遗传算法求解可行域分离的结构优化问题

应用遗传算法求解了两类可行域分离的结构优化问题：局部屈曲约束的桁架拓扑优化问题和动力响应约束优化问题．对第一类问题，提出了新的数学表达式，适合于遗传算法求解．采用了改进的适应度函数及约束处理方法、约束凝聚选择、交叉操作改进和竞争最优保留，提高了遗传算法的效率和可靠性．算例说明，该方法能够克服可行域分离给传统优化算法带来的困难，有效地在多连通可行域中搜索全局最优解．

GENETIC ALGORITHM APPLIED TO STRUCTURAL OPTIMIZATION PROBLEMS WITH DISJOINTED FEASIBLE DOMAINS

Genetic algorithm (GA) is applied to solve two kinds of structural optimization problems with disjointed feasible domains, which include problems of topology optimization for truss structures subject to stress and local buckling constraints and problems with dynamic response constraints. A new mathematic formula is proposed to the first kind of problems to make it fit the solution of GA. Some improvements on GA are proposed, such as improvement on fitness function and constraints handling, surrogate reproduction, improvement on crossover operator and competitive elitist model. This way, the efficiency and reliability of GA are improved. The numerical examples given in the paper show that GA can overcome difficulties result from disjointed feasible domains to the traditional optimization algorithms, and effectively search the global optimum from multi-connected feasible domains.