切削过程优化问题的边界极值解法

Boundary Value Comparison Method for Cutting Process Optimization Problem

本文首先讨论切削过程优化问题目标函数的极值问题,并完成切削过程优化问题目标函数无极值的证明,给出了在刀具耐用度满足泰勒公式条件下的特例证明。在此基础上提出了该类问题的边界极值解法,把两维空间内的求极值问题转化为一维问题求解,大大减小了计算量。本文还讨论了边界极值求解方法在计算机实现过程中若干问题,包括约束分类方法、约束边界的组合方法、约束边界在计算机内的表达方式等问题。本文最后给出了一个应用边界相比求解的实际例子,并与采用传统的数学规划求解方法进行了比较。结果表明,两者计算结果一致,采用边界极值法的计算速度比数学规划方法提高了一个数量级。

In this paper the objective function of Cutting Process Optimization Problem is proved to be a function without extreme values. On this basis, a boundary value comparison method is proposed for porblem solving. With the new method, the original two dimen-tional problem is turned into a one dimentional problem and consequently the computation al complexity is greatly reduced. In the paper, the procedure of application programming of the boundary value comparison method on a computer and several relevant problems, including constraint classification, constraint boundary combination, etc. are discussed. Finaly, an example of the application of the method is given. The results show that the computational time may be reduced more than 10 times as compared with that of the commonly used mathematical programming method.