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Erschienen in: Soft Computing 9/2019

11.12.2017 | Methodologies and Application

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

verfasst von: Tinkle Chugh, Karthik Sindhya, Jussi Hakanen, Kaisa Miettinen

Erschienen in: Soft Computing | Ausgabe 9/2019

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Abstract

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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Literatur
Zurück zum Zitat Aarts E, Lenstra JK (eds) (2003) Local search in combinatorial optimization. Princeton University Press, PrincetonMATH Aarts E, Lenstra JK (eds) (2003) Local search in combinatorial optimization. Princeton University Press, PrincetonMATH
Zurück zum Zitat Ackley D (1987) A connectionist machine for genetic hillclimbing. Kluwer Academic Publishers, Boston Ackley D (1987) A connectionist machine for genetic hillclimbing. Kluwer Academic Publishers, Boston
Zurück zum Zitat Akhtar T, Shoemaker CA (2015) Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection. J Glob Optim 64:17–32MathSciNetMATH Akhtar T, Shoemaker CA (2015) Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection. J Glob Optim 64:17–32MathSciNetMATH
Zurück zum Zitat Alexandrov NM, Dennis JE Jr, Lewis RM, Torczon V (1998) A trust-region framework for managing the use of approximation models in optimization. Struct Optim 15:16–23 Alexandrov NM, Dennis JE Jr, Lewis RM, Torczon V (1998) A trust-region framework for managing the use of approximation models in optimization. Struct Optim 15:16–23
Zurück zum Zitat Arias-Montano A, Coello CAC, Mezura-Montes E (2010) MODE-LD+SS: A novel differential evolution algorithm incorporating local dominance and scalar selection mechanisms for multi-objective optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8 Arias-Montano A, Coello CAC, Mezura-Montes E (2010) MODE-LD+SS: A novel differential evolution algorithm incorporating local dominance and scalar selection mechanisms for multi-objective optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8
Zurück zum Zitat Arias-Montano A, Coello CAC, Mezura-Montes E (2012) Multi-objective airfoil shape optimization using a multiple-surrogate approach. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8 Arias-Montano A, Coello CAC, Mezura-Montes E (2012) Multi-objective airfoil shape optimization using a multiple-surrogate approach. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8
Zurück zum Zitat Aytug H, Sayin S (2009) Using support vector machines to learn the efficient set in multiple objective discrete optimization. Eur J Oper Res 193:510–519MATH Aytug H, Sayin S (2009) Using support vector machines to learn the efficient set in multiple objective discrete optimization. Eur J Oper Res 193:510–519MATH
Zurück zum Zitat Azzouz N, Bechikh S, Said LB (2014) Steady state IBEA assisted by MLP neural networks for expensive multi-objective optimization problems. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 581–588 Azzouz N, Bechikh S, Said LB (2014) Steady state IBEA assisted by MLP neural networks for expensive multi-objective optimization problems. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 581–588
Zurück zum Zitat Bäck T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, New YorkMATH Bäck T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, New YorkMATH
Zurück zum Zitat Bandaru S, Ng AHC, Deb K (2014) On the performance of classification algorithms for learning Pareto-dominance relations. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1139–1146 Bandaru S, Ng AHC, Deb K (2014) On the performance of classification algorithms for learning Pareto-dominance relations. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1139–1146
Zurück zum Zitat Bandyopadhyay S, Saha S, Maulik U, Deb K (2008) A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans Evol Comput 12:269–283 Bandyopadhyay S, Saha S, Maulik U, Deb K (2008) A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans Evol Comput 12:269–283
Zurück zum Zitat Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Springer, US Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Springer, US
Zurück zum Zitat Branke J, Schmidt C (2005) Faster convergence by means of fitness estimation. Soft Comput 9:13–20 Branke J, Schmidt C (2005) Faster convergence by means of fitness estimation. Soft Comput 9:13–20
Zurück zum Zitat Chen J-H, Goldberg DE, Ho S-Y, Sastry K (2002) Fitness inheritance in multiobjective optimization. In: Langdon WB et al (eds) Proceedings of the genetic and evolutionary computation conference. Morgan Kaufmann, Burlington Chen J-H, Goldberg DE, Ho S-Y, Sastry K (2002) Fitness inheritance in multiobjective optimization. In: Langdon WB et al (eds) Proceedings of the genetic and evolutionary computation conference. Morgan Kaufmann, Burlington
Zurück zum Zitat 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 12:14–27 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 12:14–27
Zurück zum Zitat Chen T, Tang K, Chen G, Yao X (2012) A large population size can be unhelpful in evolutionary algorithms. Theor Comput Sci 436:54–70MathSciNetMATH Chen T, Tang K, Chen G, Yao X (2012) A large population size can be unhelpful in evolutionary algorithms. Theor Comput Sci 436:54–70MathSciNetMATH
Zurück zum Zitat Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20:773–791 Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20:773–791
Zurück zum Zitat Chugh T, Sindhya K, Miettinen K, Hakanen J, Jin Y (2016b) On constraint handling in surrogate assisted evolutionary many-objective optimization. In: Handl J et al (eds) Proceedings of the 14th parallel problem solving from nature-PPSN, vol XIV. Springer, Berlin, pp 214–224 Chugh T, Sindhya K, Miettinen K, Hakanen J, Jin Y (2016b) On constraint handling in surrogate assisted evolutionary many-objective optimization. In: Handl J et al (eds) Proceedings of the 14th parallel problem solving from nature-PPSN, vol XIV. Springer, Berlin, pp 214–224
Zurück zum Zitat Coello CAC, Lamont GB (eds) (2004) Applications of multi-objective evolutionary algorithms. World Scientific, Singapore Coello CAC, Lamont GB (eds) (2004) Applications of multi-objective evolutionary algorithms. World Scientific, Singapore
Zurück zum Zitat Coello CAC, Pulido GT (2001) A micro multi-objective genetic algorithm for multi-objective optimizations. In: Zitzler E, Thiele L, Deb K, Coello CAC, Corne D (eds) Proceedings of the evolutionary multi-criterion optimization. Springer, Berlin, pp 126–140 Coello CAC, Pulido GT (2001) A micro multi-objective genetic algorithm for multi-objective optimizations. In: Zitzler E, Thiele L, Deb K, Coello CAC, Corne D (eds) Proceedings of the evolutionary multi-criterion optimization. Springer, Berlin, pp 126–140
