在差分进化算法框架下,结合抽象凸理论,提出一种局部抽象凸区域剖分差分进化算法(Local partition based differential evolution,LPDE).首先,通过对新个体的邻近个体构建分段线性下界支撑面,实现搜索区域的动态剖分;然后,利用区域剖分...在差分进化算法框架下,结合抽象凸理论,提出一种局部抽象凸区域剖分差分进化算法(Local partition based differential evolution,LPDE).首先,通过对新个体的邻近个体构建分段线性下界支撑面,实现搜索区域的动态剖分;然后,利用区域剖分特性逐步缩小搜索空间,同时根据下界估计信息指导种群更新,并筛选出较差个体;其次,借助下界支撑面的广义下降方向作局部增强,并根据进化信息对搜索区域进行二次剖分;最后,根据个体的局部邻域下降方向对部分较差个体作增强处理.数值实验结果表明了所提算法的有效性.展开更多
This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak ...This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak regions,the proposed optimizationmethod sequentially implements finite element analysis(FEA)in these regions.After standard FEA in the solid regions,the boundary displacement of the weak regions is constrained using the numerical solution of the solid regions as Dirichlet boundary conditions.This treatment can alleviate the negative effect of the material interpolation model of the topology optimization method in the weak regions,such as the condition number of the structural global stiffness matrix.For optimization,in which the forward problem requires nonlinear structural analysis,a linear solver can be applied in weak regions to avoid numerical singularities caused by the over-deformedmesh.To enhance the robustness of the proposedmethod,the nonmanifold point and island are identified and handled separately.The performance of the proposed method is verified by three 2D minimum compliance examples.展开更多
文摘在差分进化算法框架下,结合抽象凸理论,提出一种局部抽象凸区域剖分差分进化算法(Local partition based differential evolution,LPDE).首先,通过对新个体的邻近个体构建分段线性下界支撑面,实现搜索区域的动态剖分;然后,利用区域剖分特性逐步缩小搜索空间,同时根据下界估计信息指导种群更新,并筛选出较差个体;其次,借助下界支撑面的广义下降方向作局部增强,并根据进化信息对搜索区域进行二次剖分;最后,根据个体的局部邻域下降方向对部分较差个体作增强处理.数值实验结果表明了所提算法的有效性.
基金supported by the National Science Foundation of China (Grant No.51675506).
文摘This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak regions,the proposed optimizationmethod sequentially implements finite element analysis(FEA)in these regions.After standard FEA in the solid regions,the boundary displacement of the weak regions is constrained using the numerical solution of the solid regions as Dirichlet boundary conditions.This treatment can alleviate the negative effect of the material interpolation model of the topology optimization method in the weak regions,such as the condition number of the structural global stiffness matrix.For optimization,in which the forward problem requires nonlinear structural analysis,a linear solver can be applied in weak regions to avoid numerical singularities caused by the over-deformedmesh.To enhance the robustness of the proposedmethod,the nonmanifold point and island are identified and handled separately.The performance of the proposed method is verified by three 2D minimum compliance examples.
