Operation and operator technologies introduced by geometrical product specification（GPS） provide the necessary knowledge basis for digitization and standardization of verification process of geometrical products.The operator formation for axis error evaluation in perpendicularity to end surface is analyzed

and mathematical models and the optimal target functions of every fitting operation based on the minimum-zone is presented.A genetic algorithm based real coding is introduced.Basic idea and process of the algorithm are described in detail.realizes the evaluation process of the axis line error in perpendicularity to end surface based on real-coding genetic algorithm through an example.The experimental results indicate that the proposed process is canonical

effective and feasible.