中文摘要：

现代产品几何技术规范（GPS）提出的操作与操作算子技术,为实现几何产品检验/认证过程的数字化和规范化评定提供了必要的技术基础。研究分析了垂直度误差和轴线对端面垂直度误差评定过程中操作算子的构成,并建立了基于最小区域的各拟合操作的数学模型和优化目标函数。介绍了一种基于实数编码的遗传算法来解决误差评定中的目标优化问题,阐述了算法的基本思想和步骤。通过实例介绍了基于实数编码的遗传算法的轴线对端面垂直度误差评定过程。结果表明：该过程规范、有效、可操作性强。

英文摘要：

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.