This article addresses the integrated train blocking and shipment path (TBSP) problem. The problem aims to route and classify railcar flows while satisfying railway line and station capacity constraints. At the same time, the problem tries to minimize the total operational costs. In this article, a new linear arc-node mathematical model is developed for the TBSP problem. In order to solve the model, a novel matheuristic solution method is proposed, which includes the hybridization of tabu search (TS) metaheuristic as well as mathematical programming techniques. The solution method reduces the search space of the problem by iteratively solving an LP relaxation form of the original model. At each iteration, inspired by the TS, a penalization procedure is applied to the coefficients of the LP objective function according to the solutions. Finally, a restricted MIP model is generated based on the LP solutions. For solving all the LP and the MIP models, a black-box MIP solver is employed. Experimental results confirm that the solution method can solve the problem in a reasonable time and achieve a solution of high quality in terms of the total incurred cost.

中文翻译：

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综合列车阻塞和运输路径问题的数学公式和基于LP的邻域搜索数学求解方法

本文解决了综合列车阻塞和运输路径 (TBSP) 问题。该问题旨在在满足铁路线和车站容量限制的同时对轨道车流进行路由和分类。同时，该问题试图最小化总运营成本。在本文中，针对 TBSP 问题开发了一种新的线性弧节点数学模型。为了求解该模型，提出了一种新的数学求解方法，其中包括禁忌搜索（TS）元启发式和数学规划技术的混合。该求解方法通过迭代求解原始模型的 LP 松弛形式来减少问题的搜索空间。在每次迭代中，受 TS 的启发，根据解对 LP 目标函数的系数应用惩罚程序。最后，基于 LP 解决方案生成受限 MIP 模型。为了求解所有 LP 和 MIP 模型，采用了黑盒 MIP 求解器。实验结果证实，该求解方法可以在合理的时间内解决问题，并在总发生成本方面获得高质量的解决方案。