Abstract

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.

中文翻译：

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使用混合整数线性规划并在运行时生成约束的简化桁架布局优化

摘要

采用地面结构方法的传统桁架布局优化通常会生成过于复杂而无法在实践中制作的布局。为了解决这个问题，可以使用混合整数线性编程来强制执行可构建性约束，从而简化桁架形式。可以对结构中的接缝数量和/或连接的构件之间的最小角度施加限制，其中要考虑由成对的构件的交叉引起的接缝。但是，在布局优化中，“跨接点”产生的约束数量随着问题的大小以及计算费用的增加而迅速增加。为了解决这个问题，这里仅根据需要动态生成交叉约束并在运行时将其添加（所谓的惰性约束）。观察到超过20倍的加速，同时确保解决方案质量没有损失。此外，显示了布局优化步骤的结果可为非线性几何优化步骤提供合适的起点，从而能够获得与文献解决方案一致的结果。还表明，对称问题可能没有对称的最优​​解，并且可以找到多个不同且均等的最优解。