数值与符号的耦合约束求解模型

Model for solving numerical and symbolic coupling constraints

采用约束关系依赖图(CRDG)表达耦合约束之间的依赖关系,从而建立数值与符号耦合约束模型。提出耦合约束的求解算法:对CRDG进行最小独立子图分解,对存在耦合约束的子图用"孪生变量法"进行一阶解耦,对没有耦合约束的子图用传统方法进行独立求解,求解之后再对孪生变量进行等效性验算。该耦合约束模型及其求解算法拓展了传统约束理论,实现了数学求解和推理求解有机地结合。

A constraint relation dependence graph （CRDG） is applied to express the dependence of coupling constraints, and establish the numerical and symbolic coupling constraints model. Then an algorithm for solving the coupling constraints is proposed, which contains the following steps： dividing the CRDG into minimal sub-graphs at first, breaking the coupling constraints with first order by twin-variables if the coupling constraints exist, solving the sub-graphs with no coupling constraints by traditional methods, and checking computations for twin-variables at last. The model and the algorithm presented here advances the traditional constraint theory and makes mathematical methods and inferential ones integrated.