求解布尔与非线性数值约束相混合的约束问题(英文)

Solving Boolean Combinations of Nonlinear Numerical Constraints

布尔与数值变量相混合的约束问题有着广泛的应用,但是当约束中的数值变量间存在非线性关系时该问题求解起来十分困难.目前的许多求解方法都是不完备的,即这些方法不能完全肯定某些包含非线性数值表达式的约束是否能够成立.针对这种问题,提出了将非线性数值约束转化为特殊形式的优化问题,采用全局优化算法对其进行求解的方法.已经实现了一个基于此方法的原型工具.实验结果表明,该方法能够有效地求解非线性混合约束问题,并且总能够得到该约束条件是否可满足的结果.

Constraints involving Boolean and numerical variables are used widely, but it is difficult to solve especially when they contain nonlinear numerical expressions. Many existing methods for solving such constraints are incomplete. A new method is presented in this paper to solve Boolean combinations of nonlinear numerical constraints completely. This method transforms the nonlinear constraints into a special-formed optimization problem to solve them. A prototype tool is implemented, and some experiments are made. The experimental results show that the method is effective.