论文标题

部分可观测时空混沌系统的无模型预测

A machine learning based column-and-row generation approach for integrated air cargo recovery problem

论文作者

Huang, Lei, Xiao, Fan, Liang, Zhe

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

Freighter airlines need to recover both aircraft and cargo schedules when disruptions happen. This process is usually divided into three sequential decisions to recovery flights, aircraft, and cargoes. This study focuses on the integrated recovery problem that makes aircraft and cargo recovery decisions simultaneously. We formulate two integrated models based on the flight connection network, one is the arc-based model, and the other is the string-based model. The arc-based model makes the flight delay decisions by duplicating flight copies, and is solved directly by commercial solvers such as Cplex. The string-based model makes the flight delay decisions in the variable generation process. The main difficulty of the string-based model is that the number of constraints grows with the newly generated flight delay decisions. Therefore, the traditional column generation method can not be applied directly. To tackle this challenge, we propose a machine learning based column-and-row generation approach. The machine learning method is used to uncover the critical delay decisions of short through connections in each column-and-row generation iteration by eliminating the poor flight delay decisions. We also propose a set of valid inequality constraints which can greatly improve the objective of LP relaxation solution and reduce the integral gap. The effectiveness and efficiency of our model is tested by simulated scenarios based on real operational data from the largest Chinese freighter airlines. The computational results show that a significant cost reduction can be achieved with the proposed string-based model in reasonable time.

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