A Superellipse-Based Gradient-Free Topology Optimization Method with Application to Magnetic Actuator Design

Structural optimization plays a crucial role in enhancing the performance of magnetic actuators. Traditional design approaches, such as parametric scanning, are limited by their reliance on empirical geometries. Meanwhile, widely used topology optimization techniques—including the Solid Isotropic Material with Penalization (SIMP) method and level-set methods—often encounter difficulties such as a large number of design variables, high computational cost, and unclear structural boundaries. To overcome these limitations, this paper proposes a novel gradient-free topology optimization method based on superellipses for designing magnetic actuator yokes. The proposed approach offers three key benefits: (1) It requires very few design variables, with each superellipse described by only seven parameters, thereby reducing the dimensionality of the design space and simplifying the optimization problem. (2) It yields clear and smooth structural boundaries without the need for post-processing. (3) It operates without gradient information, employing stochastic algorithms such as genetic algorithms that rely solely on objective function evaluations. A case study on yoke optimization demonstrates that our method achieves magnetic force output comparable to or better than the SIMP method, but with significantly fewer variables and a simpler implementation. This work provides an efficient and new tool for the conceptual design of magnetic actuators and related electromagnetic devices.