Motivated by the needs from an airline crew scheduling application, we
introduce structured convolutional kernel networks (Struct-CKN), which combine
CKNs from Mairal et al. (2014) in a structured prediction framework that
supports constraints on the outputs. CKNs are a particular kind of
convolutional neural networks that approximate a kernel feature map on training
data, thus combining properties of deep learning with the non-parametric
flexibility of kernel methods. Extending CKNs to structured outputs allows us
to obtain useful initial solutions on a flight-connection dataset that can be
further refined by an airline crew scheduling solver. More specifically, we use
a flight-based network modeled as a general conditional random field capable of
incorporating local constraints in the learning process. Our experiments
demonstrate that this approach yields significant improvements for the
large-scale crew pairing problem (50,000 flights per month) over standard
approaches, reducing the solution cost by 17% (a gain of millions of dollars)
and the cost of global constraints by 97%.

引入了结构卷积核网络（Struct-CKN）作为一种支持输出约束的结构化预测框架，将 Mairal 等人的 CKN 结合起来，将 CKNs 推广到了结构化输出，通过一个基于航班的网络建模实现了航空公司机组人员调度问题的初始解。实验证明，这种方法在标准方法上取得了重大改进，降低了解决方案成本 17％，全局约束成本降低了 97％。