In this paper, we illustrate that the traditional Ndetect ATPG is unoptimized in terms of the size of the generated pattern set. The optimization problem is formulated as a minimum covering problem. Integer Linear Programming (ILP) is applied to obtain an Ndetection ATPG pattern set with the minimum number of patterns. A heuristic method is also proposed to obtain sub-optimal solutions efficiently. Experimental results demonstrate that by using the proposed method, the number of N-detection patterns can be reduced by about 18% for N=3 and about 13% for N=5 without compromising N-detection objective.