This paper describes the evolutionary planning strategies for mobile robot to move along the streamlined collision-free paths in a known static environment. The Cognitive Map method is combined with genetic algorithm to derive the mobile robot optimal moving path towards its goal functions. In this study, multi-objectives genetic algorithm (MOGA) is utilized due to there are more than one objective need to be achieved while planning for the robot moving path. Goal-factor and obstacle-factor are the key parameters incorporated in the MOGA fitness functions. The simulation results showed that the hybrid Cognitive Map approach with MOGA is capable of navigating a robot situated among non-moving obstacles. The proposed hybrid method demonstrates good performance in planning and optimizing mobile robot moving path with stationary obstacles and goal.