Zurück zum Zitat Coello CAC, Lamont GB, Veldhuizen DAV (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New YorkMATH Coello CAC, Lamont GB, Veldhuizen DAV (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New YorkMATH
Zurück zum Zitat Corne DW, Jerram NR, Knowles JD, Oates MJ (2001) PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of the genetic and evolutionary computation conference, pp 283–290, Morgan Kaufmann Corne DW, Jerram NR, Knowles JD, Oates MJ (2001) PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of the genetic and evolutionary computation conference, pp 283–290, Morgan Kaufmann
Zurück zum Zitat Couckuyt I, Deschrijver D, Dhaene T (2014) Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization. J Glob Optim 60:575–594MathSciNetMATH Couckuyt I, Deschrijver D, Dhaene T (2014) Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization. J Glob Optim 60:575–594MathSciNetMATH
Zurück zum Zitat Currin C, Mitchell M, Morris M, Ylvisaker D (1998) A Bayesian approach to the design and analysis of computer experiments, technical report. Oak Ridge National Laboratory, Oak Ridge Currin C, Mitchell M, Morris M, Ylvisaker D (1998) A Bayesian approach to the design and analysis of computer experiments, technical report. Oak Ridge National Laboratory, Oak Ridge
Zurück zum Zitat Custodio AL, Madeira JFA, Vaz AIF, Vicente LN (2011) Direct multisearch for multiobjective optimization. SIAM J Optim 21:1109–1140MathSciNetMATH Custodio AL, Madeira JFA, Vaz AIF, Vicente LN (2011) Direct multisearch for multiobjective optimization. SIAM J Optim 21:1109–1140MathSciNetMATH
Zurück zum Zitat Datta R, Regis RG (2016) A surrogate-assisted evolution strategy for constrained multi-objective optimization. Expert Syst Appl 57:270–284 Datta R, Regis RG (2016) A surrogate-assisted evolution strategy for constrained multi-objective optimization. Expert Syst Appl 57:270–284
Zurück zum Zitat Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, ChichesterMATH Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, ChichesterMATH
Zurück zum Zitat Deb K, Nain P (2007) An evolutionary multi-objective adaptive meta-modelling procedure using artificial neural networks. In: Yan S, Ong Y-S, Jin Y (eds) Proceedings of the evolutionary compitation in dynamic and uncertain environments. Springer, Berlin, pp 297–322 Deb K, Nain P (2007) An evolutionary multi-objective adaptive meta-modelling procedure using artificial neural networks. In: Yan S, Ong Y-S, Jin Y (eds) Proceedings of the evolutionary compitation in dynamic and uncertain environments. Springer, Berlin, pp 297–322
Zurück zum Zitat Deb K, Prarap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197 Deb K, Prarap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197
Zurück zum Zitat Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. Springer, London, pp 105–145MATH Deb K, Thiele L, Laumanns M, Zitzler E (2005) Scalable test problems for evolutionary multiobjective optimization. Springer, London, pp 105–145MATH
Zurück zum Zitat Deb K, Miettinen K, Chaudhuri S (2010) Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Trans Evol Comput 6:821–841 Deb K, Miettinen K, Chaudhuri S (2010) Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Trans Evol Comput 6:821–841
Zurück zum Zitat Dennis JE, Torczon V (1995) Managing approximation models in optimization. In: Alexandrov NM, Hussaini N (eds) Proceedings of the multidisciplinary design optimization: state-of-the-art, pp 330–347 Dennis JE, Torczon V (1995) Managing approximation models in optimization. In: Alexandrov NM, Hussaini N (eds) Proceedings of the multidisciplinary design optimization: state-of-the-art, pp 330–347
Zurück zum Zitat Ducheyne E, Baets BD, Wulf RD (2003) Is fitness inheritance useful for real-world applications? In: Fonseca CM, Fleming PJ, Zitzler E, Thiele L, Deb K (eds) Proceedings of the evolutionary multi-criterion optimization. Springer, Berlin, pp 31–42 Ducheyne E, Baets BD, Wulf RD (2003) Is fitness inheritance useful for real-world applications? In: Fonseca CM, Fleming PJ, Zitzler E, Thiele L, Deb K (eds) Proceedings of the evolutionary multi-criterion optimization. Springer, Berlin, pp 31–42
Zurück zum Zitat Durillo J, Nebro A, Alba E (2010) The jmetal framework for multi-objective optimization: design and architecture. In Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8 Durillo J, Nebro A, Alba E (2010) The jmetal framework for multi-objective optimization: design and architecture. In Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8
Zurück zum Zitat Emmerich M, Giotis A, Özdemir M, Bäck T, Giannakoglou K (2002) Metamodel-assisted evolution strategies. In: Merelo-Guervós JJ et al (eds) Proceedings of the parallel problem solving from nature-PPSN VII. Springer, Berlin, pp 361–370 Emmerich M, Giotis A, Özdemir M, Bäck T, Giannakoglou K (2002) Metamodel-assisted evolution strategies. In: Merelo-Guervós JJ et al (eds) Proceedings of the parallel problem solving from nature-PPSN VII. Springer, Berlin, pp 361–370
Zurück zum Zitat Emmerich M, Beume N, Naujoks B (2005) An EMO algorithm using the hypervolume measure as selection criterion. In: Coello CAC, Aguirre AH, Zitzler E (eds) Proceedings of the evolutionary multi-criterion optimization. Springer, Berlin, pp 62–76 Emmerich M, Beume N, Naujoks B (2005) An EMO algorithm using the hypervolume measure as selection criterion. In: Coello CAC, Aguirre AH, Zitzler E (eds) Proceedings of the evolutionary multi-criterion optimization. Springer, Berlin, pp 62–76
Zurück zum Zitat Emmerich M, Giannakoglou K, Naujoks B (2006) Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Trans Evol Comput 10:421–439 Emmerich M, Giannakoglou K, Naujoks B (2006) Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Trans Evol Comput 10:421–439
Zurück zum Zitat Emmerich M, Deutz AH, Klinkenberg JW (2011) Hypervolume-based expected improvement: monotonicity properties and exact computation. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 2147–2154 Emmerich M, Deutz AH, Klinkenberg JW (2011) Hypervolume-based expected improvement: monotonicity properties and exact computation. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 2147–2154
Zurück zum Zitat Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3(1):1–16 Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3(1):1–16
Zurück zum Zitat Forrester A, Keane A (2009) Recent advances in surrogate-based optimization. Progr Aerospace Sci 45:50–79 Forrester A, Keane A (2009) Recent advances in surrogate-based optimization. Progr Aerospace Sci 45:50–79
