In this paper, we present the comparison of different optimization algorithms that are used to optimize the parameters of a simulated legged robotic platform. We compare the results obtained by applying different algorithms on the same model and show the relative advantages and disadvantages of these algorithms. The tested algorithms are Particle Swarm Optimization, Binary Coded Genetic Algorithm, Broyden-Fletcher-Goldfrab-Shannon Algorithm and Method of Zoutendijk. We showed that the globally optimal parameter set reduces the total dissipated energy approximately 50% with respect to the reference paremeter set in the literature. The implemented optimization methods can also be applied to other legged platforms to obtain efficient systems without affecting the performance and the stability.