An efficient multi-objective optimization method based on the adaptive approximation model of the radial basis function

Considering the high computational cost caused by solving multi-objective optimization (MOO) problems, an efficient multi-objective optimization method based on the adaptive approximation model is developed. Firstly, the Latin hypercube design (LHD) is employed for obtaining the initial sample points. Secondly, initial approximation models of objective functions and constraints are established by using the radial basis function (RBF). For ensuring the accuracy of the approximation models, the reverse shape parameter analysis method (RSPAM) is proposed to obtain improved approximation models. Thirdly, the micro multi-objective genetic algorithm (μMOGA) is adopted to solve the Pareto optimal set and the local-densifying approximation method is also applied to strengthen the ability of solving accurate Pareto optimal sets. Finally, the effectiveness and practicability of the proposed method is demonstrated by two numerical examples and two engineering examples.

[1]  Ming Zhou,et al.  Performance Optimization of Flywheel Motor by Using NSGA-2 and AKMMP , 2018, IEEE Transactions on Magnetics.

[2]  Javad Alikhani Koupaei,et al.  Finding a good shape parameter of RBF to solve PDEs based on the particle swarm optimization algorithm , 2018, Alexandria Engineering Journal.

[3]  C. Lacor,et al.  Multi-objective optimization of turbomachinery using improved NSGA-II and approximation model , 2011 .

[4]  Xiang Peng,et al.  Nonparametric uncertainty representation method with different insufficient data from two sources , 2018, Structural and Multidisciplinary Optimization.

[5]  Yin Lairong,et al.  Structural reliability analysis based on probability and probability box hybrid model , 2017 .

[6]  Xu Han,et al.  An efficient multi-objective optimization approach based on the micro genetic algorithm and its application , 2011, International Journal of Mechanics and Materials in Design.

[7]  G. Gary Wang,et al.  Trust Region Based Mode Pursuing Sampling Method for Global Optimization of High Dimensional Design Problems , 2015 .

[8]  Dick den Hertog,et al.  Space-filling Latin hypercube designs for computer experiments , 2008 .

[9]  Jianguang Fang,et al.  Hybrid Learning Algorithm of Radial Basis Function Networks for Reliability Analysis , 2021, IEEE Transactions on Reliability.

[10]  Vwani P. Roychowdhury,et al.  Parallel randomized sampling for support vector machine (SVM) and support vector regression (SVR) , 2008, Knowledge and Information Systems.

[11]  Long Teng,et al.  Aerodynamic and Stealthy Performance Optimization of Airfoil Based on Adaptive Surrogate Model , 2016 .

[12]  S. N. Omkar,et al.  Applied Soft Computing Artificial Bee Colony (abc) for Multi-objective Design Optimization of Composite Structures , 2022 .

[13]  Baotong Li,et al.  Construction of probability box model based on maximum entropy principle and corresponding hybrid reliability analysis approach , 2020, Structural and Multidisciplinary Optimization.

[14]  K. M. Liew,et al.  Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates , 2004 .

[15]  G. G. Wang,et al.  Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points , 2003 .

[16]  Gregory E. Fasshauer,et al.  On choosing “optimal” shape parameters for RBF approximation , 2007, Numerical Algorithms.

[17]  Jianguang Fang,et al.  Crashworthiness design of foam-filled bitubal structures with uncertainty , 2014 .

[18]  Morteza Kiani,et al.  A Comparative Study of Non-traditional Methods for Vehicle Crashworthiness and NVH Optimization , 2016 .

[19]  Behrooz Attaran,et al.  Improved design of an active landing gear for a passenger aircraft using multi-objective optimization technique , 2018, Structural and Multidisciplinary Optimization.

[20]  Yin Lairong,et al.  The multi-objective reliability-based design optimization for structure based on probability and ellipsoidal convex hybrid model , 2019, Structural Safety.

[21]  N. Strömberg,et al.  Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias , 2017 .

[22]  Jelena Svorcan,et al.  Multi-objective design optimization strategies for small-scale vertical-axis wind turbines , 2016 .

[23]  Wei Hao,et al.  Casualty risk of e-bike rider struck by passenger vehicle using China in-depth accident data , 2020, Traffic injury prevention.

[24]  M. D. Manshadi,et al.  Optimizing a Two-Element Wing Model with Morphing Flap by Means of the Response Surface Method , 2017 .

[25]  Lin Hu,et al.  An efficient reliability analysis approach for structure based on probability and probability box models , 2017 .

[26]  Iftekhar A. Karimi,et al.  Smart Sampling Algorithm for Surrogate Model Development , 2017, Comput. Chem. Eng..

[27]  Beom-Seon Jang,et al.  Adaptive approximation in multi-objective optimization for full stochastic fatigue design problem , 2009 .

[28]  Ye Tian,et al.  An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility , 2018, IEEE Transactions on Evolutionary Computation.

[29]  Yongbin Lee,et al.  Design optimization using support vector regression , 2008 .

[30]  Prasanth B. Nair,et al.  Sparse radial basis function approximation with spatially variable shape parameters , 2018, Appl. Math. Comput..

[31]  Chang-Wan Kim,et al.  Kriging Model Based Optimization of MacPherson Strut Suspension for Minimizing Side Load using Flexible Multi-Body Dynamics , 2018, International Journal of Precision Engineering and Manufacturing.

[32]  Scott A. Sarra,et al.  A random variable shape parameter strategy for radial basis function approximation methods , 2009 .

[33]  Jeong‐Soo Park.  Optimal Latin-hypercube designs for computer experiments , 1994 .

[34]  Bengt Fornberg,et al.  On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere , 2008, J. Comput. Phys..

[35]  Beom-Seon Jang,et al.  Managing approximation models in multiobjective optimization , 2003 .

[36]  Dejie Yu,et al.  Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method , 2015 .

[37]  V. R. Joseph,et al.  Maximum projection designs for computer experiments , 2015 .

[38]  Van-Hai Bui,et al.  Multi-Objective Optimization for Determining Trade-Off between Output Power and Power Fluctuations in Wind Farm System , 2019, Energies.

[39]  Guido Morgenthal,et al.  Single and multi-objective shape optimization of streamlined bridge decks , 2020 .

[40]  Lin Sun,et al.  An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model , 2019, Structural and Multidisciplinary Optimization.

[41]  Jie Liu,et al.  Time-Variant Reliability Analysis through Response Surface Method , 2017 .

[42]  G. Gary Wang,et al.  ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS , 2001 .