An Efficient Gradient-Free Topology Optimization Method Based on Superellipse Curves and a Multilayer Perceptron Surrogate

Topology optimization is an effective method for obtaining high-performance material distributions with novel configurations. However, its application to complex electromagnetic devices remains challenging because of the difficulty of deriving sensitivities and the low computational efficiency associated with repeated finite element method (FEM) evaluations for nonlinear materials. This paper proposes an efficient gradient-free topology optimization method that integrates superellipse curves with a multilayer perceptron (MLP) surrogate model while accounting for nonlinearity. First, based on the general superellipse curve, an improved expression is introduced, in which the size, shape, and position can be flexibly controlled by only seven parameters. Then, a parameterized superellipse-curve-based gradient-free topology optimization framework is established, which can be applied to complex electromagnetic devices with nonlinear materials and complex objective functions. Moreover, a lightweight MLP-based surrogate model is constructed using limited training samples generated by Latin hypercube sampling and FEM, and it can replace FEM for evaluating nonlinear material behavior with negligible computational cost. Finally, the proposed topology optimization framework is applied to the design of a magnetic actuator, both with and without considering nonlinear B–H characteristics, demonstrating its effectiveness.