A low profile high directivity antenna is designed to operate at 5.9 GHz for Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communications to ensure connectivity in different propagation channels. Patch antennas are still an ongoing topic of interest due to their advantages: low profile, low cost, and ease of fabrication. One disadvantage of the patch antenna is low directivity which results in low range performance. In this paper, we introduce an efficient and novel way to improve the directivity of patch antenna using topology optimization and design of experiments (DoE). Numerical simulations are done using Method of Moments (MoM) technique in the commercially available tool, FEKO. We use global response surface method (GRSM) for double objectives topology optimization. Numerical results show a promising use of topology optimization and DoE techniques for the systematic design of high directivity of low profile single element patch antennas. The optimized directivity is 10.4 dBi, which is 3 dB higher than the directivity of the original patch antenna.