ID 原文 译文
18135 该方法将初始化的N个个体看做一个N行D列的矩阵，然后对矩阵的列向量求最大线性无关组，从而减少矩阵的冗余度，达到降低维度的目的。 In this method, the initialized N individuals are regarded asa matrix of N rows and D columns, and then the maximum linear independent group is calculated for thecolumn vector of the matrix, so as to reduce the redundancy of the matrix and reduce the dimension.
18136 在此过程中，由于剩余的任意列向量组均可由最大线性无关组表示，所以通过对最大线性无关组施加一个随机系数来维持种群的多样性和完整性。 In thisprocess, since any remaining column vector group can be represented by the maximum linearly independentgroup, a random coefficient is applied to the maximum linearly independent group to maintain the diversityand integrity of the population.
18137 将该文所提策略分别应用到标准遗传算法(GA)和粒子群优化算法(PSO)中，并与标准粒子群算法、遗传算法以及目前主流的对维数进行优化的4个算法对比， The standard genetic algorithm and particle swarm optimization using NDR strategy compare with Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and the four mainstream algorithms for dimension optimization.
18138 实验证明，改进的算法对大部分标准测试函数都具有很强的全局收敛能力，其寻优能力超过了上述6个算法，同时改进后的算法在运行时间上远优于对比算法。 Experiments show that the improved algorithm has strong globalconvergence ability and better time complexity for most standard test functions.
18139 近年来，超多目标优化问题(MaOPs)成为了进化计算领域的研究热点。 In recent year, the Many-objective Optimization Problems (MaOPs) have become an increasingly hotresearch area in evolutionary computation.
18140 然而，在处理各种优化问题中，如何有效地平衡收敛性和多样性仍是一个难题。 However, it is still a difficult problem to achieve a good balancebetween convergence and diversity on solving various kinds of MaOPs.
18141 为了解决上述的问题，该文提出了一种基于分解和支配关系的超多目标进化算法(DdrEA)。 To alleviate this issue mentioned above,a Decomposition and dominance relation based many-objective Evolutionary Algorithm(DdrEA) is proposed in this paper.
18142 首先利用权重向量把整个种群分解为一组子种群，这些子种群将进行协同优化； Firstly, the population is decomposed into numbers of sub-populations by using a set of uniformweight vectors, in which they are optimized in a cooperative manner.
18143 然后利用角度和角度支配关系计算子种群内每个解的值； Then, the fitness value of solution in eachsub-population is calculated by angle dominance relation and angle.
18144 最后根据适应度值进行精英选择，即在每个子空间内选取适应度值最小的解作为精英解进入下一代。 Finally, elite selection strategy is performedaccording to its corresponding fitness value. That is, in each subspace, the solution with the smallest fitnessvalue is selected as the elite solution to enter the next generation.