput Struct 178(C):58–70. https://doi.org/10.1016/j.compstruc.2016.10.004
Vincenzi L, Savoia M (2015) Coupling response surface and differential evolution for parameter identification problems. Comput Aided Civ Infrastruct Eng 30(5):376–393. https://doi.org/10.1111/mice.12124
Zhang Y, Gong C, Li C (2020) Surrogate-assisted memetic algorithm with adaptive patience criterion for computationally expensive optimization. In: 2020 IEEE congress on evolutionary computation (CEC), pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185731
Yu M, Li X, Liang J (2020) A dynamic surrogate-assisted evolutionary algorithm framework for expensive structural optimization. Struct Multidisc Optim 61(2):711–729. https://doi.org/10.1007/s00158-019-02391-8
Biswas S, Cobb AD, Sistrunk A, Ramakrishnan N, Jalaian B (2020) Better call surrogates: A hybrid evolutionary algorithm for hyperparameter optimization. arxiv: 2012.06453
Oliveira JA, Almeida MS, Santos RYC, de Gusmão RP, Britto A (2020) New surrogate approaches applied to meta-heuristic algorithms. In: Rutkowski L, Scherer R, Korytkowski M, Pedrycz W, Tadeusiewicz R, Zurada JM (eds) Artif Intell Soft Comput. Springer International Publishing, Cham, pp 400–411
Yang Z, Qiu H, Gao L, Jiang C, Zhang J (2019) Two-layer adaptive surrogate-assisted evolutionary algorithm for high-dimensional computationally expensive problems. J Glob Optim 74(2):327–359. https://doi.org/10.1007/s10898-019-00759-0
Habib A, Singh KH, Ray T (2019) A multiple surrogate assisted multi/many-objective multi-fidelity evolutionary algorithm. Inf Sci 502:537–557. https://doi.org/10.1016/j.ins.2019.06.016
Wang X, Wang GG, Song B, Wang P, Wang Y (2019) A novel evolutionary sampling assisted optimization method for high-dimensional expensive problems. IEEE Trans Evol Comput 23(5):815–827. https://doi.org/10.1109/TEVC.2019.2890818
Dong H, Li C, Song B, Wang P (2018) Multi-surrogate-based differential evolution with multi-start exploration (mdeme) for computationally expensive optimization. Adv Eng Softw 123:62–76. https://doi.org/10.1016/j.advengsoft.2018.06.001
Wang Y, Yin D, Yang S, Sun G (2019) Global and local surrogate-assisted differential evolution for expensive constrained optimization problems with inequality constraints. IEEE Trans Cybern 49(5):1642–1656. https://doi.org/10.1109/TCYB.2018.2809430
Zhang J, Sanderson AC (2009) Jade: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958. https://doi.org/10.1109/TEVC.2009.2014613
Cai X, Gao L, Li X, Qiu H (2019) Surrogate-guided differential evolution algorithm for high dimensional expensive problems. Swarm Evol Comput 48:288–311. https://doi.org/10.1016/j.swevo.2019.04.009
Liu D, Huang S, Zhong J (2018) Surrogate-assisted multi-tasking memetic algorithm. In: 2018 IEEE Congress on evolutionary computation (CEC), pp 1–8. https://doi.org/10.1109/CEC.2018.8477830
Dong H, Sun S, Song B, Wang P (2019) Multi-surrogate-based global optimization using a score-based infill criterion. Struct Multidiscip Optim 59(2):485–506. https://doi.org/10.1007/s00158-018-2079-z
Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: 2013 IEEE congress on evolutionary computation, pp 71–78. https://doi.org/10.1109/CEC.2013.6557555
Awad NH, Ali MZ, Mallipeddi R, Suganthan PN (2018) An improved differential evolution algorithm using efficient adapted surrogate model for numerical optimization. Inf Sci 451–452:326–347. https://doi.org/10.1016/j.ins.2018.04.024
Mininno E, Neri F, Cupertino F, Naso D (2011) Compact differential evolution. IEEE Trans Evol Comput 15(1):32–54. https://doi.org/10.1109/TEVC.2010.2058120
Yang Z, Qiu H, Gao L, Cai X, Jiang C, Chen L (2020) Surrogate-assisted classification-collaboration differential evolution for expensive constrained optimization problems. Inf Sci 508:50–63. https://doi.org/10.1016/j.ins.2019.08.054
Jin C, Qin AK, Tang K (2015) Local ensemble surrogate assisted crowding differential evolution. In: 2015 IEEE congress on evolutionary computation (CEC), pp 433–440. https://doi.org/10.1109/CEC.2015.7256922
