## 1 Introduction  
Optimization is an essential part of research, both in science and in engineering. In many cases, the goal of the design is the outcome of an optimization problem [1; 2; 3; 4; 5], as is the case for electrical machinery, which belongs to the most general branch of mathematical optimization problems, both in the case of transformers and rotating machines [2; 3; 4; 5; 6; 7; 8]. Due to its complexity, the design optimization of electrical machines is usually split into different sub-tasks [6; 8; 9]. The two main sub-tasks are the design and the (preliminary) design optimization of the electrical machine. During the design optimization stage, the engineers' goal is to find the optimal key-performance parameters with a feasible scheme for a given application by investigating different topologies and multi-disciplinary analysis of the machine [1; 2; 3; 4; 5; 9; 10]. Then, the most minute details of the machine are worked out during the final design stage. Here, many sub-domain optimization tasks are performed to fine-tune the final design [5; 11; 12; 13]. A wide range of numerical methods have been used to solve electrical machine optimization problems since the first appearance of computers in the industry [6], from simple heuristics to sophisticated mathematical optimization methods. For instance, transformer optimization was one of the first applications of geometric programming [9; 14], but other deterministic methods, such as gradient based, trust-region, and interior-point based, were used to solve electrical machine related problems [15; 16; 17]. Here, the final solutions may depend on the initial starting points, and engineers need to simplify some functions to fit within the limitations of the applied mathematical programming method [14]. Besides, the computation of some of these functions is computationally expensive and cannot be calculated without numerical integration. Evolutionary algorithms provide a flexible and accurate framework to overcome these problems, and many genetic and evolutionary based electrical machine optimization methods have been published in the literature [5; 8; 18; 19; 20; 21; 22]. However, the selection of the right bio-inspired algorithm for a given application or the process of tuning its parameters is not straightforward. This task has its own challenges [23]. Due to the \"no free lunch\" theorem of mathematical optimization [24], none of the evolutionary optimization algorithms can outperform the others if they are averaged over all possible problems. However, metaheuristic based optimization solvers always have to be benchmarked from the point of view of the specific electrical machine optimization problem. As there is a most appropriate metaheuristic solver for a specific application, this is an important consequence of the \"no free lunch\" theorem. It is a challenging problem; there are a wide range of applications, and the optimized electrical machine models have had higher and higher complexity during the last few decades. Currently, most of the published electrical machine optimization methods are based on some FEM calculation methodology, to consider more details and achieve higher precision on the calculation of the performance parameters [8; 9; 25]. Many modern design methodologies optimize the electrical machine at the system level, together with its application; e.g., [PERSON] et al. in [26] considered a hybrid electric vehicle application for electrical machine design optimization, and [PERSON] et al. in [27] took wider applications into account and considered the load profiles of the drives as well. However, the solutions of these complex, system-level models are computationally expensive. The calculation time of one solution is usually longer than the time spent sorting the results [28].