Two evolutionary gait generation methods for Cartesian and Joint coordinates space are compared to develop a fast locomotion for quadruped robots. GA(Genetic Algorithm) based approaches seek to optimize a pre-selected set of parameters for the locus of paw and initial position in cartesian coordinates space. GP(Genetic Programming) based technique generate few joint trajectories using symbolic regression in joint coordinates space as a form of polynomials. Optimization for two proposed methods are executed using Webots simulation for the quadruped robot which is built by Bioloid. Furthermore, simulation results for two proposed methods are analysed in terms of different coordinate spaces.