In the context of the optimization of rotating electric machines, many different objective functions are of interest and considering this during the optimization is of crucial importance. While evolutionary algorithms can provide a Pareto front straightforwardly and are widely used in this context, derivative-based optimization algorithms can be computationally more efficient. In this case, a Pareto front can be obtained by performing several optimization runs with different weights. In this work, we focus on a free-form shape optimization approach allowing for arbitrary motor geometries. In particular, we propose a way to efficiently obtain Pareto-optimal points by moving along to the Pareto front exploiting a homotopy method based on second order shape derivatives.

翻译：在旋转电机优化问题中，多种目标函数具有实际研究价值，在优化过程中考虑这些目标至关重要。虽然进化算法可直接生成帕累托前沿并在该领域得到广泛应用，但基于梯度的优化算法在计算效率上更具优势。针对后者情况，可通过设置不同权重进行多次优化运行来获得帕累托前沿。本研究聚焦于允许任意几何结构的自由形状优化方法，特别提出一种基于二阶形状导数的同伦方法，通过沿帕累托前沿移动实现帕累托最优解的高效获取。