Response Surface-Assisted Trust-Region Method for Optimization of Electromagnetic Devices

In this article, a trust-region method based optimization approach is proposed for optimization of electromagnetic devices using a reduced number of finite-element method (FEM) simulations. This approach relies on a computationally efficient approximation of the objective function using a response surface model. A second-order polynomial model is used because of its simplicity. The design of experiments technique is used to build this model. Moreover, this approach allows the use of coarser mesh in the FEM model because of its smoothing capabilities under noisy objective function. The algorithm is tested on two benchmark problems: Loney's solenoid design optimization and TEAM workshop problem 22. The proposed method has shown clear advantage of reduced number of FEM simulations compared to the existing algorithms tested on these problems. Later, this methodology is used for optimization of a Halbach array-based magnetic levitation device where the objective is to maximize permanent magnet utilization. This device is considered for various numbers of Halbach segments per pole. Improvement in the range of 5%-10% is observed over the past optimized results from the literature. Furthermore, this improvement is verified using a commercial optimization software, and the proposed method is found competitive to this software.