桁架拓扑优化的多点逼近遗传算法

提出一种基于多点逼近函数和遗传算法的桁架拓扑优化方法。该方法建立了包含连续尺寸和离散拓扑两类变量的优化模型，并通过构造多点逼近函数建立了结构优化问题的第一级序列显式近似，然后采用分层优化方法：在外层对拓扑变量采用遗传算法进行优化；在内层对尺寸变量通过可由对偶法求解的第二级序列近似问题进行优化。几个经典的桁架拓扑优化算例表明该方法能以较少的结构分析次数获得比较理想的概率意义上的最优解。

Truss topology optimization by using multi-point approximation and GA

A new method for truss topology optimization based on the multi|point approximate function and the genetic algorithm (GA) is proposed. In the work, an optimization model including continuously cross|sectional size variables and discrete topology variables is created, and then a series of first level approximate problems of the created structural optimization problem are constructed using the multi|point approximate function. To solve the first|level approximate problems with mixed|variables, a layered optimization strategy is introduced. The topology variables of the trusses are optimized through GA in the external layer, and the cross|sectional areas of bars are optimized in the internal layer through a series of second level approximate problems that can be solved by the dual method. The required structural analyses for truss topology optimization can be dramatically decreased as GA is only used to solve the approximate problems in the external layer where no structural analysis is needed. On the other hand, a relatively small number of species is taken in GA as the design variables of cross|sectional areas are determined in internal layer. The results of the classical examples of truss topology optimization show that the proposed method can reach the optimum solutions after an extremely few structural analyses.