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Drone routing with energy function: Formulation and exact algorithm
Transportation Research Part B: Methodological ( IF 5.8 ) Pub Date : 2020-07-11 , DOI: 10.1016/j.trb.2020.06.011
Chun Cheng , Yossiri Adulyasak , Louis-Martin Rousseau

Drone delivery is known as a potential contributor in improving efficiency and alleviating last-mile delivery problems. For this reason, drone routing and scheduling has become a highly active area of research in recent years. Unlike the vehicle routing problem, however, designing drones’ routes is challenging due to multiple operational characteristics including multi-trip operations, recharge planning, and energy consumption calculation. To fill some important gaps in the literature, this paper solves a multi-trip drone routing problem, where drones’ energy consumption is modeled as a nonlinear function of payload and travel distance. We propose adding logical cuts and subgradient cuts in the solution process to tackle the more complex nonlinear (convex) energy function, instead of using the linear approximation method as in the literature, which can fail to detect infeasible routes due to excess energy consumption. We use a 2-index formulation to model the problem and develop a branch-and-cut algorithm for the formulation. Benchmark instances are first generated for this problem. Numerical tests indicate that even though the original model is nonlinear, the proposed approach can solve large problems to optimality. In addition, in multiple instances, the linear approximation model yields routes that under the nonlinear energy model would be energy infeasible. Use of a linear approximation for drone energy leads to differences in energy consumption of about 9% on average compared to the nonlinear energy model.



中文翻译:

具有能量功能的无人机路由:公式化和精确算法

无人机交付被认为是提高效率和缓解最后一英里交付问题的潜在推动者。因此,无人机路由和调度已成为近年来研究的高度活跃的领域。但是,与车辆路径问题不同,由于多种运行特性(包括多程运行,补给计划和能耗计算),设计无人机的路径具有挑战性。为了填补文献中的一些重要空白,本文解决了多程无人机路由问题,其中无人机的能耗被建模为有效载荷和行进距离的非线性函数。我们建议在求解过程中添加逻辑割和次梯度割以解决更复杂的非线性(凸)能量函数,而不是像文献中那样使用线性逼近方法,由于过多的能耗,可能无法检测到不可行的路线。我们使用2指标公式化对问题进行建模,并为该公式开发分支剪切算法。首先针对此问题生成基准实例。数值测试表明,即使原始模型是非线性的,所提出的方法也可以解决较大的问题。另外,在多种情况下,线性逼近模型产生的路线在非线性能量模型下将是能量不可行的。与非线性能量模型相比,对无人机能量使用线性近似会导致平均能量消耗差异约9%。我们使用2指标公式化对问题进行建模,并为该公式开发分支剪切算法。首先针对此问题生成基准实例。数值测试表明,即使原始模型是非线性的,所提出的方法也可以解决较大的问题。另外,在多种情况下,线性近似模型得出的路线在非线性能量模型下将是能量不可行的。与非线性能量模型相比,对无人机能量使用线性近似会导致平均能量消耗差异约9%。我们使用2指标公式化对问题进行建模,并为该公式开发分支剪切算法。首先针对此问题生成基准实例。数值测试表明,即使原始模型是非线性的,所提出的方法也可以解决较大的问题。另外,在多种情况下,线性近似模型得出的路线在非线性能量模型下将是能量不可行的。与非线性能量模型相比,对无人机能量使用线性近似会导致平均能量消耗差异约9%。线性逼近模型得出的路线在非线性能量模型下是不可行的。与非线性能量模型相比,对无人机能量使用线性近似会导致平均能量消耗差异约9%。线性逼近模型得出的路线在非线性能量模型下将是不可行的。与非线性能量模型相比,对无人机能量使用线性近似会导致平均能量消耗差异约9%。

更新日期:2020-07-13
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