单亲遗传算法在有限元网格节点编号优化问题中的应用

Optimal Scheme of Node Labels in Finite Element Mesh by Partheno-genetic Algorithm

单亲遗传算法(PGA)是一种序号编码遗传算法。它具有遗传操作简单、不要求初始群体的广泛多样性、不存在"早熟收敛"现象等特点,非常适合于求解组合优化问题。在有限元分析中,网格节点编号顺序决定了有限元整体刚度矩阵中非零数据的位置,对矩阵的带宽有直接的影响。为了减小在实际计算时的存储量、缩短计算时间,将单亲遗传算法引入有限元网格节点编号优化问题,减小了有限元整体刚度矩阵的半带宽;给出了优化计算过程;与已有优化结果进行了对比,实例表明该算法是有效的,具有通用性。

Partheno-genetic algorithm（PGA）,in which the genetic operation is simpler and initial population need not to be varied and there is not immature convergence,is a genetic algorithm using ordinal strings and is very fit for solving combinatorial optimum problem.In finite element analysis,the sequence of mesh node labels determines the location of nonzero data in the global stiffness matrix,and affects the bandwidth of matrix directly.In order to reduce the computational store and shorting the computational time,partheno-genetic algorithm is used to optimize the sequence of mesh node labels.In this algorithm,the semi-bandwidth is decreased in global stiffness matrix and the calculating steps are given.The examples indicate that the algorithm is valid and universal.