利用类圆映射优化PCA算法的高维多目标可视化方法研究

Research on high-dimensional multi-objective visualization method of PCA algorithm optimized by circle like mapping

为避免现有的高维多目标可视化方法无法有效保持解集的Pareto支配关系和前沿密度分布关系,在基于主成分分析法基础上引入类圆决策空间算法,将多目标按相关性排列在单位圆圆弧上,然后根据适应度函数值将解集映射为类圆空间内的一个多边形,通过映射多边形的几何中心和面积对多目标优化问题解集进行构建,最终利用BASes以及拓展函数进行对比实验。实验结果表明类圆映射可视化法在保留原始解集Pareto支配关系和密度分配关系基础上,还能够有效反应解集Pareto前沿密度分布。

For avoiding the existing high dimensional multi-objective visualization methods can not effectively maintain the Pareto dominance relation and the frontier density distribution relation,it introduces the algorithm of circle-like decision-making space based on principal component analysis,arranges the multi-objectives on the unit circle arc according to correlation,then maps the solution set into a polygon in the circle-like space according to the fitness function value,and finally constructs the multi-objective optimization problem set by mapping the geometric center and area of the polygon.Finally,bases and extension functions are used.Compared with experiments,the results show that the circle-like mapping visualization method can also effectively reflect the Pareto front density distribution based on preserving the dominant and density-allocation relations of the original solution set.