title: RF cavity design exploiting a new derivative-free trust region optimization approach.
abstract: In this article, a novel derivative-free (DF) surrogate-based trust region optimization approach is proposed. In the proposed approach, quadratic surrogate models are constructed and successively updated. The generated surrogate model is then optimized instead of the underlined objective function over trust regions. Truncated conjugate gradients are employed to find the optimal point within each trust region. The approach constructs the initial quadratic surrogate model using few data points of order O(n), where n is the number of design variables. The proposed approach adopts weighted least squares fitting for updating the surrogate model instead of interpolation which is commonly used in DF optimization. This makes the approach more suitable for stochastic optimization and for functions subject to numerical error. The weights are assigned to give more emphasis to points close to the current center point. The accuracy and efficiency of the proposed approach are demonstrated by applying it to a set of classical bench-mark test problems. It is also employed to find the optimal design of RF cavity linear accelerator with a comparison analysis with a recent optimization technique.
authors.affiliation: Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
authors.forename: Abdel-Karim S O
authors.initials: AK
authors.lastname: Hassan
authors.affiliation: Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
authors.forename: Hany L
authors.initials: HL
authors.lastname: Abdel-Malek
authors.affiliation: Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
authors.forename: Ahmed S A
authors.initials: AS
authors.lastname: Mohamed
authors.affiliation: Electronics and Electrical Communications Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
authors.forename: Tamer M
authors.initials: TM
authors.lastname: Abuelfadl
authors.affiliation: Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt.
authors.forename: Ahmed E
authors.initials: AE
authors.lastname: Elqenawy
keywords: Derivative-free optimization; Linear accelerator; Optimal design; Quadratic surrogate model; Trust region