The High Efficiency Video Coding (HEVC) standard provides a number of encoding tools with different encoding quality and complexity tradeoffs [1]. Although numerous studies have been conducted on the complexity-compression trade-off of HEVC encoding tools [2], [4]-[11], and based on such studies, many algorithms have been proposed to reduce the complexity of various HEVC encoding modules and tasks, in most cases, these algorithms work in a statistical sense, i.e. best efforts are made to select a sensible subset of HEVC encoding tools that are expected to achieve good rate distortion (RD) results for the current input video sequence. Even though such algorithms have received wide applications in HEVC encoders for real time applications [3], it remains a challenge to achieve the optimal RD HEVC encoding while fully utilizing the available computational resources. In this paper, we propose a framework that addresses the issue of optimal HEVC encoding under an overall complexity constraint. Experimental results show that the proposed system can accurately achieve pre-defined target computational complexity while achieving RD performance superior to other encoders with similar complexity.