The Gerotor pumps are the most important positive displacement pumps which have a vast amount of application in industries. These pumps are specially used in the most internal combustion engines. Considering the applications of these pumps, the optimization of them is more needed. In this project, first the geometric equations of the Epitrochoid profile have been derived by using the envelope theory, and the volumetric and dynamic characteristics have been introduced according to the geometry of the rotors profile. The optimization problem cost functions included flow ripple, wear rate proportional factor, area efficiency and influence area.The non-undercutting and pump volumetric displacement are the main constraints and have been formulated too. In order to have general optimum solution and reduce number of design variables, all the design variables, except number of outer rotor teeth, have normalized to the non-dimensional variables by using the outer rotor lobe center radius. Using the normalized design variables causes the non-dimensional cost functions too. By attention to integer variables and disconnected cost functions, two mixed integer non-linear optimization programming (MINLP) methods have been used to optimize the single-objective optimization problem. Considering more than one cost function, it is necessary to change multi-objective optimization problem to single-objective one. The Global Criterion Method has been used to change multi-objective optimization to single-objective optimization problem. The optimization programming has been implemented for several values of non-dimensional displacement. First the single-objective optimization problems have been solved for each case and the optimum point, optimum value, optimum profile, flow rate curve and wear rate proportional factor curve have been resulted. On the other hand, the influence of varied parameter such as number of rotors teeth and the value of non-dimensional displacement have been surveyed on each of the cost functions and the combinations of them. Finally for better comparison, several sample pumps which reported in literatures have been optimized by use of varied combination of cost functions. The results show significant improvement by considering only one cost function but in multi-objective optimization problems the flow ripple cost function did not improve in some cases.Other cost functions that are mentioned above have been improved in all cases. Also the optimum results which are obtained by both optimization methods are in agreement with each other which show the global optimization of the problems. Keywords: Gerotor Pump, Epitrochoid, Flow Ripple, WRPF, Area Efficiency, Influence Area, Envelope Theory, Mixed Integer Optimization