In this work, it is described a gait multiobjective optimization system that allows to obtain fast but stable robot quadruped crawl gaits. We combine bio-inspired Central Patterns Generators (CPGs) and Genetic Algorithms (GA). A motion architecture based on CPGs oscillators is used to model the locomotion of the robot dog and a GA is used to search parameterizations of the CPGs parameters which minimize the body vibration, maximize the velocity and maximize the wide stability margin. In this problem, there are several conflicting objectives that leads to a multiobjective formulation that is solved using the Weighted Tchebycheff scalarization method. Several experimental results show the effectiveness of this proposed approach.