Zurück zum Zitat Gano SE, Renaud JE, Martin JD, Simpson TW (2006) Update strategies for Kriging models used in variable fidelity optimization. Struct Multidiscip Optim 32:287–298 Gano SE, Renaud JE, Martin JD, Simpson TW (2006) Update strategies for Kriging models used in variable fidelity optimization. Struct Multidiscip Optim 32:287–298
Zurück zum Zitat Giannakoglou KC, Kampolis IC (2010) Multilevel optimization algorithms based on metamodel-and fitness inheritance-asisted evolutionary algorithms. In: Tenne Y, Goh C-K (eds) Computational intelligence in expensive optimization problems. Springer, Berlin, pp 61–84 Giannakoglou KC, Kampolis IC (2010) Multilevel optimization algorithms based on metamodel-and fitness inheritance-asisted evolutionary algorithms. In: Tenne Y, Goh C-K (eds) Computational intelligence in expensive optimization problems. Springer, Berlin, pp 61–84
Zurück zum Zitat Gorissen D, Couckuyt I, Demeester P, Dhaene T, Crombecq K (2010) A surrogate modelling and adaptive sampling toolbox for computer based design. J Mach Learn Res 11:2051–2055 Gorissen D, Couckuyt I, Demeester P, Dhaene T, Crombecq K (2010) A surrogate modelling and adaptive sampling toolbox for computer based design. J Mach Learn Res 11:2051–2055
Zurück zum Zitat 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 Y-S, Jin Y (eds) Evolutionary computation in dynamic and uncertain environments. Springer, Berlin, pp 225–250 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 Y-S, Jin Y (eds) Evolutionary computation in dynamic and uncertain environments. Springer, Berlin, pp 225–250
Zurück zum Zitat Hansen MP, Jaskiewicz A (1998) Evaluating the quality of approximation to the non-dominated set. Technical report, Technical University of Denmark Hansen MP, Jaskiewicz A (1998) Evaluating the quality of approximation to the non-dominated set. Technical report, Technical University of Denmark
Zurück zum Zitat Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9:159–195 Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9:159–195
Zurück zum Zitat Herrera M, Guglielmetti A, Xiao M, Coelho RF (2014) Metamodel-assisted optimization based on multiple kernel regression for mixed variables. Struct Multidiscip Optim 49:979–991 Herrera M, Guglielmetti A, Xiao M, Coelho RF (2014) Metamodel-assisted optimization based on multiple kernel regression for mixed variables. Struct Multidiscip Optim 49:979–991
Zurück zum Zitat Horn D, Wagner T, Biermann D, Weihs C, Bischl B (2015) Model-based multi-objective optimization: taxonomy, multi-point proposal, toolbox and benchmark. In: Gasper-Cunha A, Antunes CH, Coello CC (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 64–78 Horn D, Wagner T, Biermann D, Weihs C, Bischl B (2015) Model-based multi-objective optimization: taxonomy, multi-point proposal, toolbox and benchmark. In: Gasper-Cunha A, Antunes CH, Coello CC (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 64–78
Zurück zum Zitat Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of the international joint conference on neural networks, IEEE, pp 985–990 Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of the international joint conference on neural networks, IEEE, pp 985–990
Zurück zum Zitat Huband S, Barone L, While L, Hingston P (2005) A scalable multi-objective test problem toolkit. In: Coello CAC, Aguirre AH, Zitzler E (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 280–295 Huband S, Barone L, While L, Hingston P (2005) A scalable multi-objective test problem toolkit. In: Coello CAC, Aguirre AH, Zitzler E (eds) Evolutionary multi-criterion optimization. Springer, Berlin, pp 280–295
Zurück zum Zitat Husain A, Kim K-Y (2010) Enhanced multi-objective optimization of a microchannel heat sink through evolutionary algorithm coupled with multiple surrogate models. Appl Thermal Eng 30:1683–1691 Husain A, Kim K-Y (2010) Enhanced multi-objective optimization of a microchannel heat sink through evolutionary algorithm coupled with multiple surrogate models. Appl Thermal Eng 30:1683–1691
Zurück zum Zitat Igel C, Hansen N, Roth S (2007) Covariance matrix adaptation for multi-objective optimization. Evol Comput 15:1–28 Igel C, Hansen N, Roth S (2007) Covariance matrix adaptation for multi-objective optimization. Evol Comput 15:1–28
Zurück zum Zitat Ishibuchi H, Hitotsuyanagi Y, Tsukamoto N, Nojima Y (2008) Use of heuristic local search for single-objective optimization in multiobjective memetic algorithms. In: Rudolph G, Jansen T, Lucas S, Poloni C, Beume N (eds) Proceedings of the parallel problem solving from nature-PPSN X. Springer, Berlin, pp 743–752 Ishibuchi H, Hitotsuyanagi Y, Tsukamoto N, Nojima Y (2008) Use of heuristic local search for single-objective optimization in multiobjective memetic algorithms. In: Rudolph G, Jansen T, Lucas S, Poloni C, Beume N (eds) Proceedings of the parallel problem solving from nature-PPSN X. Springer, Berlin, pp 743–752
Zurück zum Zitat Ishibuchi H, Hitotsuyanagi Y, Wakamatsu Y, Nojima Y (2010) How to choose solutions for local search in multiobjective combinatorial memetic algorithms. In: Schaefer R, Cotta C, Kolodziej J, Rudolph G (eds) Parallel problem solving from nature-PPSN XI. Springer, Berlin, pp 516–525 Ishibuchi H, Hitotsuyanagi Y, Wakamatsu Y, Nojima Y (2010) How to choose solutions for local search in multiobjective combinatorial memetic algorithms. In: Schaefer R, Cotta C, Kolodziej J, Rudolph G (eds) Parallel problem solving from nature-PPSN XI. Springer, Berlin, pp 516–525
Zurück zum Zitat Jain H, Deb K (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18:602–622 Jain H, Deb K (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18:602–622
Zurück zum Zitat Jain AK, Dubes RC (1998) Algorithms for clustering data. Prentice-Hall, Upper Saddle RiverMATH Jain AK, Dubes RC (1998) Algorithms for clustering data. Prentice-Hall, Upper Saddle RiverMATH
Zurück zum Zitat Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31:264–323 Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31:264–323
Zurück zum Zitat Jang B-S, Ko D-E, Suh Y-S, Yang Y-S (2009) Adaptive approximation in multi-objective optimization for full stochastic fatigue design problem. Marine Struct 22:610–632 Jang B-S, Ko D-E, Suh Y-S, Yang Y-S (2009) Adaptive approximation in multi-objective optimization for full stochastic fatigue design problem. Marine Struct 22:610–632
Zurück zum Zitat Jeong S, Obayashi S (2005) Efficient global optimization (EGO) for multi-objective problem and data mining. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 2138–2145 Jeong S, Obayashi S (2005) Efficient global optimization (EGO) for multi-objective problem and data mining. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 2138–2145
