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.