中文摘要：

遗传算法已经在多目标优化问题中得到了广泛应用及深入研究，NSGA-II是求解多目标优化问题的代表算法之一，其中聚集距离在收敛性和分布均匀性上均起到了重要作用, 但算法没有充分考虑微观的个体本身和宏观的种群整体的作用。为了能更合理的估计区域密度，使所求解集更好更均匀地收敛于Pareto 最优边界，本文基于均匀聚集区间和基尼权重构造了一种均匀聚集距离算子，并基于该算子提出了一种改进的NSGA-II算法。最后，通过对6个标准多目标测试问题的实验验证了算法的有效性。

英文摘要：

With the wide application and further study of the genetic algorithm in multi-objective optimization problems, the NSGA-Ⅱ has been one of the representative evolutionary algorithms for multi- objective optimization problems. Crowding distance in the NSGA- Ⅱ plays an important role in convergence and uniform distribution of the solutions, but the NSGA-Ⅱ does not fully take the effect of each individual and the whole population into consideration. To estimate the region density more reasonably so as to make the solution set more uniformly converge to the Pareto optimal front, we design a uniformly crowding distance operator based on the uniformly crowding range and Gini weight, and propose an improved NSGA- Ⅱ algorithm. Finally, the effectiveness of the proposed algorithm is verified by experiments on six multi- objective optimization test functions.