中文摘要：

在电磁装置设计中，通常需要同时优化几个相互冲突的目标函数。在传统的优化方法中，一般首先采用标量化技术将多目标函数转化成单目标函数。然后求解。因此需要预先设定不同目标函数的优先级或权因子，而这种方法通常每次只能搜索到一个Pareto解，不能得到完整的Pareto曲面。有鉴于此，本文提出了多目标优化设计的一种改进矢量进化算法，以实现通过一次搜索即可得到平滑、完整的Pareto曲线的目标。典型数学函数和无芯螺线管线圈优化设计问题的实例计算结果，验证了本文算法的有效性和正确性。

英文摘要：

The design of an electromagnetic device usually involves the simultaneous optimization of several incommensurable criteria, and is traditionally solved by using some scalar techniques. Due to the predefined weighting coefficients, such treatment has the disadvantage of missing concave portions of the trade-off curve. To give enough number of trade-off solutions of this kind of problems, an improved evolutionary algorithm is proposed to obtain directly the Pareto optimal solutions of multi-objective designs of electromagnetic devices. The simulation resuits on solving a mathematical function and a prototype problem reveal that the proposed method is effective in sampling the entire Pareto-optimal front and distributing the generated solutions over the trade-off surface.