Sarker RA, Elsayed SM, Ray T (2014) Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans Evol Comput 18(5):689–707. https://doi.org/10.1109/TEVC.2013.2281528
Elsayed SM, Ray T, Sarker RA (2014) A surrogate-assisted differential evolution algorithm with dynamic parameters selection for solving expensive optimization problems. In: 2014 IEEE congress on evolutionary computation (CEC), pp 1062–1068. https://doi.org/10.1109/CEC.2014.6900351
Yu H, Tan Y, Zeng J, Sun C, Jin Y (2018) Surrogate-assisted hierarchical particle swarm optimization. Inf Sci 454–455:59–72. https://doi.org/10.1016/j.ins.2018.04.062
Wang H, Jin Y, Doherty J (2017) Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems. IEEE Trans Cybern 47(9):2664–2677. https://doi.org/10.1109/TCYB.2017.2710978
Sun C, Jin Y, Zeng J, Yu Y (2015) A two-layer surrogate-assisted particle swarm optimization algorithm. Soft Comput 19(6):1461–1475. https://doi.org/10.1007/s00500-014-1283-z
Regis RG (2014) Particle swarm with radial basis function surrogates for expensive black-box optimization. J Comput Sci 5(1):12–23. https://doi.org/10.1016/j.jocs.2013.07.004
Praveen C, Duvigneau R (2009) Low cost pso using metamodels and inexact pre-evaluation: application to aerodynamic shape design. Comput Methods Appl Mech Eng 198(9):1087–1096. https://doi.org/10.1016/j.cma.2008.11.019
Qu M, Wang J, Shi X, Chen X (2020) Trust regions in surrogate-assisted local search for industrial columns’ mass transfer efficiencies estimation. In: 2020 IEEE congress on evolutionary computation (CEC), pp 1–6. https://doi.org/10.1109/CEC48606.2020.9185656
Li F, Cai X, Gao L, Shen W (2021) A surrogate-assisted multiswarm optimization algorithm for high-dimensional computationally expensive problems. IEEE Trans Cybern 51(3):1390–1402. https://doi.org/10.1109/TCYB.2020.2967553
Regis RG (2018) Surrogate-assisted particle swarm with local search for expensive constrained optimization. In: Korošec P, Melab N, Talbi EG (eds) Bioinspired optimization methods and their applications. Springer International Publishing, Cham, pp 246–257
Sun C, Jin Y, Cheng R, Ding J, Zeng J (2017) Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems. IEEE Trans Evol Comput 21(4):644–660. https://doi.org/10.1109/TEVC.2017.2675628
Tian J, Tan Y, Zeng J, Sun C, Jin Y (2019) Multiobjective infill criterion driven gaussian process-assisted particle swarm optimization of high-dimensional expensive problems. IEEE Trans Evol Comput 23(3):459–472. https://doi.org/10.1109/TEVC.2018.2869247
Tian J, Sun C, Tan Y, Zeng J (2020) Granularity-based surrogate-assisted particle swarm optimization for high-dimensional expensive optimization. Knowl Based Syst 187:104815. https://doi.org/10.1016/j.knosys.2019.06.023
Yu H, Tan Y, Sun C, Zeng J (2019) A generation-based optimal restart strategy for surrogate-assisted social learning particle swarm optimization. Knowl Based Syst 163:14–25. https://doi.org/10.1016/j.knosys.2018.08.010
Cai X, Qiu H, Gao L, Jiang C, Shao X (2019) An efficient surrogate-assisted particle swarm optimization algorithm for high-dimensional expensive problems. Knowl Based Syst 184:104901. https://doi.org/10.1016/j.knosys.2019.104901
Guo D, Jin Y, Ding J, Chai T (2019) Heterogeneous ensemble-based infill criterion for evolutionary multiobjective optimization of expensive problems. IEEE Trans Cybern 49(3):1012–1025. https://doi.org/10.1109/TCYB.2018.2794503
Dan Guo, Chai T, Jinliang Ding, Jin Y (2016) Small data driven evolutionary multi-objective optimization of fused magnesium furnaces. In: 2016 IEEE symposium series on computational intelligence (SSCI), Athens, Greece, pp 1–8. https://doi.org/10.1109/SSCI.2016.7850211
Isaacs A, Ray T, Smith W (2009) Multiobjective design optimization using multiple adaptive spatially distributed surrogates. Int J Product Dev 9(1):188–217. https://doi.org/10.1504/IJPD.2009.026179
