Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is divided between these two parts. In routing or scheduling applications, the problems are mostly defined on a network, and the PP is usually an NP-hard shortest path problem with resource constraints. In this work, we propose a new heuristic pricing algorithm based on machine learning. By taking advantage of the data collected during previous executions, the objective is to reduce the size of the network and accelerate the PP, keeping only the arcs that have a high chance to be part of the linear relaxation solution. The method has been applied to two specific problems: the vehicle and crew scheduling problem in public transit and the vehicle routing problem with time windows. Reductions in computational time of up to 40% can be obtained.

翻译：列生成是一种迭接方法, 用于解决各种优化问题。 它将问题分解成两个部分: 总问题和一个或多个定价问题( PP)。 计算方法所用的总时间在这两个部分之间是分开的。 在路由或排期应用中, 问题大多在网络上定义, PP通常是资源限制下最短的NP硬路径问题。 在这项工作中, 我们提出基于机器学习的新的超自然定价算法。 通过利用在以往处决期间收集的数据, 目标是缩小网络规模并加速 PPP, 只保留极有可能成为线性放松解决方案一部分的弧。 这种方法被应用于两个具体问题: 公共交通中的车辆和乘务人员排期问题以及时间窗口中的车辆路由问题。 计算时间可缩短40%的计算时间 。