Zurück zum Zitat Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9:3–12 Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9:3–12
Zurück zum Zitat Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1:61–70 Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1:61–70
Zurück zum Zitat Jin Y, Sendhoff B (2004) Reducing fitness evaluations using clustering techniques and neural network ensembles. In: Deb K (ed) Proceedings of the genetic and evolutionary computation conference. Springer, Berlin, pp 688–699 Jin Y, Sendhoff B (2004) Reducing fitness evaluations using clustering techniques and neural network ensembles. In: Deb K (ed) Proceedings of the genetic and evolutionary computation conference. Springer, Berlin, pp 688–699
Zurück zum Zitat Jin Y, Olhofer M, Sendhoff B (2002) A framework for evolutionary optimization with approximate fitness functions. IEEE Trans Evol Comput 6:481–494 Jin Y, Olhofer M, Sendhoff B (2002) A framework for evolutionary optimization with approximate fitness functions. IEEE Trans Evol Comput 6:481–494
Zurück zum Zitat Jin Y, Olhofer M, Sendhoff B (2000) On evolutionary optimization with approximate fitness functions. In: Proceedings of the genetic and evolutionary computation conference, pp 786–793. Morgan Kaufmann Jin Y, Olhofer M, Sendhoff B (2000) On evolutionary optimization with approximate fitness functions. In: Proceedings of the genetic and evolutionary computation conference, pp 786–793. Morgan Kaufmann
Zurück zum Zitat Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plan Inference 26:131–148MathSciNet Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plan Inference 26:131–148MathSciNet
Zurück zum Zitat Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492MathSciNetMATH Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492MathSciNetMATH
Zurück zum Zitat Kampolis IC, Giannakoglou KC (2008) A multilevel approach to single and multiobjective aerodynamic optimization. Comput Methods Appl Mech Eng 197:2963–2975MATH Kampolis IC, Giannakoglou KC (2008) A multilevel approach to single and multiobjective aerodynamic optimization. Comput Methods Appl Mech Eng 197:2963–2975MATH
Zurück zum Zitat Keane AJ (2006) Statistical improvement criteria for use in multiobjective design optimization. AIAA J 44:879–891 Keane AJ (2006) Statistical improvement criteria for use in multiobjective design optimization. AIAA J 44:879–891
Zurück zum Zitat Kim H-S, Cho S-B (2001) An efficient genetic algorithm with less fitness evaluation by clustering. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 887–894 Kim H-S, Cho S-B (2001) An efficient genetic algorithm with less fitness evaluation by clustering. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 887–894
Zurück zum Zitat Knowles J (2006) ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput 10:50–66 Knowles J (2006) ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput 10:50–66
Zurück zum Zitat Knowles J (2009) Closed-loop evolutionary multiobjective optimization. IEEE Comput Intell Mag 4:77–91 Knowles J (2009) Closed-loop evolutionary multiobjective optimization. IEEE Comput Intell Mag 4:77–91
Zurück zum Zitat Knowles J, Nakayama H (2008) Meta-modeling in multiobjective optimization. In: Branke J, Deb K, Miettinen K, Slowinski R (eds) Multiobjective optimization: interactive and evolutionary approaches. Springer, Berlin, pp 245–284 Knowles J, Nakayama H (2008) Meta-modeling in multiobjective optimization. In: Branke J, Deb K, Miettinen K, Slowinski R (eds) Multiobjective optimization: interactive and evolutionary approaches. Springer, Berlin, pp 245–284
Zurück zum Zitat Kourakos G, Mantoglou A (2009) Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models. Adv Water Resour 32:507–521 Kourakos G, Mantoglou A (2009) Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models. Adv Water Resour 32:507–521
Zurück zum Zitat Kourakos G, Mantoglou A (2013) Development of a multi-objective optimization algorithm using surrogate models for coastal aquifer management. J Hydrol 479:13–23 Kourakos G, Mantoglou A (2013) Development of a multi-objective optimization algorithm using surrogate models for coastal aquifer management. J Hydrol 479:13–23
Zurück zum Zitat Kursawe Frank (1991) A variant of evolution strategies for vector optimization. In: Proceedings of the 1st workshop on parallel problem solving from nature-PPSN I, pp 193–197. Springer Kursawe Frank (1991) A variant of evolution strategies for vector optimization. In: Proceedings of the 1st workshop on parallel problem solving from nature-PPSN I, pp 193–197. Springer
Zurück zum Zitat Lattarulo V, Seshadri P, Parks GT (2013) Optimization of a supersonic airfoil using the multi-objective alliance algorithm. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 1333–1340 Lattarulo V, Seshadri P, Parks GT (2013) Optimization of a supersonic airfoil using the multi-objective alliance algorithm. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 1333–1340
Zurück zum Zitat Lee DS, Gonzalez LF, Periaux J, Srinivas K (2008) Robust design optimisation using multi-objective evolutionary algorithms. Comput Fluids 37:565–583MATH Lee DS, Gonzalez LF, Periaux J, Srinivas K (2008) Robust design optimisation using multi-objective evolutionary algorithms. Comput Fluids 37:565–583MATH
Zurück zum Zitat Lee S, Almon PV, Fink W, Petropoulos AE, Terrile RJ (2005) Comparison of multi-objective genetic algorithms in optimizing q-law low-thrust orbit transfers. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 25–29 Lee S, Almon PV, Fink W, Petropoulos AE, Terrile RJ (2005) Comparison of multi-objective genetic algorithms in optimizing q-law low-thrust orbit transfers. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 25–29
Zurück zum Zitat Li H, Zhang Q (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 12:284–302 Li H, Zhang Q (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 12:284–302
Zurück zum Zitat Li M, Li G, Azarm S (2008) A kriging metamodel assisted multi-objective genetic algorithm for design optimization. J Mech Des 130:1–10 Li M, Li G, Azarm S (2008) A kriging metamodel assisted multi-objective genetic algorithm for design optimization. J Mech Des 130:1–10
Zurück zum Zitat Li G, Li M, Azarm S, Hashimi SA, Ameri TA, Qasas NA (2009) Improving multi-objective genetic algorithm with adaptive design of experiments and online metamodeling. Struct Multidiscip Optim 37:447–461 Li G, Li M, Azarm S, Hashimi SA, Ameri TA, Qasas NA (2009) Improving multi-objective genetic algorithm with adaptive design of experiments and online metamodeling. Struct Multidiscip Optim 37:447–461
