改进罚函数分级遗传算法及其在桁架结构优化设计中的应用  

The hierarchical genetic algorithm with improved penalty function and its application in design optimization of truss structures

作　　者：皇甫尚乾 徐安[1] 

机构地区：[1]广州大学广州大学-淡江大学工程结构灾害与控制联合研究中心,广东广州510006

出　　处：《广州大学学报（自然科学版）》2017年第5期33-39,共7页Journal of Guangzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目(51478130;51208127);广州市科技计划资助项目(2014J4100141)

摘　　要：遗传算法在应用于结构优化设计时无需将约束条件显式表达,可以方便地处理各类位移和应力约束问题,因而在桁架结构的优化设计中得到广泛应用.基本遗传算法结合罚函数法在处理桁架结构优化设计等有约束优化设计问题时存在迭代代数过多、收敛不稳定等问题.文章提出根据种群中个体偏离约束限值的程度进行惩罚的罚函数法,能够较好地处理非可行解,扩大搜索的区域;通过分级、排序操作保证优秀个体优先被选择,良好的基因得以遗传;采用锦标赛选择方法根据个体的种群级别、约束偏离程度进行选择,在算法进化过程中较好地保持种群的多样性,避免陷入局部最优解陷阱.通过对2个经典的桁架结构案例进行算法可行性的验证,优化结果表明,相对于传统的遗传算法,采用文章的方法可以快速稳定地收敛到全局最优解,该方法可以推广到其他结构体系的优化设计中.Without constraints being explicitly formulated,the genetic algorithm( GA) is convenient in tackling the problems with displacement or stress constraints,and is widely applied in structural design optimization. The basic genetic algorithm combined with the penalty function method has some problems such as too many iterations,unstable convergence and so on. In this paper,an improved penalty function method is proposed. By moderately decreasing the punishment for the cases of constraints not being satisfied,this method reserves some unfeasible solutions that have potential to evolve to the optimal solution. Moreover,the proposed method ensures the better gene being inherited to the next generation by grading and ranking. The tournament selection method can maintain the diversity of the population,and ensure that the evolution does not fall into the trap of local optimization. The case studies of two truss structures show that compared to traditional GA method,the proposed method can converge stably with much higher possibility of reaching the optimal solution,and can be extended to the structural optimization of other structural systems.

关 键 词：遗传算法 结构优化设计 约束条件 罚函数 分级排序 

分 类 号：TU323[建筑科学—结构工程]