Di Nuovo AG, Ascia G, Catania V (2012) A study on evolutionary multi-objective optimization with fuzzy approximation for computational expensive problems. In: Coello CAC, Cutello V, Deb K, Forrest S, Nicosia G, Pavone M (eds) Parallel problem solving from nature—PPSN XII, Springer Berlin Heidelberg, Taormina, Italy, Lecture Notes in Computer Science, vol 7492, pp 102–111
Daniel Marjavaara B, Staffan Lundström T, Goel T, Mack Y, Shyy W (2007) Hydraulic turbine diffuser shape optimization by multiple surrogate model approximations of pareto fronts. J Fluids Eng 129(9):1228–1240. https://doi.org/10.1115/1.2754324
Liu Y, Collette M (2014) Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm. Appl Soft Comput 24:482–493. https://doi.org/10.1016/j.asoc.2014.07.022
Palar PS, Tsuchiya T, Parks G (2015) Comparison of scalarization functions within a local surrogate assisted multi-objective memetic algorithm framework for expensive problems. In: 2015 IEEE congress on evolutionary computation (CEC), pp 862–869. https://doi.org/10.1109/CEC.2015.7256981
Wang H, Jin Y (2020) A random forest-assisted evolutionary algorithm for data-driven constrained multiobjective combinatorial optimization of trauma systems. IEEE Trans Cybern 50(2):536–549. https://doi.org/10.1109/TCYB.2018.2869674
Lu Z, Deb K, Goodman E, Banzhaf W, Boddeti VN (2020) Nsganetv2: evolutionary multi-objective surrogate-assisted neural architecture search. In: Vedaldi A, Bischof H, Brox T, Frahm JM (eds) Computer vision—ECCV 2020. Springer International Publishing, Cham, pp 35–51
Ruan X, Li K, Derbel B, Liefooghe A (2020) Surrogate assisted evolutionary algorithm for medium scale multi-objective optimisation problems. In: Proceedings of the 2020 genetic and evolutionary computation conference, Association for Computing Machinery, New York, NY, USA, GECCO ’20, p 560–568. https://doi.org/10.1145/3377930.3390191,
Ahmed MYM, Qin N (2012) Surrogate-based multi-objective aerothermodynamic design optimization of hypersonic spiked bodies. AIAA J 50(4):797–810. https://doi.org/10.2514/1.J051018
Herrera M, Guglielmetti A, Xiao M, Filomeno Coelho R (2014) Metamodel-assisted optimization based on multiple kernel regression for mixed variables. Struct Multidiscip Optim 49(6):979–991. https://doi.org/10.1007/s00158-013-1029-z
Pilát M, Neruda R (2013) Aggregate meta-models for evolutionary multiobjective and many-objective optimization. Neurocomputing 116:392–402. https://doi.org/10.1016/j.neucom.2012.06.043
Loshchilov I, Schoenauer M, Sebag M (2010a) Dominance-based pareto-surrogate for multi-objective optimization. In: Deb K, Bhattacharya A, Chakraborti N, Chakroborty P, Das S, Dutta J, Gupta SK, Jain A, Aggarwal V, Branke J, Louis SJ, Tan KC (eds) Simulated evolution and learning, Springer Berlin Heidelberg, Berlin, Heidelberg, Lecture Notes in Computer Science, vol 6457, pp 230–239
Loshchilov I, Schoenauer M, Sebag M (2010b) A mono surrogate for multiobjective optimization. Genetic and Evolutionary Computation Conference 2010 (GECCO-2010) https://doi.org/10.1145/1830483.1830571
Chun-Wei Seah, Ong Y, Tsang IW, Siwei Jiang (2012) Pareto rank learning in multi-objective evolutionary algorithms. In: 2012 IEEE congress on evolutionary computation, IEEE, Brisbane, QLD, Australia, pp 1–8. https://doi.org/10.1109/CEC.2012.6252865
Pilát M, Neruda R (2014) Hypervolume-based local search in multi-objective evolutionary optimization. In: Proceedings of the 2014 annual conference on genetic and evolutionary computation, Association for Computing Machinery, New York, NY, USA, GECCO ’14, p 637–644. https://doi.org/10.1145/2576768.2598332
Le MN, Ong YS, Menzel S, Chun-Wei Seah, Sendhoff B (2012) Multi co-objective evolutionary optimization: Cross surrogate augmentation for computationally expensive problems. In: 2012 IEEE congress on evolutionary computation, IEEE, pp 1–8. https://doi.org/10.1109/CEC.2012.6252915
