# A Novel Multi-Agent-Based Approach for Train Rescheduling in Large-Scale Railway Networks
## 2 Literature Review
### Railway Traffic Management Approaches  
Due to the nature of railway systems, a rail service can be conceptualized as the occupation of a series of track circuits. Consequently, the train rescheduling problem can be modeled as a job-shop scheduling problem with additional constraints, which can be solved using mathematical programming or similar techniques [7]. One notable system, RECIFE-MILP, proposed by [PERSON] et al. [8,9], represents the railway network at a microscopic level. In this system, the optimized variables include train timetables at specific junctions and station points within the network. The MILP problem is addressed using rule-based dispatching methods, advanced search algorithms, or CPLEX software, all aimed at minimizing the propagation of delays to other trains in the network. [PERSON] et al. introduced an ant colony optimization algorithm designed for the train routing selection problem [10]. This approach, tested on two practical networks in France, generates near-optimal solutions that minimize consecutive train delays. Moreover, the optimal timing for solving the train routing selection problem is discussed in [11], which proposes search algorithms tailored for tactical, operational, and real-time traffic management levels. In another study, [PERSON] et al. applied a differential evolution algorithm to solve train rescheduling problems in railway bottleneck sections. This algorithm outperformed First-Come-First-Served (FCFS) and automatic route setting, generating optimized solutions within 2-3 s in a British network [12].  
Another common method for modeling railway infrastructure involves graph-based approaches. The concept of an alternative graph was first introduced by [PERSON] [13]. In an alternative graph, train movements are represented as the occupation of a track circuit over a certain period, with the entire journey of a train structured as a branch within the graph. This branch comprises nodes in the railway network and journey times for each track element. Building on this model, several resolution approaches have been developed for different levels of railway traffic problems. For instance, the ROMA system employs a branch-and-bound algorithm, as introduced by [PERSON] et al. [7]. Rule-based routing approaches and various resolution algorithms are compared in [14]. Additionally, algorithms optimizing train speed profiles, rescheduling, and rerouting solutions are explored in [15; 16; 17]. [PERSON] et al. introduced the concept of a dynamic impact zone for services within the network and proposed a conflict prevention strategy that explores rerouting options, as well as retiming and reordering plans [18]. [PERSON] et al. proposed a C-DAS system for freight trains in mixed-service networks, which outputs advisory time and speed profiles to help freight trains find feasible time windows to join other rail corridors based on stairway predictions [19]. Additionally, there is also literature discussing cross-disciplinary approaches that bridge infrastructure design and operational efficiency. For example, the strategy for lightweight designing of a railway vehicle car body, including composite material and dynamic structural optimization, is discussed in [20], which also provides a comparative analysis and dynamic size optimization of aluminum and carbon fiber thin-walled structures of railway vehicle car body. Also, the vehicle aeromechanical performance of improved bogie design and its influence on train dynamics is discussed [21].