###### Abstract  
This paper reviews the recent developments of design optimization methods for electromagnetic devices, with a focus on machine learning methods. First, the recent advances in multi-objective, multidisciplinary, multilevel, topology, fuzzy, and robust design optimization of electromagnetic devices are overviewed. Second, a review is presented to the performance prediction and design optimization of electromagnetic devices based on the machine learning algorithms, including artificial neural network, support vector machine, extreme learning machine, random forest, and deep learning. Last, to meet modern requirements of high manufacturing/production quality and lifetime reliability, several promising topics, including the application of cloud services and digital twin, are discussed as future directions for design optimization of electromagnetic devices.  
electromagnetic devices; electrical machines; optimization methods; machine learning; deep learning; reliability; topology optimization; robust design +
Footnote †: journal: Medical  
how to improve the optimization efficiency (or reduce the computation cost) is a challenge for efficient design optimization of many electromagnetic devices.  
Furthermore, the practical performance of electromagnetic devices is affected significantly by the inevitable material diversities and uncertainties in the manufacturing or production process. To improve the manufacturing quality of the optimized electromagnetic devices, design optimization in the presence of uncertainties should be conducted at the early stage of the development. From the perspective of industrial production, the performance of a good design of an electromagnetic device, like a transformer, should not be sensitive to those uncertainties. To achieve this goal, reliability-based and robust optimizations have attracted significant research attention recently, especially when the industrial big data about the material and manufacturing process are considered [6; 10; 11; 12; 13; 14; 15]. These topics are of ever-growing significance for smart manufacturing in the context of industry 4.0. However, the application of multidisciplinary analysis and/or industrial big data also brings many challenges to the design optimization process and degrades the optimization performance with conventional optimization methods. Advanced technologies, such as machine learning and cloud computing, will greatly improve the handling of these design optimization problems.  
This paper reviews the recent developments in design optimization of electromagnetic devices, with a focus on machine learning methods. Compared to the current state of the art, this review has three new contributions. First, this review covers more types of electromagnetic devices, instead of specific types, like electrical machines and antennas [4; 5; 7; 13; 14]. Second, besides the review of recent developments in typical optimization methods, such as multi-objective and multidisciplinary optimizations, this work reviews the topology optimization, fuzzy optimization, and new optimization strategies like space-reduction strategy. Third, a systematic review of machine learning algorithms is presented, and four promising research directions are proposed to integrate these algorithms with other emerging technologies like digital twin.  
The remainder of this paper is organized as follows. Section 2 presents an overview of the recent advances in design optimization of electromagnetic devices, including multi-objective, multidisciplinary, multilevel, topology, and robust optimization methods. Three examples are investigated, including superconducting magnetic energy storage (SMES), high-frequency transformers, and permanent magnet (PM) motors. Section 3 reviews the design optimization of electromagnetic devices based on machine learning methods, with two examples. Section 4 discusses several promising topics as future directions for this research field, followed by the conclusion.