Test points selection for integer-coded fault wise table is a discrete optimization problem. The global minimum set of test points can only be guaranteed by an exhaustive search which is compu-tationally expensive. In this paper, this problem is formulated as a heuristic depth-first graph search problem at first. The graph node expanding method and rules are given. Then, rollout strategies are applied, which can be combined with the heuristic graph search algorithms, in a computationally more efficient manner than the optimal strategies, to obtain solutions superior to those using the greedy heuristic algorithms. The proposed roilout-based test points selection algorithm is illustrated and tested using an analog circuit and a set of simulated integer-coded fault wise tables. Computa-tional results are shown, which suggest that the rollout strategy policies are significantly better than other strategies.