Alternating Direction Method of Multipliers as Simple Heuristic for Topology Optimization of a Truss With Uniformed Member Cross Sections
Alternating Direction Method of Multipliers as Simple Heuristic for Topology Optimization of a Truss With Uniformed Member Cross Sections
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DOI：
10.1115/1.4041174
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发表时间：
2018-10
影响因子：
3.3
通讯作者：
Y. Kanno
中科院分区：
文献类型：
--
作者：
Y. Kanno
本文提出了一种简单有效的启发式算法，用于桁架结构的拓扑优化，该算法以桁架的所有杆件具有公共截面积为约束条件。所提出的方法包括多个重新启动的交替方向的乘法器（ADMM）与随机初始点。结果表明，ADMM的每次迭代可以很容易地进行。在数值实验中，所提出的启发式的效率与现有的全局优化方法的基础上的混合整数二阶锥规划（MISOCP）进行了比较。结果表明，即使是大规模的问题的情况下，全局优化方法不能解决在实际可接受的计算成本，所提出的方法往往可以找到一个可行的解决方案，具有相当不错的目标值在适度的计算时间。
This paper presents a simple and effective heuristic for topology optimization of a truss under the constraint that all the members of the truss have the common cross-sectional area. The proposed method consists of multiple restarts of the alternating direction method of multipliers (ADMM) with random initial points. It is shown that each iteration of the ADMM can be carried out very easily. In the numerical experiments, the efficiency of the proposed heuristic is compared with the existing global optimization method based on the mixed-integer second-order cone programming (MISOCP). It is shown that even for large-scale problem instances that the global optimization method cannot solve within practically acceptable computational cost, the proposed method can often find a feasible solution having a fairly good objective value within moderate computational time.