An ever increasing use of digital video applications such as video telephony, broadcast and the storage of high and ultra-high definition videos has steered the development of video coding standards. The state of the art video coding standard is High Efficiency Video Coding (HEVC) or otherwise known as H.265. It promises to be 50 percent more efficient than the previous video coding standard H.264. Ultimately, H.265 provides significant improvement in compression at the expense of computational complexity. HEVC encoder is very complex and 50 percent of the encoding consists of Motion Estimation (ME). It uses a Test Zone (TZ) fast search algorithm for its motion estimation, which compares a block of pixels with a few selected blocks in the search region of a referenced frame. However, the encoding time is not suitable to meet the needs of real time video applications. So, there is a requirement to improve the search algorithm and to provide comparable results to TZ search to save a substantial amount of time. In our paper, we aim to study the effects of a meta-heuristic algorithm on motion estimation. One such suitable algorithm for this task is the Firefly Algorithm (FA). FA is inspired by the social behavior of fireflies and is generally used to solve optimization problems. Our results show that implementing FA for ME saves a considerable amount of time with a comparable encoding efficiency.