A Single- and Multi-objective Optimization Algorithm for Electromagnetic Devices Assisted by Adaptive Kriging Based on P
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ORIGINAL ARTICLE
A Single‑ and Multi‑objective Optimization Algorithm for Electromagnetic Devices Assisted by Adaptive Kriging Based on Parallel Infilling Strategy Bin Xia1 · Ren Liu2 · Zhiwei He3 · Chang‑Seop Koh3 Received: 18 August 2020 / Revised: 17 September 2020 / Accepted: 23 September 2020 © The Korean Institute of Electrical Engineers 2020
Abstract A computationally efficient surrogate model is suggested to approximate the objective and constraint function values, which replace expensive evaluation of the objective and constraint function values in numerical simulation-based optimization. Kriging surrogate model has been widely used in surrogate-based design optimization (SBDO) to replace the highly nonlinear black-box functions. In this paper, a novel adaptive Kriging model based on parallel infilling strategy is proposed to improve both the numerical accuracy and efficiency of the SBDO methods. The parallel infilling strategy consists of two parts: local sampling and globaluthor sampling. In the local sampling, new additional sampling points are generated only within a limited region that is determined according to the optimal point at the last iteration, while in global sampling they are generated based on the fitting error estimation in the whole region. The effectiveness of the proposed algorithm is verified through applications to analytical functions. Then the algorithm is applied to the multi-objective optimal design of an ironless permanent magnet synchronous linear motor. Keywords Kriging · Fitting error · Infilling strategy · Multi-objective optimization · Surrogate function
1 Introduction In order to improve the design quality and reduce the design cost, optimization technology is being applied more and more widely in engineering design problems. At present, most modern engineering design problems involve huge numerical computation of objective and constraint function values by using numerical methods such as computational * Chang‑Seop Koh [email protected] Bin Xia [email protected] Ren Liu [email protected] Zhiwei He [email protected] 1
School of Electrical Engineering, Shenyang University of Technology, Shenyang, China
2
Guizhou Aerospace Linquan Motor Co. Ltd, Guiyang, China
3
College of Electrical and Computer Engineering, Chungbuk National University, Cheongju, South Korea
fluid dynamics CFD and finite element analysis (FEA). In the past two decades, meta-intelligent optimization algorithm based on surrogate model such as radial basis functions, support vector machines and Kriging has been widely used in the optimal design of electromagnetic devices [1–3]. For some high-dimensional and nonlinear multi-objective optimization problems, it is very important to build a highly accurate and computationally efficient surrogate model [4]. Unlike other surrogate models, the Kriging surrogate model gives information on the mean square error (MSE) of the point as well as predicts the response value at a point in the design region with high accuracy [5]. This is very import
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