CONORBIT: constrained optimization by radial basis function interpolation in trust regions†. (4th May 2017)

• Record Type: Journal Article
• Authors: Regis, Rommel G.; Wild, Stefan M.
• Is Part Of: Optimization methods and software. Volume 32:Number 3(2017)
• Page Start: 552
• Page End: 580
• Publication Date: 2017-05-04
• Subjects: constrained optimization -- black-box optimization -- computationally expensive function -- simulation-based optimization -- trust region -- fully linear model -- radial basis function interpolation; 65K05 -- 90C56; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1226305
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : This paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm [S.M. Wild, R.G. Regis and C.A. Shoemaker, ORBIT: optimization by radial basis function interpolation in trust-regions, SIAM J. Sci. Comput. 30 (2008), pp. 3197–3219]. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA (Powell 1994), a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.