This paper introduces decomposition and distributed optimization approaches for the real-time railway traffic management problem considering microscopic infrastructure characteristics, aiming at an improved computational efficiency when tackling large-scale railway networks.

Based on the nature of the railway traffic management problem, we consider three decomposition methods, namely a geography-based (GEO) decomposition, a train-based (TRA) decomposition, and a time-interval-based (TIN) decomposition, in order to partition the large railway traffic management optimization problem into several subproblems. In particular, an integer linear programming (ILP) model is developed to generate the optimal GEO solution, with the objectives of minimizing the number of interconnections among regions and of balancing the size of regions. The decomposition creates couplings among the subproblems, in terms of either capacity usage or transit time consistency; therefore the whole problem gets a non-separable structure. To handle the couplings, we introduce three distributed optimization approaches, namely an Alternating Direction Method of Multipliers (ADMM) algorithm, a priority-rule-based (PR) algorithm, and a Cooperative Distributed Robust Safe But Knowledgeable (CDRSBK) algorithm, which operate iteratively.

We test all combinations of the three decomposition methods and the three distributed optimization algorithms on a large-scale railway network in the South-East of the Netherlands, in terms of feasibility, computational efficiency, and optimality. Overall the CDRSBK algorithm with the TRA decomposition performs best, where high-quality (optimal or near-optimal) solutions can be found within 10 s of computation time.

本文针对微观铁路基础设施特点，介绍了针对实时铁路交通管理问题的分解和分布式优化方法，旨在解决大规模铁路网时提高的计算效率。

根据铁路交通管理问题的性质，我们依次考虑三种分解方法，即基于地理的分解（GEO），基于火车的分解（TRA）和基于时间间隔的分解（TIN）将大型铁路交通管理优化问题分为几个子问题。特别是，开发了整数线性规划（ILP）模型以生成最佳的GEO解决方案，其目的是最大程度地减少区域之间的互连数量并平衡区域的大小。分解会在容量使用或传输时间一致性方面在子问题之间产生耦合；因此，整个问题具有不可分离的结构。为了处理耦合，我们介绍了三种分布式优化方法，

在可行性，计算效率和最优性方面，我们在荷兰东南部的大型铁路网络上测试了三种分解方法和三种分布式优化算法的所有组合。总体而言，带有TRA分解的CDRSBK算法表现最佳，可以在10 s的计算时间内找到高质量（最佳或接近最佳）的解决方案。