FindingSymbolicandAllNumericalSolutionsforDesignOptimizationBasedonMonotonicityAnalysisandSolvingPol

A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.

基于单调性分析和GROEBNER基法的符号优化方法

本文提出了一种用Ｇｒｏｅｂｎｅｒ基法求基于单调性分析的优化设计问题符号形式最优解的方法。该法对优化问题的从单调性分析得出的子问题的等价方程组直接求解，根据该方程组的特点建立了方程项和变量的排序的法则，从而快速地得到以三角化Ｇｒｏｅｂｎｅｒ基形式表示的优化问题的符号形式的最优解。文中具体算例说明了方法的有效性和优点。

一种求解工程问题规律性知识的方法

设计规律性知识的获取是智能设计要解决的基本问题之一。本文根据工程问题符号表达的优化设计模型的特点，提出了一种求解符号优化模型的方法，利用该方法可求出一类问题的最优解的用非线性代数系统的标准基（Ｇｒｏｅｂｎｅｒ基）来描述的解析表达式，从而得出有规律性的知识和指导设计。