A Classification-Based Surrogate-Assisted Evolutionary Algorithm for Expensive Many-Objective Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have been developed mainly for solving expensive optimization problems where only a small number of real fitness evaluations are allowed. Most existing SAEAs are designed for solving low-dimensional single or multiobjective optimization problems, which are not well suited for many-objective optimization. This paper proposes a surrogate-assisted many-objective evolutionary algorithm that uses an artificial neural network to predict the dominance relationship between candidate solutions and reference solutions instead of approximating the objective values separately. The uncertainty information in prediction is taken into account together with the dominance relationship to select promising solutions to be evaluated using the real objective functions. Our simulation results demonstrate that the proposed algorithm outperforms the state-of-the-art evolutionary algorithms on a set of many-objective optimization test problems.

[1]  Ke Tang,et al.  Classification- and Regression-Assisted Differential Evolution for Computationally Expensive Problems , 2012, Journal of Computer Science and Technology.

[2]  Aimin Zhou,et al.  A Multiobjective Evolutionary Algorithm Based on Decomposition and Preselection , 2015, BIC-TA.

[3]  Kalyanmoy Deb,et al.  On the performance of classification algorithms for learning Pareto-dominance relations , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[4]  Aimin Zhou,et al.  A classification and Pareto domination based multiobjective evolutionary algorithm , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

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

[6]  S Sapna,et al.  Backpropagation Learning Algorithm Based on Levenberg Marquardt Algorithm , 2012 .

[7]  Prakash Ranjitkar,et al.  Bus Dwell Time Modeling Using Gene Expression Programming , 2015, Comput. Aided Civ. Infrastructure Eng..

[8]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[9]  Ye Tian,et al.  An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[10]  Kaisa Miettinen,et al.  A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms , 2017, Soft Computing.

[11]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[12]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Comput. Intell. Mag..

[13]  Yaochu Jin,et al.  Surrogate-Assisted Multicriteria Optimization: Complexities, Prospective Solutions, and Business Case , 2017 .

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

[15]  D G Krige,et al.  A statistical approach to some mine valuation and allied problems on the Witwatersrand , 2015 .

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

[17]  Yaochu Jin,et al.  Surrogate-assisted evolutionary computation: Recent advances and future challenges , 2011, Swarm Evol. Comput..

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

[19]  Derek J. Pike,et al.  Empirical Model‐building and Response Surfaces. , 1988 .

[20]  Tapabrata Ray,et al.  A Novel Constraint Handling Strategy for Expensive Optimization Problems , 2015 .

[21]  Bernhard Sendhoff,et al.  Generalizing Surrogate-Assisted Evolutionary Computation , 2010, IEEE Transactions on Evolutionary Computation.

[22]  Chee Keong Kwoh,et al.  Feasibility Structure Modeling: An Effective Chaperone for Constrained Memetic Algorithms , 2010, IEEE Transactions on Evolutionary Computation.

[23]  Bernhard Sendhoff,et al.  A framework for evolutionary optimization with approximate fitness functions , 2002, IEEE Trans. Evol. Comput..

[24]  Barbara S. Minsker,et al.  Optimal groundwater remediation design using an Adaptive Neural Network Genetic Algorithm , 2006 .

[25]  Xin Yao,et al.  Two_Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[27]  Ivor W. Tsang,et al.  Pareto Rank Learning in Multi-objective Evolutionary Algorithms , 2012, 2012 IEEE Congress on Evolutionary Computation.

[28]  Daniel Svozil,et al.  Introduction to multi-layer feed-forward neural networks , 1997 .

[29]  Saúl Zapotecas Martínez,et al.  Combining surrogate models and local search for dealing with expensive multi-objective optimization problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[30]  Miguel Pinzolas,et al.  Neighborhood based Levenberg-Marquardt algorithm for neural network training , 2002, IEEE Trans. Neural Networks.

