A new convex quadratically-constrained quadratic programming (QCQP) model is proposed for modeling side-slopes volumes in the minimization of earthwork operations to compute the vertical alignment of a resource road while satisfying design and safety constraints. The new QCQP model is convex but nonlinear; it is compared to a state-of-the-art mixed integer linear programming (MILP) model. The QCQP model can be viewed as the limit of this MILP model. Numerical results show that for roads with less than 100 stations, the QCQP model has similar computation time to the MILP model. However, the QCQP model significantly outperforms the MILP model for other roads, in some cases finding a global optimum in minutes while the MILP model fails to find any solution in hours. The technique is directly applicable for resource roads and has potential for other types of road.

中文翻译：

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使用凸优化对垂直线形资源道路建设中的边坡进行建模

提出了一种新的凸二次约束二次规划 (QCQP) 模型，用于在最小化土方工程中对边坡体积进行建模，以计算资源道路的垂直线形，同时满足设计和安全约束。新的 QCQP 模型是凸的但非线性的；将其与最先进的混合整数线性规划 (MILP) 模型进行比较。QCQP模型可以看作是这个MILP模型的极限。数值结果表明，对于少于 100 个站点的道路，QCQP 模型的计算时间与 MILP 模型相似。然而，对于其他道路，QCQP 模型明显优于 MILP 模型，在某些情况下，它可以在几分钟内找到全局最优解，而 MILP 模型在数小时内无法找到任何解决方案。