基于遗传算法的抗震钢框架多目标优化设计

MULTIOBJECTIVE OPTIMIZATION DESIGN OF ASEISMIC STEEL FRAMES USING GENETIC ALGORITHM

考虑抗震钢框架优化问题具有多目标的特点,在遗传算法的基础上对抗震钢框架多目标优化设计进行了探讨．在无约束Pareto排序遗传算法的基础上,提出了一个简单、实用而又可以避免采用罚函数的全新排序方法,在此基础上形成了一种求解有约束多目标优化问题的Pareto遗传算法(CMOPGA),并给出了具体的算法流程图．以钢框架重量最轻和结构总动应变能最小为目标,基于相关的设计规范,给出了抗震钢框架多目标优化问题的一种合理提法．采用CMOPGA对一个两跨六层抗震钢框架实例进行了多目标优化设计,并提出了一个在Pareto最优解集的基础上选取妥协解的相对最小距离妥协原则．算例结果表明,采用CMOPGA求解抗震钢框架多目标优化问题是可行和有效的．

The optimal design of an aseismic steel frame is a multiobjective optimization problem. This paper studies the optimization method based on genetic algorithm （GA）. A new ranking approach without using penalty function methods is proposed to handle a constrained multiobjective optimization problem. This approach can deal with objective and constraint functions separately. Based on the new ranking approach, a GA-based optimization method for constrained multiobjective optimization problems （CMOPGA） is proposed, together with its flow chart. To minimize the weight of an aseismic steel frame and its total dynamic strain energy, a mathematical formulation of the multiobjective optimization design for the aseismic steel frame is established based on related codes. An example of a two-bay six-story aseismic steel frame is provided, and a compromise principle of relative minimum distance is proposed for designers to select the compromise solution from a Pareto optimal set in the absence of engineering experience. The optimal results show that CMOPGA is effective for the multiobjective optimization design of aseismic steel frames.