[31]  Yaochu Jin,et al.  A radial space division based evolutionary algorithm for many-objective optimization , 2017, Appl. Soft Comput..

[32]  Wolfgang Ponweiser,et al.  Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted -Metric Selection , 2008, PPSN.

[33]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

[34]  Allan Pinkus,et al.  Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function , 1991, Neural Networks.

[35]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[36]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[37]  Ye Tian,et al.  A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[38]  Bernhard Sendhoff,et al.  A systems approach to evolutionary multiobjective structural optimization and beyond , 2009, IEEE Computational Intelligence Magazine.

[39]  P J Webros.  BACKPROPAGATION THROUGH TIME: WHAT IT DOES AND HOW TO DO IT , 1990 .

[40]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[41]  Hirotaka Nakayama,et al.  GENERATION OF PARETO FRONTIERS USING SUPPORT VECTOR MACHINE , 2004 .

[42]  Claudio Moraga,et al.  The Influence of the Sigmoid Function Parameters on the Speed of Backpropagation Learning , 1995, IWANN.

[43]  Kaisa Miettinen,et al.  A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[44]  José António Tenreiro Machado,et al.  Multi-objective Genetic Manipulator Trajectory Planner , 2004, EvoWorkshops.

[45]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[46]  Jacek M. Zurada,et al.  Introduction to artificial neural systems , 1992 .

[47]  Peter J. Fleming,et al.  A Real-World Application of a Many-Objective Optimisation Complexity Reduction Process , 2013, EMO.

[48]  Aimin Zhou,et al.  A Multioperator Search Strategy Based on Cheap Surrogate Models for Evolutionary Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[49]  T. Simpson,et al.  Efficient Pareto Frontier Exploration using Surrogate Approximations , 2000 .

[50]  Yang Yu,et al.  A two-layer surrogate-assisted particle swarm optimization algorithm , 2014, Soft Computing.

[51]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

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

[53]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox , 2002 .

[54]  Dominique Douguet,et al.  e-LEA3D: a computational-aided drug design web server , 2010, Nucleic Acids Res..

[55]  Zhi-Hua Zhou,et al.  Ensemble Methods: Foundations and Algorithms , 2012 .

[56]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[57]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

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

[59]  Yong Wang,et al.  A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator , 2012, Appl. Soft Comput..

[60]  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.

[61]  Miqing Li,et al.  Benchmark Functions for the CEC'2017 Competition on Many-Objective Optimization , 2017 .

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

[63]  Chee Keong Kwoh,et al.  Classification-Assisted Memetic Algorithms for Equality-Constrained Optimization Problems , 2009, Australasian Conference on Artificial Intelligence.

[64]  Francisco Rivas-Dávalos,et al.  An Approach Based on the Strength Pareto Evolutionary Algorithm 2 for Power Distribution System Planning , 2005, EMO.

[65]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[66]  Jianchao Zeng,et al.  A fitness approximation assisted competitive swarm optimizer for large scale expensive optimization problems , 2018, Memetic Comput..

[67]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[68]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[69]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

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

[71]  Qingfu Zhang,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 RM-MEDA: A Regularity Model-Based Multiobjective Estimation of , 2022 .

[72]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[73]  Yuping Wang,et al.  Multiobjective bilevel optimization for production-distribution planning problems using hybrid genetic algorithm , 2014, Integr. Comput. Aided Eng..

[74]  Ye Tian,et al.  Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization , 2017, Complex & Intelligent Systems.

[75]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[76]  Kaisa Miettinen,et al.  On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization , 2016, PPSN.

[77]  Ye Tian,et al.  A region division based diversity maintaining approach for many-objective optimization , 2017, Integr. Comput. Aided Eng..

[78]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[79]  Patrick M. Reed,et al.  Many‐objective groundwater monitoring network design using bias‐aware ensemble Kalman filtering, evolutionary optimization, and visual analytics , 2011 .

[80]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.