Computer-Aided Design 62 (2015) 57–63 Contents lists available at ScienceDirect Computer-Aided Design journal homepage: www.elsevier.com/locate/cad Potential of support vector regression for optimization of lens system Torki A. Altameem a,* , Vlastimir Nikolić b , Shahaboddin Shamshirband c,d,** , Dalibor Petković b , Hossein Javidnia e , Miss Laiha Mat Kiah c , Abdullah Gani c a College of Computing & Information Science, King Saud University, Salah ElDin St., Riyadh 11437, 28095, Saudi Arabia b University of Niš, Faculty of Mechanical Engineering, Department for Mechatronics and Control, Aleksandra Medvedeva 14, 18000, Niš, Serbia c Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia d Department of Computer Science, Chalous Branch, Islamic Azad University (IAU), 46615-397 Chalous, Iran e Department of Computer Engineering, Faculty of Engineering, University of Guilan, 1841, Rasht, Iran highlights • Lens system design represents a crucial factor for good image quality. • Optimization procedure is the main part of the lens system design methodology. • Soft computing methodologies optimization application. • Adaptive neuro-fuzzy inference system (ANFIS) application. • Support vector regression (SVR application). article info Article history: Received 2 May 2014 Accepted 23 October 2014 Keywords: Lens system Optimization Spot diagram SVR Soft computing abstract Lens system design is an important factor in image quality. The main aspect of the lens system design methodology is the optimization procedure. Since optimization is a complex, non-linear task, soft computing optimization algorithms can be used. There are many tools that can be employed to measure optical performance, but the spot diagram is the most useful. The spot diagram gives an indication of the image of a point object. In this paper, the spot size radius is considered an optimization criterion. Intelligent soft computing scheme Support Vector Regression (SVR) is implemented. In this study, the polynomial and radial basis functions (RBF) are applied as the SVR kernel function to estimate the optimal lens system parameters. The performance of the proposed estimators is confirmed with the simulation results. The SVR results are then compared with other soft computing techniques. According to the results, a greater improvement in estimation accuracy can be achieved through the SVR with polynomial basis function compared to other soft computing methodologies. The SVR coefficient of determination R 2 with the polynomial function was 0.9975 and with the radial basis function the R 2 was 0.964. The new optimization methods benefit from the soft computing capabilities of global optimization and multi- objective optimization rather than choosing a starting point by trial and error and combining multiple criteria into a single criterion in conventional lens design techniques. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction Lens system design is a complex engineering task in analytical approaches [1,2] due to strong interactions among parameters and * Corresponding author. ** Corresponding author at: Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia. Tel.: +60 146266763. E-mail addresses: altameem@ksu.edu.sa (T.A. Altameem), shamshirband@um.edu.my, shahab1396@gmail.com (S. Shamshirband). many local optima. There are also several design criteria, such as Seidel aberrations, chromatic aberrations, size and cost [3,4]. Lens system design mainly comprises two steps: calculating the initial lens and further optimization. The optimization method presents better and more robust results than the initial design [5,6]. Optimization is very important to lens system design [7]. For decades, various optimization methods have been successfully used in lens system design [8,9]. Optimization of a lens system involves determining the surface parameters defining the shape and position of each lens surface [10]. The mathematical model for this problem is generally complicated [11,12]. http://dx.doi.org/10.1016/j.cad.2014.10.003 0010-4485/© 2014 Elsevier Ltd. All rights reserved.