一种新的全局排序高维多目标优化算法

针对传统高维多目标优化问题解决方法存在解集收敛性与解集分布均匀性缺陷的问题, 提出将全局排序方法与灰色关联分析两种方法相结合, 设计一种新的全局排序高维多目标优化算法. 通过设计最小函数值母序列和个体目标函数值子序列, 利用灰色关联分析法计算其关联度, 并结合个体目标适应度计算策略, 解决解集分布不均匀的问题. 该算法不仅可提高非支配个体的选择能力, 还具有良好的收敛性. 为测试该算法的性能, 选择3种经典多目标进化算法, 在标准测试函数集DTLZ{2,4,5,6}上进行对比实验. 实验结果表明, 该算法在解决高维多目标问题时, 其收敛性与解集分布均匀性均优于其他3种算法.

A Novel High-Dimensional Multi-objective Optimization Algorithm for Global Sorting

Aiming at the problem that the traditional methods for solving  high-dimensional multi-objective optimization problems had the defects of convergence and distribution uniformity of solution sets. We   proposed to design a novel high-dimensional multi-objective optimization algorithm based on the combination of global sorting method and  grey association analysis. By designing the parent sequence of minimum function values and the subsequence of individual objective function values, the grey association analysis method  was used to calculate  the association degree, and  combined with  the individual objective  fitness calculation strategy, the problem of uneven distribution of solution sets was solved. The algorithm could not only improve the selection ability of non-dominant individuals, but also had good convergence. In order to test the  performance of the algorithm, we chose three classical multi-objective evolution algorithms to carry out  comparative experiments on the standard test function set DTLZ {2,4,5,6}. Experimental results show that the proposed algorithm has better convergence and uniform distribution of solution set than  the other three algorithms in  solving the high-dimensional multi-objective problems.