Yagoubi M, Bederina H (2023) Surrogate-assisted nsga-ii algorithm for expensive multiobjective optimization. In: Proceedings of the companion conference on genetic and evolutionary computation, Association for Computing Machinery, New York, NY, USA, GECCO ’23 Companion, p 431–434. https://doi.org/10.1145/3583133.3590746,
Liu G, Han X, Jiang C (2008) A novel multi-objective optimization method based on an approximation model management technique. Comput Methods Appl Mech Eng 197(33):2719–2731. https://doi.org/10.1016/j.cma.2007.12.014
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(1):14–27. https://doi.org/10.1016/j.asoc.2011.09.011
Li G, Li M, Azarm S, Al Hashimi S, Al Ameri T, Al Qasas N (2009) Improving multi-objective genetic algorithms with adaptive design of experiments and online metamodeling. Struct Multidiscip Optim 37(5):447–461. https://doi.org/10.1007/s00158-008-0251-6
Yang BS, Yeun YS, Ruy WS (2002) Managing approximation models in multiobjective optimization. Struct Multidisc Optim 24(2):141–156. https://doi.org/10.1007/s00158-002-0224-0
Rigoni E, Turco A (2010) Metamodels for fast multi-objective optimization: trading off global exploration and local exploitation. In: Deb K, Bhattacharya A, Chakraborti N, Chakroborty P, Das S, Dutta J, Gupta SK, Jain A, Aggarwal V, Branke J, Louis SJ, Tan KC (eds) Simulated evolution and learning, Springer Berlin Heidelberg, Kanpur, India, Lecture Notes in Computer Science, vol 6457, pp 523–532
Kampolis IC, Giannakoglou KC (2008) A multilevel approach to single- and multiobjective aerodynamic optimization. Comput Methods Appl Mech Eng 197(33):2963–2975. https://doi.org/10.1016/j.cma.2008.01.015
Gaspar-Cunha A, Vieira A (2005) A multi-objective evolutionary algorithm using neural networks to approximate fitness evaluations. Int J Comput Syst Signals 6:18–36
Akhtar T, Shoemaker CA (2016) Multi objective optimization of computationally expensive multi-modal functions with rbf surrogates and multi-rule selection. J Glob Optim 64(1):17–32. https://doi.org/10.1007/s10898-015-0270-y
Zapotecas-Martínez S, Coello C (2013) Moea/d assisted by rbf networks for expensive multi-objective optimization problems. In: Blum C (ed) GECCO 2013—proceedings of the 2013 genetic and evolutionary computation conference, Association for Computing Machinery, New York, NY, United States, Amsterdam, The Netherlands, pp 1405–1412, https://doi.org/10.1145/2463372.2465805
Zhang Q, Liu W, Tsang E, Virginas B (2010) Expensive multiobjective optimization by moea/d with gaussian process model. IEEE Trans Evol Comput 14(3):456–474. https://doi.org/10.1109/TEVC.2009.2033671
Chen X, Wu B, Sheng P (2019) A multiobjective evolutionary algorithm based on surrogate individual selection mechanism. Personal Ubiquitous Comput 23(3):421–434. https://doi.org/10.1007/s00779-019-01211-6
Pavelski LM, Delgado MR, De Almeida CP, Gonçalves RA, Venske SM (2014) Elmoea/d-de: Extreme learning surrogate models in multi-objective optimization based on decomposition and differential evolution. In: 2014 Brazilian conference on intelligent systems, pp 318–323. https://doi.org/10.1109/BRACIS.2014.64
Martínez SZ, Coello CAC (2013) Combining surrogate models and local search for dealing with expensive multi-objective optimization problems. In: 2013 IEEE congress on evolutionary computation, Cancun, Mexico, pp 2572–2579. https://doi.org/10.1109/CEC.2013.6557879
Li F, Gao L, Garg A, Shen W, Huang S (2020) A comparative study of pre-screening strategies within a surrogate-assisted multi-objective algorithm framework for computationally expensive problems. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05258-y
Li F, Gao L, Shen W, Cai X, Huang S (2020) A surrogate-assisted offspring generation method for expensive multi-objective optimization problems. In: 2020 IEEE congress on evolutionary computation (CEC), pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185691
Wang X, Jin Y, Schmitt S, Olhofer M (2020) An adaptive bayesian approach to surrogate-assisted evolutionary multi-objective optimization. Inf Sci 519:317–331. https://doi.org/10.1016/j.ins.2020.01.048
