The optimization design of a tri-polar parallel gear pump is carried out by taking the minimum volume of the pump body as the objective function.In the mathematical model,the gear parameters such as modulus,tooth numbers,and thickness are taken as design variables,and the constraint condition is that the tri-polar parallel gear pump can meet the prescribed performance requirements.In the objective function,the volume of pump is replaced by the total volume of 4 mounting holes of addendum circles,which accurately reflects the volume of pump.In the process of solving optimization mathematical model,a new three-dimensional step-by-step search algorithm is proposed according to the characteristic that the formula of the objective function is very complex and the modulus,tooth numbers of gears are discrete variables.Thus an optimization algorithm for the tri-polar parallel gear pump designing is provided,and through an example,the feasibility and effectiveness of the algorithm are verified.