中文摘要：

电气工程中的设计问题常归结为多目标优化问题。对于目标函数超过三维的高维多目标优化设计，目前基于非控关系的多目标进化算法很难获得理想的优化结果。为此，人们提出了多重单目标Pareto采样（Muhiple Single Objective Pareto Sampling，MSOPS）算法。该算法结构简单，计算复杂度低。然而，研究表明，这种方法的最终优化结果往往缺乏多样性。为此，本文对MSOPS算法进行了改进研究，提出了目标矢量的拥挤操作，非均匀的目标矢量更新以及附加外部档案等改进措施以提高优化结果的多样性。通过与MSOPS-11、HypE以及NSGA．11算法在求解测试函数上的性能比较，证明了改进算法在Pareto解集上获得了更好的收敛性与多样性。最后，通过八木天线的优化设计验证了改进算法解决实际问题的有效性。

英文摘要：

Multi-objective optimization problems occur frequently in electrical engineering. However, existing nondominance based multi-objective optimization algorithms have difficulties in solving multi-objective problems with more than three objectives, termed many-objective optimization problems. To address this problem, MSOPS or MSOPS-I1 algorithm is proposed. This algorithm is simple in implementations and has low computational complexi- ty. However, investigations have revealed that the algorithm frequently losses the diversity of the population. In this point of view, an improved MSOPS is proposed by incorporating a crowding operation of target vectors, a non-uni- form target vector updating mechanism, and an external archive. Compared with MSOPS-II , HypE and NSGA-I1 in view of solving test functions, the proposed algorithm achieves a better trade-off between the convergence and the diversity towards the Pareto front. Finally, the optimization of a Yagi-Uda array validates the effectiveness of the proposed algorithm in the real-world applications.