A specialized primal-dual interior point method for the plastic truss layout optimization
A specialized primal-dual interior point method for the plastic truss layout optimization
复制标题
用于塑料桁架布局优化的专用原对偶内点法
DOI：
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复制
发表时间：
2018
影响因子：
2.2
通讯作者：
J. Gondzio
中科院分区：
文献类型：
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作者：
A. G. Weldeyesus;J. Gondzio
本文研究塑性桁架布局优化中的线性规划问题。我们遵循地面结构的方法与节点之间的所有可能的连接。对于非常密集的地面结构，这样的问题的解决方案收敛到所谓的广义米歇尔桁架。显然，解决大节点密度的问题可能是计算上禁止的，由于所产生的巨大规模的优化问题。一种称为成员添加的技术，与列生成相对应，用于生成一系列较小的子问题，最终近似于原始问题。虽然这些子问题是显着小于完整的配方，他们仍然很大，需要计算效率的解决方案技术。在这篇文章中，我们提出了一个特殊用途的原始-对偶内点方法调整到这样的问题。该算法利用问题的代数结构，将算法产生的法方程组简化为更小的线性方程组。此外，这些系统使用迭代方法求解。最后，由于在执行少量成员添加迭代后子问题之间的高度相似性，该方法使用热启动策略，并在较少的内点迭代内实现收敛。数值实验证明了该方法的有效性和鲁棒性。
We are concerned with solving linear programming problems arising in the plastic truss layout optimization. We follow the ground structure approach with all possible connections between the nodal points. For very dense ground structures, the solutions of such problems converge to the so-called generalized Michell trusses. Clearly, solving the problems for large nodal densities can be computationally prohibitive due to the resulting huge size of the optimization problems. A technique called member adding that has correspondence to column generation is used to produce a sequence of smaller sub-problems that ultimately approximate the original problem. Although these sub-problems are significantly smaller than the full formulation, they still remain large and require computationally efficient solution techniques. In this article, we present a special purpose primal-dual interior point method tuned to such problems. It exploits the algebraic structure of the problems to reduce the normal equations originating from the algorithm to much smaller linear equation systems. Moreover, these systems are solved using iterative methods. Finally, due to high degree of similarity among the sub-problems after preforming few member adding iterations, the method uses a warm-start strategy and achieves convergence within fewer interior point iterations. The efficiency and robustness of the method are demonstrated with several numerical experiments.