离散变量结构优化设计的连续化方法

Continuous Approach to Discrete Structural Optimization

把离散变量结构优化设计问题转化为一般的0-1规划问题,进一步把该问题转化为一个带有互补约束的优化问题,利用NCP函数,最终得到待以求解的连续优化问题。离散优化到基于NCP函数的连续优化变换在理论上是等价的,可以利用普通的数学规划方法实施求解。数值算例的计算结果验证了该连续化方法的可行性与有效性。

A continuous approach to solving discrete optimum design is proposed,where the discrete variables are represented by the linear combination of components of the discrete set with 0-1 coefficients as new variables,then are replaced with complementary conditions to convert the original problem into a equivalent continuous optimization problem.In the implementation,each complementary condition is reduced to an equation by means of so-called NCP function to solve,the discrete structural optimization problems with standard optimization software.The numerical results verify the validity and efficiency of this approach.