Tan Z, Wang H (2020) A kriging-assisted evolutionary algorithm using feature selection for expensive sparse multi-objective optimization. In: 2020 IEEE congress on evolutionary computation (CEC), pp 1–8. https://doi.org/10.1109/CEC48606.2020.9185825
Emmerich M, Beume N, Naujoks B (2005) An emo algorithm using the hypervolume measure as selection criterion. In: Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 62–76
Igel C, Suttorp T, Hansen N (2007) Steady-state selection and efficient covariance matrix update in the multi-objective cma-es. In: Obayashi S, Deb K, Poloni C, Hiroyasu T, Murata T (eds) Evolutionary multi-criterion optimization. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 171–185
Pilát M, Neruda R (2015) Hypervolume-based surrogate model for mo-cma-es. In: 2015 IEEE 27th International conference on tools with artificial intelligence (ICTAI), pp 604–611, https://doi.org/10.1109/ICTAI.2015.93
Nebro AJ, Durillo JJ, Garcia-Nieto J, Coello Coello CA, Luna F, Alba E (2009) Smpso: a new pso-based metaheuristic for multi-objective optimization. In: 2009 IEEE symposium on computational intelligence in multi-criteria decision-making (MCDM), pp 66–73. https://doi.org/10.1109/MCDM.2009.4938830
Liu Q, Wu X, Lin Q, Ji J, Wong KC (2021) A novel surrogate-assisted evolutionary algorithm with an uncertainty grouping based infill criterion. Swarm Evol Comput 60:100787. https://doi.org/10.1016/j.swevo.2020.100787
Li G, Wang Z, Gong M (2023) Expensive optimization via surrogate-assisted and model-free evolutionary optimization. IEEE Trans Syst Man Cybern Syst 53(5):2758–2769. https://doi.org/10.1109/TSMC.2022.3219080
Voigt H, Lange JM (1998) Local evolutionary search enhancement by random memorizing. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), pp 547–552. https://doi.org/10.1109/ICEC.1998.700087
Nocedal J, Wright S (2006) Numerical optimization. Springer Science & Business Media
Tenne Y, Armfield SW (2008) A framework for memetic optimization using variable global and local surrogate models. Soft Comput 13(8):781. https://doi.org/10.1007/s00500-008-0348-2
Lu X, Sun T, Tang K (2019) Evolutionary optimization with hierarchical surrogates. Swarm Evol Comput 47:21–32. https://doi.org/10.1016/j.swevo.2019.03.005
Yu H, Tan Y, Sun C, Zeng J (2019) A comparison of quality measures for model selection in surrogate-assisted evolutionary algorithm. Soft Comput 23(23):12417–12436. https://doi.org/10.1007/s00500-019-03783-0
Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100. https://doi.org/10.1016/S0305-0548(97)00031-2
Zhu C, Byrd RH, Lu P, Nocedal J (1997) Algorithm 778: L-bfgs-b: fortran subroutines for large-scale bound-constrained optimization. ACM Trans Math Softw 23(4):550–560. https://doi.org/10.1145/279232.279236
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313. https://doi.org/10.1093/comjnl/7.4.308
Byrd RH, Hribar ME, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. SIAM J Optim 9(4):877–900. https://doi.org/10.1137/S1052623497325107
Habib A, Singh HK, Chugh T, Ray T, Miettinen K (2019) A multiple surrogate assisted decomposition-based evolutionary algorithm for expensive multi/many-objective optimization. IEEE Trans Evol Comput 23(6):1000–1014. https://doi.org/10.1109/TEVC.2019.2899030
Yao Xin, Liu Yong, Lin Guangming (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102. https://doi.org/10.1109/4235.771163
Tong H, Huang C, Liu J, Yao X (2019) Voronoi-based efficient surrogate-assisted evolutionary algorithm for very expensive problems. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp 1996–2003. https://doi.org/10.1109/CEC.2019.8789910
Kůdela J, MatouŠek R (2023) Combining lipschitz and rbf surrogate models for high-dimensional computationally expensive problems. Inf Sci 619:457–477. https://doi.org/10.1016/j.ins.2022.11.045
