高维多目标优化中基于稀疏特征选择的目标降维方法

目标降维算法通过去除冗余的目标达到简化问题规模的目的,为求解高维多目标优化问题提供了一种新的思路和方法.近似解集的几何结构特征和Pareto占优关系从不同侧面反映了多目标优化问题的内在结构特性,而现有算法仅利用其中一种特征分析目标之间的关系,具有较大局限性.本文提出基于稀疏特征选择的目标降维方法,该方法利用近似解集的几何结构特征构建稀疏回归模型,求解高维目标空间映射为低维目标子空间的稀疏投影矩阵,依据此矩阵度量目标的重要性,并利用Pareto占优关系改变程度选择满足误差阈值的目标子集,实现目标降维.通过与其他已有目标降维算法比较,实验结果表明本文提出的降维算法具有较高的准确性,并且受近似解集质量的影响较小.

Objective Reduction with Sparse Feature Selection for Many Objective Optimization Problem

Objective reduction approach is an effective means for many-objective optimization problems by eliminating redundant objectives with respect to the original objective set.The geometrical structural characteristics and Pareto-dominance relation of approximation set can represent the characteristics of the original problem in different aspects.This paper proposed a new algorithm based on sparse feature selection.It used the geometrical structural characteristics to construct a graph representing the original problem.A sparse projection matrix mapping the high dimensional data into low dimensional space was then learned by a sparse regression model,which was used to measure the importance of each objective.The change of Pareto-dominance relation induced by reduced set was also adopted to identify a minimum set with error not exceeding threshold value.By comparing with other algorithms,the experimental results show that the accuracy of the new algorithm outperforms other dimension reduction techniques,and is scarcely effected by the quality of approximation set.