Evolutionary Topology Optimization Considering Geometric Minimum Thickness and Its Application to Electric Machine Design

Abstract

Evolutionary topology optimization often produces structures with excessively thin features that are difficult to manufacture. To address this issue, this paper presents a mesh-based geometric constraint, in which the minimum thickness of generated structures is explicitly evaluated. Although the proposed minimum-thickness constraint is non-differentiable, it can be directly incorporated into evolutionary topology optimization frameworks through constraint-handling techniques. The proposed method is applied to the topology optimization of an interior permanent magnet synchronous motor using the covariance matrix adaptation evolution strategy (CMA-ES). The numerical results show that the proposed minimum-thickness constraint successfully suppresses unmanufacturable thin features in the resulting rotor shapes. However, direct activation of the constraint from the initial iteration makes the problem constraint-dominant and degrades the convergence behavior of CMA-ES. Therefore, a two-stage constraint activation strategy is investigated, i.e., the constraint is deactivated in the first stage and activated in the second stage. The results show that the success ratio and objective function value are improved by the two-stage strategy compared with single-stage optimization. In addition, the CMA-ES step-size history provides a practical indicator for selecting the activation timing of the constraint. These findings show that the proposed minimum-thickness constraint and two-stage activation strategy are effective for obtaining resulting structures that do not contain thin features under prescribed thickness in evolutionary topology optimization.