A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

[1]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[2]  Akira Todoroki,et al.  Modified Efficient Global Optimization for a Hat-Stiffened Composite Panel with Buckling Constraint , 2008 .

[3]  Edmondo A. Minisci,et al.  Multi-objective evolutionary optimization of subsonic airfoils by kriging approximation and evolution control , 2005, 2005 IEEE Congress on Evolutionary Computation.

[4]  Roman Neruda,et al.  Aggregate meta-models for evolutionary multiobjective and many-objective optimization , 2013, Neurocomputing.

[5]  Ian Griffin,et al.  An informed convergence accelerator for evolutionary multiobjective optimiser , 2007, GECCO '07.

[6]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[7]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[8]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Richard C. Chapman,et al.  Application of Particle Swarm to Multiobjective Optimization , 1999 .

[10]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[11]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[12]  Roman Neruda,et al.  LAMM-MMA: multiobjective memetic algorithm with local aggregate meta-model , 2011, GECCO '11.

[13]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[14]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[15]  Kevin Tucker,et al.  Response surface approximation of pareto optimal front in multi-objective optimization , 2004 .

[16]  Haym Hirsh,et al.  Informed operators: Speeding up genetic-algorithm-based design optimization using reduced models , 2000, GECCO.

[17]  Michèle Sebag,et al.  A mono surrogate for multiobjective optimization , 2010, GECCO '10.

[18]  D Nam,et al.  Multiobjective simulated annealing: a comparative study to evolutionary algorithms , 2000 .

[19]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[20]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

[21]  Carlos M. Fonseca,et al.  Multi-Objective Optimization : Hybridization of an Evolutionary Algorithm with Artificial Neural Networks for fast Convergence , 2004 .

[22]  Carlos A. Coello Coello,et al.  MODE-LD+SS: A novel Differential Evolution algorithm incorporating local dominance and scalar selection mechanisms for multi-objective optimization , 2010, IEEE Congress on Evolutionary Computation.

[23]  Carlos A. Coello Coello,et al.  Knowledge Incorporation in Multi-objective Evolutionary Algorithms , 2008, Multi-Objective Evolutionary Algorithms for Knowledge Discovery from Databases.

[24]  Carlos A. Coello Coello,et al.  Multi-objective airfoil shape optimization using a multiple-surrogate approach , 2012, 2012 IEEE Congress on Evolutionary Computation.

[25]  Saúl Zapotecas Martínez,et al.  MOEA/D assisted by rbf networks for expensive multi-objective optimization problems , 2013, GECCO '13.

[26]  Roman Neruda,et al.  ASM-MOMA: Multiobjective memetic algorithm with aggregate surrogate model , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[27]  Qing Li,et al.  Multiobjective optimization for crash safety design of vehicles using stepwise regression model , 2008 .

[28]  Michael T. M. Emmerich,et al.  Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels , 2006, IEEE Transactions on Evolutionary Computation.

[29]  António Gaspar-Cunha,et al.  A Multi-Objective Evolutionary Algorithm Using Neural Networks to Approximate Fitness Evaluations , 2005, Int. J. Comput. Syst. Signals.

[30]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[31]  Tapabrata Ray,et al.  An Evolutionary Algorithm with Spatially Distributed Surrogates for Multiobjective Optimization , 2007, ACAL.

[32]  Juan J. Alonso,et al.  AIAA 2004 – 1758 Design of a Low-Boom Supersonic Business Jet Using Evolutionary Algorithms and an Adaptive Unstructured Mesh Method , 2004 .

[33]  Liang Shi,et al.  Multiobjective GA optimization using reduced models , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[34]  Edmondo A. Minisci,et al.  MOPED: A Multi-objective Parzen-Based Estimation of Distribution Algorithm for Continuous Problems , 2003, EMO.

[35]  G. Matheron.  Principles of geostatistics , 1963 .

[36]  Meng-Sing Liou,et al.  Multi-Objective Optimization of Transonic Compressor Blade Using Evolutionary Algorithm , 2005 .

[37]  Kyriakos C. Giannakoglou,et al.  Multiobjective Metamodel–Assisted Memetic Algorithms , 2009 .

[38]  Qingfu Zhang,et al.  Expensive Multiobjective Optimization by MOEA/D With Gaussian Process Model , 2010, IEEE Transactions on Evolutionary Computation.

[39]  Saúl Zapotecas Martínez,et al.  A Memetic Algorithm with Non Gradient-Based Local Search Assisted by a Meta-model , 2010, PPSN.

[40]  Carlos A. Coello Coello,et al.  A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization , 2010 .

[41]  Ingo Hahn,et al.  Kriging-Assisted Multi-Objective Particle Swarm Optimization of permanent magnet synchronous machine for hybrid and electric cars , 2013, 2013 International Electric Machines & Drives Conference.

[42]  Yaochu Jin,et al.  A comprehensive survey of fitness approximation in evolutionary computation , 2005, Soft Comput..

[43]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[44]  Bithin Datta,et al.  Multi-objective management of saltwater intrusion in coastal aquifers using genetic programming and modular neural network based surrogate models. , 2010 .

[45]  Kwang-Yong Kim,et al.  Enhanced multi-objective optimization of a microchannel heat sink through evolutionary algorithm coupled with multiple surrogate models , 2010 .

[46]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[47]  Alain Ratle,et al.  Accelerating the Convergence of Evolutionary Algorithms by Fitness Landscape Approximation , 1998, PPSN.

[48]  Roman Neruda,et al.  A Surrogate Based Multiobjective Evolution Strategy with Different Models for Local Search and Pre-selection , 2012, 2012 IEEE 24th International Conference on Tools with Artificial Intelligence.

[49]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[50]  Saúl Zapotecas Martínez,et al.  A multi-objective meta-model assisted memetic algorithm with non gradient-based local search , 2010, GECCO '10.

[51]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[52]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[53]  Khaled Rasheed,et al.  A Survey of Fitness Approximation Methods Applied in Evolutionary Algorithms , 2010 .

[54]  Nielen Stander,et al.  An Adaptive Surrogate-Assisted Strategy for Multi-Objective Optimization , 2013 .

[55]  Ramana V. Grandhi,et al.  Improved Distributed Hypercube Sampling , 2002 .

[56]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[57]  Helio J. C. Barbosa,et al.  On Similarity-Based Surrogate Models for Expensive Single- and Multi-objective Evolutionary Optimization , 2010 .

[58]  Jacques Periaux,et al.  Advances in Hierarchical, Parallel Evolutionary Algorithms for Aerodynamic Shape Optimisation , 2002 .

[59]  Luis F. Gonzalez,et al.  A Generic Framework for the Design Optimisation of Multidisciplinary UAV Intelligent Systems using Evolutionary Computing , 2006 .

[60]  Andy J. Keane,et al.  Multi-Objective Optimization Using Surrogates , 2010 .

[61]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[62]  Roman Neruda,et al.  An Evolutionary Strategy for Surrogate-Based Multiobjective Optimization , 2012, 2012 IEEE Congress on Evolutionary Computation.

[63]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[64]  Hugo Jair Escalante,et al.  A hybrid surrogate-based approach for evolutionary multi-objective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[65]  G. P. Liu,et al.  A novel multi-objective optimization method based on an approximation model management technique , 2008 .

[66]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[67]  Piotr Czyzżak,et al.  Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization , 1998 .

[68]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[69]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .