基于层次分析遗传算法的SRC框架梁优化设计

Optimization of SRC frame beam based on analytic hierarchy process genetic algorithm

文章将SRC框架梁的工程造价最小和正截面抗弯承载力最大定为优化目标,并对其进行无量纲化处理,使得多目标的优化问题转化为单目标优化问题。采用线性加权法构造评价函数,通过调整加权系数来改变2个优化目标在优化中的重要程度,通过算例给出合理取值,为组合结构的多目标优化问题提供参考。SRC构件中的型钢腹板及翼缘的高度、宽度等对梁的受力状态所做的贡献不同,通过引入层次分析法理论,在遗传算法的编码过程中对各变量进行权重赋值,使得对构件受力影响较大的单元赋予较大的权重,从而更好地发挥各组成部分的作用。

The minimum project cost and the maximum flexural capacity of steel reinforced concrete（SRC） frame beam are taken as the optimization objectives which are dimensionless,thus making the multiple-objective optimization problem become the single-objective one.The evaluation function is built by the linear weighted method and the importance degree of the two objectives in the optimization can be adjusted by weighting factors.The reasonable values are given by an example,which provides references for the multi-objective optimization problem of composite structure.Because of the different contributions of the depth and width of steel web and flange in SRC component to the stress state of the beam,the analytic hierarchy process is introduced to give each variable weight in the encoding process of genetic algorithms,which makes the important members have greater weight and thus makes use of the members effectively.