Ratle A (2001) Kriging as a surrogate fitness landscape in evolutionary optimization. Artif Intell Eng Des Anal Manuf 15(1):37–49. https://doi.org/10.1017/S0890060401151024
Emmerich M, Giotis A, Özdemir M, Bäck T, Giannakoglou K (2002) Metamodel-assisted evolution strategies. In: Guervós JJM, Adamidis P, Beyer HG, Schwefel HP, Fernández-Villacañas JL (eds) Parallel problem solving from nature—PPSN VII, Springer Berlin Heidelberg, Granada, Spain, Lecture Notes in Computer Science, vol 2439. pp 361–370
Chugh T, Jin Y, Miettinen K, Hakanen J, Sindhya K (2018) A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization. IEEE Transactions on Evolutionary Computation 22(1):129–142. https://doi.org/10.1109/TEVC.2016.2622301
Mlakar M, Petelin D, Tusar T, Filipic B (2015) Gp-demo: differential evolution for multiobjective optimization based on gaussian process models. Eur J Oper Res 243(2):347–361. https://doi.org/10.1016/j.ejor.2014.04.011
Zaefferer M, Stork J, Flasch O, Bartz-Beielstein T (2018) Linear combination of distance measures for surrogate models in genetic programming. In: Auger A, Fonseca CM, Lourenço N, Machado P, Paquete L, Whitley D (eds) Parallel problem solving from nature—PPSN XV. Springer International Publishing, Cham, pp 220–231
Huang K, Wang X, Cai Y (2022) Surrogate-assisted task selection for evolutionary multitasking optimization. In: 2022 IEEE 2nd International conference on software engineering and artificial intelligence (SEAI), pp 172–177. https://doi.org/10.1109/SEAI55746.2022.9832367
Fan C, Hou B, Zheng J, Xiao L, Yi L (2020) A surrogate-assisted particle swarm optimization using ensemble learning for expensive problems with small sample datasets. Appl Soft Comput 91:106242. https://doi.org/10.1016/j.asoc.2020.106242
Stoean R (2020) Analysis on the potential of an ea-surrogate modelling tandem for deep learning parametrization: an example for cancer classification from medical images. Neural Comput Appl 32(2):313–322. https://doi.org/10.1007/s00521-018-3709-5
Datta R, Regis RG (2016) A surrogate-assisted evolution strategy for constrained multi-objective optimization. Expert Syst Appl 57:270–284. https://doi.org/10.1016/j.eswa.2016.03.044
Farina M (2002) A neural network based generalized response surface multiobjective evolutionary algorithm. In: Proceedings of the 2002 congress on evolutionary computation. CEC’02 (Cat. No.02TH8600), vol 1, pp 956–961. https://doi.org/10.1109/CEC.2002.1007054
Nakayama H, Inoue K, Yoshimori Y (2006) Approximate optimization using computaional intelligence and its application to reinforcement of cable-stayed bridges. In: Proceedings of the 2006 conference on integrated intelligent systems for engineering design, IOS Press, NLD, pp 289–304
Knowles J (2006) Parego: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput 10(1):50–66. https://doi.org/10.1109/TEVC.2005.851274
Liao P, Sun C, Zhang G, Jin Y (2020) Multi-surrogate multi-tasking optimization of expensive problems. Knowl Based Syst 205:106262. https://doi.org/10.1016/j.knosys.2020.106262
Liu N, Pan JS, Sun C, Chu SC (2020) An efficient surrogate-assisted quasi-affine transformation evolutionary algorithm for expensive optimization problems. Knowl Based Syst 209:106418. https://doi.org/10.1016/j.knosys.2020.106418
Bhattacharjee K, Ray T (2015) A novel constraint handling strategy for expensive optimization problems. In: 11th World congress on structural and multidisciplinary optimization (WCSMO-11), Sydney, Australia
Pilát M, Neruda R (2011) Asm-moma: Multiobjective memetic algorithm with aggregate surrogate model. In: 2011 IEEE congress of evolutionary computation (CEC), IEEE, New Orleans, LA, USA, pp 1202–1208. https://doi.org/10.1109/CEC.2011.5949753
Rasheed K, Vattam S, Ni x (2002) Comparison of methods for using reduced models to speed up design optimization. In: Proceedings of the 4th annual conference on genetic and evolutionary computation, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, GECCO’02, p 1180–1187