Zurück zum Zitat Lim D, Jin Y (2010) Generalizing surrogate-assisted evolutionary computation. IEEE Trans Evol Comput 14:329–354 Lim D, Jin Y (2010) Generalizing surrogate-assisted evolutionary computation. IEEE Trans Evol Comput 14:329–354
Zurück zum Zitat Liu Y, Collette M (2014) Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm. Appl Soft Comput 24:482–493 Liu Y, Collette M (2014) Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm. Appl Soft Comput 24:482–493
Zurück zum Zitat Liu GP, Han X, Jiang C (2008) A novel multi-objective optimization method based on an approximation model management technique. Comput Methods Appl Mech Eng 197:2719–2731MATH Liu GP, Han X, Jiang C (2008) A novel multi-objective optimization method based on an approximation model management technique. Comput Methods Appl Mech Eng 197:2719–2731MATH
Zurück zum Zitat Loshchilov I, Schoenauer M, Sebag M (2010) Dominance-based Pareto-surrogate for multi-objective optimization. In: Deb K, Bhattacharya A, Chakroborty N, Das S, Dutta J, Gupta SK, Jain A, Aggarwal V, Branke J, Louis SJ, Tan KC (eds) Proceedings of the simulated evolution and learning. Springer, Berlin, pp 230–239 Loshchilov I, Schoenauer M, Sebag M (2010) Dominance-based Pareto-surrogate for multi-objective optimization. In: Deb K, Bhattacharya A, Chakroborty N, Das S, Dutta J, Gupta SK, Jain A, Aggarwal V, Branke J, Louis SJ, Tan KC (eds) Proceedings of the simulated evolution and learning. Springer, Berlin, pp 230–239
Zurück zum Zitat Loshchilov I, Schoenauer M, Sebag M (2009) A mono surrogate for multiobjective optimization. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 471–478 Loshchilov I, Schoenauer M, Sebag M (2009) A mono surrogate for multiobjective optimization. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 471–478
Zurück zum Zitat Luo C, Shimoyama K, Obayashi S (2014) Kriging model based many-objective optimization with efficient calculation of expected hypervolume improvement. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1187–1194 Luo C, Shimoyama K, Obayashi S (2014) Kriging model based many-objective optimization with efficient calculation of expected hypervolume improvement. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1187–1194
Zurück zum Zitat Martinez SZ, Coello CAC (2013) MOEA/D assisted by RBF networks for expensive multi-objective optimization problems. In: Blum C (ed) Proceedings of the genetic and evolutionary computation conference. ACM, New York, pp 1405–1412 Martinez SZ, Coello CAC (2013) MOEA/D assisted by RBF networks for expensive multi-objective optimization problems. In: Blum C (ed) Proceedings of the genetic and evolutionary computation conference. ACM, New York, pp 1405–1412
Zurück zum Zitat 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 42:55–61MATH 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 42:55–61MATH
Zurück zum Zitat Mengistu T, Ghaly W (2008) Aerodynamic optimization of turbomachinery blades using evolutionary methods and ANN-based surrogate models. Optim Eng 9:239–255MathSciNetMATH Mengistu T, Ghaly W (2008) Aerodynamic optimization of turbomachinery blades using evolutionary methods and ANN-based surrogate models. Optim Eng 9:239–255MathSciNetMATH
Zurück zum Zitat Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonMATH Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonMATH
Zurück zum Zitat Mitra K, Majumder S (2011) Successive approximate model based multi-objective optimization for an industrial straight grate iron ore induration process using evolutionary algorithm. Chem Eng Sci 66:3471–3481 Mitra K, Majumder S (2011) Successive approximate model based multi-objective optimization for an industrial straight grate iron ore induration process using evolutionary algorithm. Chem Eng Sci 66:3471–3481
Zurück zum Zitat Mlakar M, Petelin D, Tusar T, Filipic B (2015) GP-DEMO: differential evolution with multiobjective optimization based on gaussian process models. Eur J Oper Res 243:347–361MathSciNetMATH Mlakar M, Petelin D, Tusar T, Filipic B (2015) GP-DEMO: differential evolution with multiobjective optimization based on gaussian process models. Eur J Oper Res 243:347–361MathSciNetMATH
Zurück zum Zitat Mogilicharla A, Chugh T, Majumder S, Mitra K (2014) Multi-objective optimization of bulk vinyl acetate polymerization with branching. Mater Manuf Process 29:210–217 Mogilicharla A, Chugh T, Majumder S, Mitra K (2014) Multi-objective optimization of bulk vinyl acetate polymerization with branching. Mater Manuf Process 29:210–217
Zurück zum Zitat Nain PKS, Deb K (2005) A multi-objective optimization procedure with successive approximate models. Technical Report 2005002, KanGAL, Indian Institute of Technology Kanpur, India Nain PKS, Deb K (2005) A multi-objective optimization procedure with successive approximate models. Technical Report 2005002, KanGAL, Indian Institute of Technology Kanpur, India
Zurück zum Zitat Nakayama H, Inoue K, Yoshimori Y (2006) Approximate optimization using computational intelligence and its application to reinforcement of cable-stayed bridges. In: Proceedings of the integrated intelligent systems for engineering design, pp 289–304. IOS press Nakayama H, Inoue K, Yoshimori Y (2006) Approximate optimization using computational intelligence and its application to reinforcement of cable-stayed bridges. In: Proceedings of the integrated intelligent systems for engineering design, pp 289–304. IOS press
Zurück zum Zitat Osyczka A, Kundu S (1995) A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Structural optimization 10(2):94–99 Osyczka A, Kundu S (1995) A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Structural optimization 10(2):94–99
Zurück zum Zitat Oyama A, Okabe Y, Shimoyama K, Fujii K (2009) Aerodynamic multiobjective design exploration of a flapping airfoil using a Navier–stokes solver. J Aerosp Comput Inf Commun 6:256–270 Oyama A, Okabe Y, Shimoyama K, Fujii K (2009) Aerodynamic multiobjective design exploration of a flapping airfoil using a Navier–stokes solver. J Aerosp Comput Inf Commun 6:256–270
Zurück zum Zitat 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: IEEE congress on evolutionary computation (CEC), pp 862–869 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: IEEE congress on evolutionary computation (CEC), pp 862–869
Zurück zum Zitat Palar PS, Tsuchiya T, Parks GT (2016) A comparative study of local search within a surrogate-assisted multi-objective memetic algorithm framework for expensive problems. Appl Soft Comput 43:1–19 Palar PS, Tsuchiya T, Parks GT (2016) A comparative study of local search within a surrogate-assisted multi-objective memetic algorithm framework for expensive problems. Appl Soft Comput 43:1–19
