Planning gaits for legged robots is an important and challenging task that requires optimizing parameters in a highly irregular and multidimensional space. Two evolutionary gait generation techniques using GA (Genetic Algorithm), GP (genetic programming) based on Cartesian and joint space are compared to develop fast locomotion for a quadruped robot. Optimizations for two proposed methods are executed and analyzed using a Webots simulation and real experiment of the quadruped robot. The performance and motion features of GA-, GP-based methods are compared and analyzed.