Pan L, He C, Tian Y, Wang H, Zhang X, Jin Y (2019) A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization. IEEE Trans Evol Comput 23(1):74–88. https://doi.org/10.1109/TEVC.2018.2802784
Francon O, Gonzalez S, Hodjat B, Meyerson E, Miikkulainen R, Qiu X, Shahrzad H (2020) Effective reinforcement learning through evolutionary surrogate-assisted prescription. In: Proceedings of the 2020 genetic and evolutionary computation conference, Association for Computing Machinery, New York, NY, USA, GECCO ’20, p 814–822. https://doi.org/10.1145/3377930.3389842
Sun Y, Wang H, Xue B, Jin Y, Yen GG, Zhang M (2020) Surrogate-assisted evolutionary deep learning using an end-to-end random forest-based performance predictor. IEEE Trans Evol Comput 24(2):350–364. https://doi.org/10.1109/TEVC.2019.2924461
Zhang J, Zhou A, Zhang G (2015) A classification and pareto domination based multiobjective evolutionary algorithm. In: 2015 IEEE congress on evolutionary computation (CEC), IEEE, Sendai, Japan, pp 2883–2890. https://doi.org/10.1109/CEC.2015.7257247
Wu X, Lin Q, Li J, Tan KC, Leung VCM (2022) An ensemble surrogate-based coevolutionary algorithm for solving large-scale expensive optimization problems. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2022.3200517
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86. https://doi.org/10.1214/aoms/1177729694
Nishihara K, Nakata M (2022) Surrogate-assisted differential evolution with adaptation of training data selection criterion. In: 2022 IEEE symposium series on computational intelligence (SSCI), pp 1675–1682. https://doi.org/10.1109/SSCI51031.2022.10022105
Wang H, Jin Y, Sun C, Doherty J (2019) Offline data-driven evolutionary optimization using selective surrogate ensembles. IEEE Trans Evol Comput 23(2):203–216. https://doi.org/10.1109/TEVC.2018.2834881
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(1):55–61. https://doi.org/10.1080/00401706.2000.10485979
Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492. https://doi.org/10.1023/A:1008306431147
Sasena M, Papalambros P, Goovaerts P (2000) Metamodeling sampling criteria in a global optimization framework. In: 8th Symposium on multidisciplinary analysis and optimization, American Institute of Aeronautics and Astronautics, Long Beach,CA, USA.,https://doi.org/10.2514/6.2000-4921
Settles B (2012) Active learning. In: Synthesis lectures on artificial intelligence and machine learning, Morgan & Claypool Publishers. https://doi.org/10.2200/S00429ED1V01Y201207AIM018
Peng C, Li Y, Cao L, Jiao L (2019) A surrogate model assisted quantum-inspired evolutionary algorithm for hyperparameter optimization in machine learning. In: 2019 IEEE congress on evolutionary computation (CEC), pp 1060–1067. https://doi.org/10.1109/CEC.2019.8790256
Dong H, Song B, Wang P, Dong Z (2018) Hybrid surrogate-based optimization using space reduction (hsosr) for expensive black-box functions. Appl Soft Comput 64:641–655. https://doi.org/10.1016/j.asoc.2017.12.046
Karakasis MK, Giannakoglou KC (2005) Metamodel-assisted, multi-objective evolutionary algorithms. In: Schilling R, Haase W, Periaux J, Baier H, G B (eds) Evolutionary and deterministic methods for design,optimization and control with applications to industrial and societal problemsEUROGEN 2005, Taylor & Francis, pp 1–11. https://doi.org/10.1080/03052150600848000,
Dushatskiy A, Mendrik AM, Alderliesten T, Bosman PAN (2019) Convolutional neural network surrogate-assisted gomea. In: Proceedings of the genetic and evolutionary computation conference, Association for Computing Machinery, New York, NY, USA, GECCO ’19, p 753–761. https://doi.org/10.1145/3321707.3321760
Runarsson TP (2006) Ordinal regression in evolutionary computation. In: Runarsson TP, Beyer HG, Burke E, Merelo-Guervós JJ, Whitley LD, Yao X (eds) Parallel problem solving from nature—PPSN IX. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 1048–1057
Nguyen TV, Bonilla EV (2014) Collaborative multi-output gaussian processes. In: Proceedings of the thirtieth conference on uncertainty in artificial intelligence, AUAI Press, Arlington, Virginia, USA, UAI’14, p 643–652