Zurück zum Zitat Pavelski LM, Delgado MR, Almeida CP, Goncalves RA, Venske SM (2014) ELMOEA/D-DE: extreme learning surrogate models in multi-objective optimization based on decomposition and differential evolution. In: Proceedings of the Brazilian conference on intelligent systems, IEEE, pp 318–323 Pavelski LM, Delgado MR, Almeida CP, Goncalves RA, Venske SM (2014) ELMOEA/D-DE: extreme learning surrogate models in multi-objective optimization based on decomposition and differential evolution. In: Proceedings of the Brazilian conference on intelligent systems, IEEE, pp 318–323
Zurück zum Zitat Pavelski LM, Delgado MR, Almeida CP, Gonaslves RA, Venske SM (2016) Extreme learning surrogate models in multi-objective optimization based on decomposition. Neurocomputing 180:55–67 Pavelski LM, Delgado MR, Almeida CP, Gonaslves RA, Venske SM (2016) Extreme learning surrogate models in multi-objective optimization based on decomposition. Neurocomputing 180:55–67
Zurück zum Zitat Pilát M, Neruda R (2011a) ASM-MOMA: multiobjective memetic algorithm with aggregate surrogate model. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1202–1208 Pilát M, Neruda R (2011a) ASM-MOMA: multiobjective memetic algorithm with aggregate surrogate model. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1202–1208
Zurück zum Zitat Pilát M, Neruda R (2011b) Improving many-objective optimizers with aggregate meta-models. In Proceedings of the 11th international conference on hybrid intelligent systems, IEEE, pp 555–560 Pilát M, Neruda R (2011b) Improving many-objective optimizers with aggregate meta-models. In Proceedings of the 11th international conference on hybrid intelligent systems, IEEE, pp 555–560
Zurück zum Zitat Pilát M, Neruda R (2014) Hypervolume-based local search in multi-objective evolutionary optimization. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 637–644 Pilát M, Neruda R (2014) Hypervolume-based local search in multi-objective evolutionary optimization. In: Proceedings of the genetic and evolutionary computation conference, ACM, pp 637–644
Zurück zum Zitat Poloni C, Giurgevich A, Onesti L, Pediroda V (2000) Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics. Comput Methods Appl Mech Eng 186(2):403–420MATH Poloni C, Giurgevich A, Onesti L, Pediroda V (2000) Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics. Comput Methods Appl Mech Eng 186(2):403–420MATH
Zurück zum Zitat Ponweiser W, Wagner T, Biermann D, Vincze M (2008) Multiobjective optimization on a limited budget of evaluations using model-assisted S-metric selection. In: Proceedings of the parallel problem solving from nature-PPSN X, pp 784–794, Springer Ponweiser W, Wagner T, Biermann D, Vincze M (2008) Multiobjective optimization on a limited budget of evaluations using model-assisted S-metric selection. In: Proceedings of the parallel problem solving from nature-PPSN X, pp 784–794, Springer
Zurück zum Zitat Ponweiser W, Wagner T, Vincze M (2008) Clustered multiple generalized expected improvement: a novel infill sampling criterion for surrogate models. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 3515–3522 Ponweiser W, Wagner T, Vincze M (2008) Clustered multiple generalized expected improvement: a novel infill sampling criterion for surrogate models. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 3515–3522
Zurück zum Zitat Qasem SN, Shamsuddin SM, Hashim SMM, Darus M, Shammari EA (2013) Memetic multiobjective particle swarm optimization-based radial basis function network for classification problems. Inf Sci 239:165–190MathSciNet Qasem SN, Shamsuddin SM, Hashim SMM, Darus M, Shammari EA (2013) Memetic multiobjective particle swarm optimization-based radial basis function network for classification problems. Inf Sci 239:165–190MathSciNet
Zurück zum Zitat Quagliarella D, Vicini A (1998) Genetic algorithms and evolutionary strategies in engineering and computer science, chapter coupling genetic algorithms and gradient based optimization techniques. Wiley, Chichester, pp 289–309 Quagliarella D, Vicini A (1998) Genetic algorithms and evolutionary strategies in engineering and computer science, chapter coupling genetic algorithms and gradient based optimization techniques. Wiley, Chichester, pp 289–309
Zurück zum Zitat Ray T, Singh HK, Isaacs A, Smith W (2009) Infeasibility driven evolutionary algorithm for constrained optimization. In: Mezura-Montes E (ed) Constraint-handling in evolutionary optimization. Springer, Berlin, pp 145–165 Ray T, Singh HK, Isaacs A, Smith W (2009) Infeasibility driven evolutionary algorithm for constrained optimization. In: Mezura-Montes E (ed) Constraint-handling in evolutionary optimization. Springer, Berlin, pp 145–165
Zurück zum Zitat Regis RG (2016) Multi-objective constrained black-box optimization using radial basis function surrogates. J Comput Sci 16:140–155MathSciNet Regis RG (2016) Multi-objective constrained black-box optimization using radial basis function surrogates. J Comput Sci 16:140–155MathSciNet
Zurück zum Zitat Reyes-Sierra M, Coello CAC (2005) A study of fitness inheritance and approximation techniques for multi-objective particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 65–72 Reyes-Sierra M, Coello CAC (2005) A study of fitness inheritance and approximation techniques for multi-objective particle swarm optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 65–72
Zurück zum Zitat Robic T, Filipic B (2005) DEMO: differential evolution for multiobjective optimization. In: Proceedings of evolutionary multi-criterion optimization, pp 520–533. Springer Robic T, Filipic B (2005) DEMO: differential evolution for multiobjective optimization. In: Proceedings of evolutionary multi-criterion optimization, pp 520–533. Springer
Zurück zum Zitat Roy PC, Deb K (2016) High dimensional model representation for solving expensive multi-objective optimization problems. Technical Report COIN Report Number 2016012, Michigan State University Roy PC, Deb K (2016) High dimensional model representation for solving expensive multi-objective optimization problems. Technical Report COIN Report Number 2016012, Michigan State University
Zurück zum Zitat Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4:409–423MathSciNetMATH Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4:409–423MathSciNetMATH
Zurück zum Zitat Santana-Quintero LV, Montano AA, Coello CAC (2010) A review of techniques for handling expensive functions in evolutionary multi-objective optimization. In: Tenne Y, Goh C-K (eds) Computational intelligence in expensive optimization problems. Springer, Berlin, pp 29–59 Santana-Quintero LV, Montano AA, Coello CAC (2010) A review of techniques for handling expensive functions in evolutionary multi-objective optimization. In: Tenne Y, Goh C-K (eds) Computational intelligence in expensive optimization problems. Springer, Berlin, pp 29–59
