caa a22 4500 445877960 CHVBK 20180317145533.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11081-010-9118-y doi (NATIONALLICENCE)springer-10.1007/s11081-010-9118-y Sequential Approximate Optimization using Radial Basis Function network for engineering optimization [Elektronische Daten] [Satoshi Kitayama, Masao Arakawa, Koetsu Yamazaki] This paper presents a Sequential Approximate Optimization (SAO) procedure that uses the Radial Basis Function (RBF) network. If the objective and constraints are not known explicitly but can be evaluated through a computationally intensive numerical simulation, the response surface, which is often called meta-modeling, is an attractive method for finding an approximate global minimum with a small number of function evaluations. An RBF network is used to construct the response surface. The Gaussian function is employed as the basis function in this paper. In order to obtain the response surface with good approximation, the width of this Gaussian function should be adjusted. Therefore, we first examine the width. Through this examination, some sufficient conditions are introduced. Then, a simple method to determine the width of the Gaussian function is proposed. In addition, anew technique called the adaptive scaling technique is also proposed. The sufficient conditions for the width are satisfied by introducing this scaling technique. Second, the SAO algorithm is developed. The optimum of the response surface is taken as a new sampling point for local approximation. In addition, it is necessary to add new sampling points in the sparse region for global approximation. Thus, an important issue for SAO is to determine the sparse region among the sampling points. To achieve this, a new function called the density function is constructed using the RBF network. The global minimum of the density function is taken as the new sampling point. Through the sampling strategy proposed in this paper, the approximate global minimum can be found with a small number of function evaluations. Through numerical examples, the validities of the width and sampling strategy are examined in this paper. Springer Science+Business Media, LLC, 2010 Response surface nationallicence Sequential approximate optimization nationallicence RBF network nationallicence Density function nationallicence Engineering optimization nationallicence Kitayama Satoshi Kanazawa University, 920-1192, Kakuma-machi, Kanazawa, Japan aut Arakawa Masao Kagawa University, 761-0396, Hayashi-chi, Takamatsu, Kagawa, Japan aut Yamazaki Koetsu Kanazawa University, 920-1192, Kakuma-machi, Kanazawa, Japan aut Optimization and Engineering Springer US; http://www.springer-ny.com 12/4(2011-12-01), 535-557 1389-4420 12:4<535 2011 12 11081 https://doi.org/10.1007/s11081-010-9118-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11081-010-9118-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kitayama Satoshi Kanazawa University, 920-1192, Kakuma-machi, Kanazawa, Japan aut NATIONALLICENCE 700 1- Arakawa Masao Kagawa University, 761-0396, Hayashi-chi, Takamatsu, Kagawa, Japan aut NATIONALLICENCE 700 1- Yamazaki Koetsu Kanazawa University, 920-1192, Kakuma-machi, Kanazawa, Japan aut NATIONALLICENCE 773 0- Optimization and Engineering Springer US; http://www.springer-ny.com 12/4(2011-12-01), 535-557 1389-4420 12:4<535 2011 12 11081 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer