We propose an electron beam (EB) shot minimization method for character projection electron beam direct writing (CP-EBDW) targeting metal layer patterns based on Integer Linear Programming (ILP). We have evaluated the proposed method with a commercial tool and demonstrated 20% shot reduction. We have also demonstrated that the runtime of the proposed EB shot minimization method grows exponentially against the number of matches. For this reason, we have suggested heuristic solutions to find the number of EB shots within a reasonable amount of time by means of segmentation of layout, limitation of runtime and setting of "relative tolerance gap parameter" in 0-1 ILP. The heuristic solutions have been proved to be effective when compared with the commercial tool for the same layout.