采用凝聚函数求解变量可分离规划

为了基于凝聚函数(K-S函数)的特性,将工程问题中的多约束、多目标凝聚为一个近似的、逼近精度参数ρ控制来求解原问题,分析了变量可分离目标函数∑ni=1fi(xi)与KS(ρ,x),并构造L(x,λ)函数,根据鞍点条件建立方程,并对该方程进行一阶Taylor公式展开,求解出拉格朗日乘子的近似解λ*及设计变量的近似解x*i.通过Matlab数学语言来编制求解可分离变量的求解程序,计算了代表性典型变量可分离算例.结果表明:该解法能够高效、快速地完成计算,收敛精度稳定.

Solution of Variable Separable Programming

To reduce a mass of calculations with solving multiple constraints for variable programming,The variable separable programming was transformed into a problem with single constraint by using coherency function. The engineering problem of multiple constraints and multi-objective condensed into a approximation and control by approximation precision parameter,to solve the original problem and analyses the variable separable objective function ∑ni = 1fi( xi) and KS( ρ,x) constructed as L( x,λ)functions. Its saddle point condition is obtained in terms of the Lagrange multiplier method. Then by mean of utilizing Taylor formula,the condition is expanded to an approximate equation. Some numerical experiments show that the proposed algorithm is feasible.