Study of Hybrid Radial Basis Function for Design Optimization Problems

2015 ◽  
Author(s):  
Renhe Shi ◽  
Li Liu ◽  
Teng Long ◽  
Jian Liu
Keyword(s):  
Radial Basis Function ◽  
Design Optimization ◽  
Basis Function ◽  
Optimization Problems ◽  
Radial Basis

Sequential Radial Basis Function-Based Optimization Method Using Virtual Sample Generation

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Yifan Tang ◽  
Teng Long ◽  
Renhe Shi ◽  
Yufei Wu ◽  
G. Gary Wang
Keyword(s):  
Radial Basis Function ◽  
Design Optimization ◽  
Basis Function ◽  
Optimization Problem ◽  
Optimization Method ◽  
Support Vector ◽  
Virtual Sample ◽  
Real Samples ◽  
Virtual Samples ◽  
Radial Basis

Abstract To further reduce the computational expense of metamodel-based design optimization (MBDO), a novel sequential radial basis function (RBF)-based optimization method using virtual sample generation (SRBF-VSG) is proposed. Different from the conventional MBDO methods with pure expensive samples, SRBF-VSG employs the virtual sample generation mechanism to improve the optimization efficiency. In the proposed method, a least squares support vector machine (LS-SVM) classifier is trained based on expensive real samples considering the objective and constraint violation. The classifier is used to determine virtual points without evaluating any expensive simulations. The virtual samples are then generated by combining these virtual points and their Kriging responses. Expensive real samples and cheap virtual samples are used to refine the objective RBF metamodel for efficient space exploration. Several numerical benchmarks are tested to demonstrate the optimization capability of SRBF-VSG. The comparison results indicate that SRBF-VSG generally outperforms the competitive MBDO methods in terms of global convergence, efficiency, and robustness, which illustrates the effectiveness of virtual sample generation. Finally, SRBF-VSG is applied to an airfoil aerodynamic optimization problem and a small Earth observation satellite multidisciplinary design optimization problem to demonstrate its practicality for solving real-world optimization problems.

Reliability Based Design Optimization by Using a SLP Approach and Radial Basis Function Networks

2016 ◽  
Author(s):  
Niclas Strömberg
Keyword(s):  
Radial Basis Function ◽  
Design Optimization ◽  
Basis Function ◽  
Physical Space ◽  
Normal Space ◽  
Radial Basis Function Networks ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Radial Basis

In this paper reliability based design optimization by using radial basis function networks (RBFN) as surrogate models is presented. The RBFN are treated as regression models. By taking the center points equal to the sampling points an interpolation is obtained. The bias of the network is taken to be known a priori or posteriori. In the latter case, the well-known orthogonality constraint between the weights of the RBFN and the polynomial basis functions of the bias is adopted. The optimization is performed by using a first order reliability method (FORM)-based sequential linear programming (SLP) approach, where the Taylor expansions are generated in intermediate variables defined by the iso-probabilistic transformation. In addition, the reliability constraints are expanded at the most probable points which are found by using Newton’s method. The Newton algorithm is derived by proposing an in-exact Jacobian. In such manner, a FORM-based LP-formulation in the standard normal space of problems with non-Gaussian variables is suggested. The solution from the LP-problem is mapped back to the physical space and the suggested procedure continues in a sequence until convergence is reached. This is implemented for five different distributions: normal, lognormal, Gumbel, gamma and Weibull. It is also presented how the FORM-based SLP approach can be corrected by using second order reliability methods (SORM) and Monte Carlo simulations. In particular, the SORM approach of Hohenbichler is studied. The outlined methodology is both efficient and robust. This is demonstrated by solving established benchmarks as well as finite element problems.

Recursive Particle Swarm Optimization Application for the Radial Basis Function Networks Modeling System

2015 ◽  
Vol 713-715 ◽  
pp. 1817-1820
Author(s):  
Ling Liu ◽  
Min Chen ◽  
Hong Yi Guo
Keyword(s):  
Particle Swarm Optimization ◽  
Radial Basis Function ◽  
Basis Function ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Basis Functions ◽  
Radial Basis Function Networks ◽  
Historical Knowledge ◽  
Swarm Optimization ◽  
Radial Basis

A Recursive Particle Swarm Optimization (RPSO) is proposed to solve dynamic optimization problems where the data is obtained not once but one by one. The position of each particle swarm is updated recursively based on the continuous data and the historical knowledge. The experiment results indicate that RPSO-based radial basis function networks needs fewer radial basis functions and gives more accurate results than traditional PSO in solving dynamic problems.

scholarly journals Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

2021 ◽  
Vol 26 (2) ◽  
pp. 31
Author(s):  
Manuel Berkemeier ◽  
Sebastian Peitz
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Optimization Problems ◽  
Trust Region ◽  
Surrogate Models ◽  
Descent Method ◽  
Information Need ◽  
Derivative Free ◽  
Radial Basis ◽  
General Scalar

We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives.

scholarly journals Design Optimization of Centrifugal Pump Using Radial Basis Function Metamodels

2014 ◽  
Vol 6 ◽  
pp. 457542 ◽  
Author(s):  
Yu Zhang ◽  
Jinglai Wu ◽  
Yunqing Zhang ◽  
Liping Chen
Keyword(s):  
Radial Basis Function ◽  
Design Optimization ◽  
Centrifugal Pump ◽  
Basis Function ◽  
Radial Basis
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