Abstract: In this paper, under the approximate condition of graphic topology, we first introduce the essential efficient solutions and the weakly essential efficient solutions of the optimization problem for upper semi-continuity maps with set-value. Second, by using the usco researching approach of generic stability, with the trembles of domain and map, the upper semi-continuity and compact properties of the weakly efficient solutions maps of this optimization problem are proved, under the approximate condition of graphic topology, and then it is generic lower semi-continuous, that is to say, in the sense of Baire Category, weakly efficient solutions maps of “most” this optimization problems are generic stability(i.e. essential) under the approximate condition of graphic topology. Last, we prove a necessary and sufficient condition of upper semi-continuity of the efficient solutions maps of this optimization problem.

Key words: upper(lower)-semi-continuity, (weakly) efficient solution, essential (weakly) efficient solution, generic continuity