Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints
Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints
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DOI：
10.1007/s00158-019-02449-7
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发表时间：
2020-05-01
影响因子：
3.9
通讯作者：
Gilbert, M.
中科院分区：
文献类型：
--
作者：
Fairclough, H.;Gilbert, M.
传统的桁架布局优化采用地面结构的方法往往会产生布局过于复杂，在实践中制造。为了解决这个问题，可以使用混合整数线性规划来强制执行可建造性约束，从而简化桁架形式。可以对结构中的接头数量和/或连接构件之间的最小角度施加限制，其中考虑了由成对构件交叉产生的接头。然而，在布局优化中，由“交叉接头”引起的约束的数量随着问题的大小而迅速增加，沿着计算费用。为了解决这个问题，交叉约束在这里动态生成，并仅在运行时根据需要添加（所谓的懒惰约束）;观察到超过20倍的加速，同时确保没有解决方案质量的损失。此外，布局优化步骤的结果被示出为非线性几何优化步骤提供合适的起点，使得能够获得与文献解决方案一致的结果。它还表明，对称问题可能没有对称的最优解，并可以找到多个不同的和同样的最优解。
Traditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from 'crossover joints' increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.