【摘要】 采用遗传算法求解具有奇异最优解现象的桁架结构拓扑优化问题。在桁架结构拓扑优化的内力约束ε-放松列式基础上,根据遗传算法特点通过引入拓扑变量提出一种新的优化模型列式。在遗传算法中改进了适应度函数及约束处理方法、选择和交叉操作等,提高了求解算法的效率和可靠性。数值算例以及两种列式的对比分析表明,本文改进的遗传算法和新提出的优化模型列式,能够得到拓扑优化问题的全局最优解。更多还原

【Abstract】 The Genetic Algorithm (GA) is applied to solve the topological design optimization problems of truss structures with singular optima. Two kinds of problem formulation are proposed for solving this kind of problem. One is the ε-relaxation formulation in which the stress constraints are first replaced with internal force constraints and then relaxed by a small parameter ε. In this way, the behaviour constraints are improved to be continuous and the feasible domain is made wider, which in turn enhance the possibility of finding the singular optima. In the second proposed problem formulation, discrete 0~1 valued topological design variables are introduced directly for each bar to represent its existence. With the use of these topological design variables, we can give a consistent description of the stress constraints in problem formulation, which is very important for the solution of singular problems. Optimization problems under different formulations are solved by GA method with improved modification of fitness function, constraint handling strategy and the reproduction and crossover operators. Numerical examples show that singular optimization problems of truss structures can be solved effectively with the proposed problem formulation and the improved GA algorithm.更多还原