Lu Y, Li B, Qian H, Hong W, Yang P, Zhou A (2023) Rm-saea: regularity model based surrogate-assisted evolutionary algorithms for expensive multi-objective optimization. In: Proceedings of the genetic and evolutionary computation conference, Association for Computing Machinery, New York, NY, USA, GECCO ’23, pp 722–730. https://doi.org/10.1145/3583131.3590435
Gaspar-Cunha A, Vieira A (2004) A hybrid multi-objective evolutionary algorithm using an inverse neural network. In: Blum C, Roli A, Sampels M (eds) Hybrid metaheuristics, first international workshop, HM 2004, Valencia, Spain, August 22-23, 2004, Proceedings, pp 25–30. http://iridia.ulb.ac.be/%7Ehm2004/proceedings/p04.pdf
Bandaru S, Ng AHC, Deb K (2014) On the performance of classification algorithms for learning pareto-dominance relations. In: 2014 IEEE congress on evolutionary computation (CEC), IEEE, Beijing, China, pp 1139–1146, https://doi.org/10.1109/CEC.2014.6900641
Yang S, Qi Y, Yang R, Ma X, Zhang H (2023) A surrogate assisted evolutionary multitasking optimization algorithm. Applied Soft Computing 132:109775. https://doi.org/10.1016/j.asoc.2022.109775https://www.sciencedirect.com/science/article/pii/S1568494622008249
Tian Y, Zhang X, Wang C, Jin Y (2020) An evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Trans Evol Comput 24(2):380–393. https://doi.org/10.1109/TEVC.2019.2918140
Ma L, Wang R, Chen S, Cheng S, Wang X, Lin Z, Shi Y, Huang M (2020) A novel many-objective evolutionary algorithm based on transfer matrix with kriging model. Inf Sci 509:437–456. https://doi.org/10.1016/j.ins.2019.01.030
Jansen T, Zarges C (2011) Analysis of evolutionary algorithms: from computational complexity analysis to algorithm engineering. In: Proceedings of the 11th Workshop proceedings on foundations of genetic algorithms, Association for Computing Machinery, New York, NY, USA, FOGA ’11, p 1–14. https://doi.org/10.1145/1967654.1967656,
Li Y, Zhong J (2022) Has-ea: a fast parallel surrogate-assisted evolutionary algorithm. Memet Comput 15:1–13. https://doi.org/10.1007/s12293-022-00376-7
Rehbach F, Zaefferer M, Stork J, Bartz-Beielstein T (2018) Comparison of parallel surrogate-assisted optimization approaches. In: Proceedings of the Genetic and Evolutionary Computation Conference, Association for Computing Machinery, New York, NY, USA, GECCO ’18, p 1348–1355. https://doi.org/10.1145/3205455.3205587,
Harada T, Kaidan M, Thawonmas R (2020) Comparison of synchronous and asynchronous parallelization of extreme surrogate-assisted multi-objective evolutionary algorithm. Nat Comput. https://doi.org/10.1007/s11047-020-09806-2
Chugh T, Sindhya K, Miettinen K, Hakanen J, Jin Y (2016) On constraint handling in surrogate-assisted evolutionary many-objective optimization. In: Handl J, Hart E, Lewis PR, López-Ibáñez M, Ochoa G, Paechter B (eds) Parallel problem solving from nature—PPSN XIV, Springer International Publishing, Edinburgh, UK, Lecture Notes in Computer Science, vol 9921, pp 214–224
Loshchilov I, Hutter F (2016) Cma-es for hyperparameter optimization of deep neural networks. https://doi.org/10.48550/ARXIV.1604.07269arxiv:1604.07269
Sun Y, Wang H, Xue B, Jin Y, Yen GG, Zhang M (2020) Surrogate-assisted evolutionary deep learning using an end-to-end random forest-based performance predictor. IEEE Trans Evol Comput 24(2):350–364. https://doi.org/10.1109/TEVC.2019.2924461
Zhan ZH, Li JY, Zhang J (2022) Evolutionary deep learning: a survey. Neurocomputing 483:42–58. https://doi.org/10.1016/j.neucom.2022.01.099
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Khaldi, M.I.E., Draa, A. Surrogate-assisted evolutionary optimisation: a novel blueprint and a state of the art survey. Evol. Intel. 17, 2213–2243 (2024). https://doi.org/10.1007/s12065-023-00882-8
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DOI: https://doi.org/10.1007/s12065-023-00882-8