Zurück zum Zitat Sasena MJ, Papalambros P, Goovaerts P (2002) Exploration of metamodeling sampling criteria for constrained global optimization. Eng Optim 34:263–278 Sasena MJ, Papalambros P, Goovaerts P (2002) Exploration of metamodeling sampling criteria for constrained global optimization. Eng Optim 34:263–278
Zurück zum Zitat Sastry K, Goldberg DE, Pelikan M (2001) Don’t evaluate, inherit. In: Proceedings of the genetic and evolutionary computation conference, pp 551–558. Morgan Kaufmann Sastry K, Goldberg DE, Pelikan M (2001) Don’t evaluate, inherit. In: Proceedings of the genetic and evolutionary computation conference, pp 551–558. Morgan Kaufmann
Zurück zum Zitat Schaffer JD (1985) Some experiments in machine learning using vector evaluated genetic algorithms. Ph.D. thesis, Vanderbilt University, Nashville Schaffer JD (1985) Some experiments in machine learning using vector evaluated genetic algorithms. Ph.D. thesis, Vanderbilt University, Nashville
Zurück zum Zitat Seah C-W, Ong Y-S, Tsang IW, Jiang S (2012) Pareto rank learning in multi-objective evolutionary algorithms. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8 Seah C-W, Ong Y-S, Tsang IW, Jiang S (2012) Pareto rank learning in multi-objective evolutionary algorithms. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8
Zurück zum Zitat 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 135:1–7 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 135:1–7
Zurück zum Zitat Sindhya K, Deb K, Miettinen K (2011) Improving convergence of evolutionary multi-objective optimization with local search: a concurrent-hybrid algorithm. Nat Comput 10:1407–1430MathSciNetMATH Sindhya K, Deb K, Miettinen K (2011) Improving convergence of evolutionary multi-objective optimization with local search: a concurrent-hybrid algorithm. Nat Comput 10:1407–1430MathSciNetMATH
Zurück zum Zitat Sindhya K, Miettinen K, Deb K (2013) A hybrid framework for evolutionary multi-objective optimization. IEEE Trans Evol Comput 17:495–511MATH Sindhya K, Miettinen K, Deb K (2013) A hybrid framework for evolutionary multi-objective optimization. IEEE Trans Evol Comput 17:495–511MATH
Zurück zum Zitat Singh HK, Ray T, Smith W (2010) Surrogate assisted simulated annealing (SASA) for constrained multi-objective optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8 Singh HK, Ray T, Smith W (2010) Surrogate assisted simulated annealing (SASA) for constrained multi-objective optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1–8
Zurück zum Zitat Singh P, Couckuyt I, Ferranti F, Dhaene T (2014) A constrained multi-objective surrogate-based optimization algorithm. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 3080–3087 Singh P, Couckuyt I, Ferranti F, Dhaene T (2014) A constrained multi-objective surrogate-based optimization algorithm. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 3080–3087
Zurück zum Zitat Smith RE, Dike BA, Stegmann SA (1995) Fitness inheritance in genetic algorithms. In: Proceedings of the ACM symposium on applied computing, ACM, pp 345–350 Smith RE, Dike BA, Stegmann SA (1995) Fitness inheritance in genetic algorithms. In: Proceedings of the ACM symposium on applied computing, ACM, pp 345–350
Zurück zum Zitat Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280MathSciNetMATH Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280MathSciNetMATH
Zurück zum Zitat Syberfeldt A, Grimm H, Ng A, John RI (2008) A parallel surrogate-assisted multi-objective evolutionary algorithm for computationally expensive optimization problems. In: Proceedings of the IEEE world congress on computational intelligence, IEEE, pp 3177–3184 Syberfeldt A, Grimm H, Ng A, John RI (2008) A parallel surrogate-assisted multi-objective evolutionary algorithm for computationally expensive optimization problems. In: Proceedings of the IEEE world congress on computational intelligence, IEEE, pp 3177–3184
Zurück zum Zitat Tenne Y, Armfield SW (2008) Metamodel accuracy assessment in evolutionary optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1505–1512 Tenne Y, Armfield SW (2008) Metamodel accuracy assessment in evolutionary optimization. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 1505–1512
Zurück zum Zitat Toscano G, Deb K (2016) Study of the approximation of the fitness landscape and the ranking process of scalarizing functions for many-objective problems. Technical Report COIN Report Number 2016018, Michigan State University Toscano G, Deb K (2016) Study of the approximation of the fitness landscape and the ranking process of scalarizing functions for many-objective problems. Technical Report COIN Report Number 2016018, Michigan State University
Zurück zum Zitat Turco A (2011) Metahybrid: Combining metamodels and gradient-based techniques in a hybrid multi-objective genetic algorithm. In: Coello CAC (ed) Proceedings of the learning and intelligent optimization. Springer, Berlin, pp 293–307 Turco A (2011) Metahybrid: Combining metamodels and gradient-based techniques in a hybrid multi-objective genetic algorithm. In: Coello CAC (ed) Proceedings of the learning and intelligent optimization. Springer, Berlin, pp 293–307
Zurück zum Zitat Ulmer H, Streichert F, Zell A (2003) Evolution strategies assisted by Gaussian processes with improved preselection criterion. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 692–699 Ulmer H, Streichert F, Zell A (2003) Evolution strategies assisted by Gaussian processes with improved preselection criterion. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 692–699
Zurück zum Zitat van Veldhuizen DA, Lamont GB (1999) Multiobjective evolutionary algorithm test suites. In: Proceedings of the 1999 ACM symposium on applied computing, ACM, pp 351–357 van Veldhuizen DA, Lamont GB (1999) Multiobjective evolutionary algorithm test suites. In: Proceedings of the 1999 ACM symposium on applied computing, ACM, pp 351–357
Zurück zum Zitat Veldhuizen DAV, Lamont GB (1998) Evolutionary computation and convergence to a Pareto front. In: Proceedings of the genetic programming, pp 221–228. Morgan Kaufmann Veldhuizen DAV, Lamont GB (1998) Evolutionary computation and convergence to a Pareto front. In: Proceedings of the genetic programming, pp 221–228. Morgan Kaufmann
Zurück zum Zitat Veldhuizen DAV (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. thesis, Graduate School of Engineering of the Air Force Institute of Technology Air University, Dayton Veldhuizen DAV (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. thesis, Graduate School of Engineering of the Air Force Institute of Technology Air University, Dayton
