微分演化算法在桁架形状优化中的应用

Truss Structure Shape Optimization with Differential Evolution Algorithm

为了获得全局最优和解决具有应力约束、几何约束以及局部稳定性约束的桁架形状优化问题中2类不同设计变量耦合给优化带来的困难,将1种新型智能优化算法——微分演化(Differential Evolution,DE)应用于桁架结构的形状优化问题中。给出了考虑节点坐标和截面面积两类不同性质的设计变量的桁架结构优化的数学模型,并对几个经典的桁架结构进行优化,将所得结果与其他优化算法结果进行了比较。数值结果表明了DE算法具有良好的收敛性和稳定性,可以有效地进行桁架结构的形状优化设计。

Differential Evolution （DE） was introduced to get the global optimum and overcome the difficulties encountered by coupling two types of design variables in the shape optimization of truss structures with stress, geometry, and local stability constraints. The basic principle of DE algorithm was presented in detail first, and then mathematical model for shape optimization of truss structures was presented, in which two types of design variables, such as the node coordinates and section areas, were considered simultaneously. Several classical problems were solved with DE algorithm, and the results were compared with those using the other optimization methods. It was shown that DE algorithm had good convergence and stability and could be applied for shape optimization of truss structures effectively.