Zurück zum Zitat Vrgut JA, Robinson BA (2007) Improved evolutionary optimization from genetically adaptive multimethod search. Proc Natl Acad Sci USA 104:708–711 Vrgut JA, Robinson BA (2007) Improved evolutionary optimization from genetically adaptive multimethod search. Proc Natl Acad Sci USA 104:708–711
Zurück zum Zitat Wagner T, Emmerich M, Deutz A, Ponweiser W (2010) On expected-improvement criteria for model-based multi-objective optimization. In: Schaefer R, Cotta C, Kolodziej J, Rudolph G (eds) Proceedings of the parallel problem solving from nature-PPSN XI. Springer, Berlin, pp 718–727 Wagner T, Emmerich M, Deutz A, Ponweiser W (2010) On expected-improvement criteria for model-based multi-objective optimization. In: Schaefer R, Cotta C, Kolodziej J, Rudolph G (eds) Proceedings of the parallel problem solving from nature-PPSN XI. Springer, Berlin, pp 718–727
Zurück zum Zitat Wang GG (2003) Adaptive response surface method using inherited latin hypercube design points. J Mech Des 125:210–220 Wang GG (2003) Adaptive response surface method using inherited latin hypercube design points. J Mech Des 125:210–220
Zurück zum Zitat Wang H, Jin Y, Jansen JO (2016) Data-driven surrogate-assisted multi-objective evolutionary optimization of a trauma system. IEEE Trans Evol Comput 20:939–952 Wang H, Jin Y, Jansen JO (2016) Data-driven surrogate-assisted multi-objective evolutionary optimization of a trauma system. IEEE Trans Evol Comput 20:939–952
Zurück zum Zitat Wilson B, Cappelleri D, Simpson TW, Frecker M (2001) Efficient pareto frontier exploration using surrogate approximations. Optim Eng 2(1):31–50MathSciNetMATH Wilson B, Cappelleri D, Simpson TW, Frecker M (2001) Efficient pareto frontier exploration using surrogate approximations. Optim Eng 2(1):31–50MathSciNetMATH
Zurück zum Zitat Yang BS, Yeun Y-S, Ruy W-S (2002) Managing approximation models in multiobjective optimization. Struct Multidiscip Optim 24:141–156 Yang BS, Yeun Y-S, Ruy W-S (2002) Managing approximation models in multiobjective optimization. Struct Multidiscip Optim 24:141–156
Zurück zum Zitat Yuan R, Guangchen B (2009) Comparison of neural network and kriging method for creating simulation-optimization metamodels. In: Yang B, Zhu W, Dai Y, Yang LT, Ma J (eds) Proceedings of the 8th IEEE international symposium on dependable, autonomic and secure computing, IEEE, pp 815–821 Yuan R, Guangchen B (2009) Comparison of neural network and kriging method for creating simulation-optimization metamodels. In: Yang B, Zhu W, Dai Y, Yang LT,  Ma J (eds) Proceedings of the 8th IEEE international symposium on dependable, autonomic and secure computing, IEEE, pp 815–821
Zurück zum Zitat Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731 Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731
Zurück zum Zitat Zhang Q, Liu W, Tsang E, Virginas B (2010) Expensive multiobjective optimization by MOEA/D with gaussian process model. IEEE Trans Evol Comput 14:456–474 Zhang Q, Liu W, Tsang E, Virginas B (2010) Expensive multiobjective optimization by MOEA/D with gaussian process model. IEEE Trans Evol Comput 14:456–474
Zurück zum Zitat Zhang Q, Liu W, Li H (2009) The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 203–208 Zhang Q, Liu W, Li H (2009) The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 203–208
Zurück zum Zitat Zhang Q, Zhau A, Zhao S, Suganthan PN, Liu W, Tiwari S (2009) Multiobjective optimization test instances for the CEC 2009 special session and competition. Technical Report CES-487, University of Essex/Nanyang Technological University, Essex, UK/Singapore Zhang Q, Zhau A, Zhao S, Suganthan PN, Liu W,  Tiwari S (2009) Multiobjective optimization test instances for the CEC 2009 special session and competition. Technical Report CES-487, University of Essex/Nanyang Technological University, Essex, UK/Singapore
Zurück zum Zitat Zheng Y, Julstrom BA, Cheng W (1997) Design of vector quantization codebooks using a genetic algorithm. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 525–529 Zheng Y, Julstrom BA, Cheng W (1997) Design of vector quantization codebooks using a genetic algorithm. In: Proceedings of the IEEE congress on evolutionary computation, IEEE, pp 525–529
Zurück zum Zitat Zhu J, Wang Y-J, Collette M (2013) A multi-objective variable-fidelity optimization method for genetic algorithms. Eng Optim 46:521–542MathSciNet Zhu J, Wang Y-J, Collette M (2013) A multi-objective variable-fidelity optimization method for genetic algorithms. Eng Optim 46:521–542MathSciNet
Zurück zum Zitat Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology Zurich Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology Zurich
Zurück zum Zitat Zitzler E, Kunzli S (2004) Indicator-based selection in multiobjective search. In: Yao X et al (eds) Proceedings of the parallel problem solving from nature-PPSN VIII. Springer, Berlin, pp 832–842 Zitzler E, Kunzli S (2004) Indicator-based selection in multiobjective search. In: Yao X et al (eds) Proceedings of the parallel problem solving from nature-PPSN VIII. Springer, Berlin, pp 832–842
Zurück zum Zitat Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms-a comparative case study. In: Eiben AE (ed) Proceedings of the parallel problem solving from nature-PPSN V. Springer, Berlin, pp 292–301 Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms-a comparative case study. In: Eiben AE (ed) Proceedings of the parallel problem solving from nature-PPSN V. Springer, Berlin, pp 292–301
Zurück zum Zitat Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195 Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195
Zurück zum Zitat Zitzler E, Laumanns M, Thiele L (2002) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou KC (ed) Proceedings of the evolutionary methods for design, optimisation and control with application to industrial problems (EUROGEN 2001). CIMNE, Barcelona, pp 95–100 Zitzler E, Laumanns M, Thiele L (2002) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou KC (ed) Proceedings of the evolutionary methods for design, optimisation and control with application to industrial problems (EUROGEN 2001). CIMNE, Barcelona, pp 95–100
Zurück zum Zitat Zitzler E, Thiele L, Laumanns M, Fonseca C, Fonseca V (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 8:117–132 Zitzler E, Thiele L, Laumanns M, Fonseca C, Fonseca V (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 8:117–132
Metadaten
Titel
A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms
verfasst von
Tinkle Chugh
Karthik Sindhya
Jussi Hakanen
Kaisa Miettinen
Publikationsdatum
11.12.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 9/2019
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2965-0

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