M. Abril

A Genetic Algorithm for Railway Scheduling Problems

This work is focused on the application of evolutionary algorithms to solve very complex real-world problems. For this purpose a Genetic Algorithm is designed to solve the Train Timetabling Problem. Optimizing train timetables on a single line track is known to be NP-hard with respect to the number of conflicts in the schedule. This makes it difficult to obtain good solutions to real life problems in a reasonable computational time and raises the need for good heuristic scheduling techniques. The railway scheduling problem considered in this work implies the optimization of trains on a railway line that is occupied (or not) by other trains with fixed timetables. The timetable for the new trains is obtained with a Genetic Algorithm (GA) that includes a guided process to build the initial population. The proposed GA is tested using real instances obtained from the Spanish Manager of Railway Infrastructure (ADIF). The results of the computational experience, point out that GA is an appropriate method to explore the search space of this complex problems and able to lead to good solutions in a short amount of time.

Domain-dependent distributed models for railway scheduling

Many combinatorial problems can be modelled as Constraint Satisfaction Problems (CSPs). Solving a general CSP is known to be NP-complete, so closure and heuristic search are usually used. However, many problems are inherently distributed and the problem complexity can be reduced by dividing the problem into a set of subproblems. Nevertheless, general distributed techniques are not always appropriate to distribute real-life problems. In this work, we model the railway scheduling problem by means of domain-dependent distributed constraint models, and we show that these models maintained better behaviors than general distributed models based on graph partitioning. The evaluation is focused on the railway scheduling problem, where domain-dependent models carry out a problem distribution by means of trains and contiguous sets of stations.

Distributed search in railway scheduling problems

Many problems of theoretical and practical interest can be formulated as Constraint Satisfaction Problems (CSPs). Solving a general CSP is known to be NP-complete; however, distributed models may take advantage of dividing the problem into a set of simpler inter-connected sub-problems which can be more easily solved. The purpose of this paper is three-fold: first, we present a technique to distribute the constraint network by means of selection of tree structures. Thus, the CSP is represented as a meta-tree CSP structure that is used as a hierarchy of communication by our distributed algorithm. Then, a distributed and asynchronous search algorithm (DTS) is presented. DTS is committed to solving the meta-tree CSP structure in a depth-first search tree. Finally, an intra-agent search algorithm is presented. This algorithm takes into account the Nogood_message to prune the search space. We have focused our research on the railway scheduling problem which can be distributed by tree structures. We show that our distributed algorithm outperforms well-known centralized algorithms.

An Interactive Train Scheduling Tool for Solving and Plotting Running Maps

We present a tool for solving and plotting train schedules which has been developed in collaboration with the National Network of Spanish Railways (RENFE). This tool transforms railway problems into formal mathematical models that can be solved and then plots the best possible solution available. Due to the complexity of problems of this kind, the use of preprocessing steps and heuristics become necessary. The results are plotted and interactively filtered by the human user.

New heuristics to solve the “CSOP” railway timetabling problem

The efficient use of infrastructures is a hard requirement for railway companies. Thus, the scheduling of trains should aim toward optimality, which is an NP-hard problem. The paper presents a friendly and flexible computer-based decision support system for railway timetabling. It implements an efficient method, based on meta-heuristic techniques, which provides railway timetables that satisfy a realistic set of constraints and, that optimize a multi-criteria objective function.

An Efficient Method to Schedule New Trains on a Heavily Loaded Railway Network

With the aim of supporting the process of adapting railway infrastructure to present and future traffic needs, we have developed a method to build train timetables efficiently. In this work, we describe the problem in terms of constraints derived from railway infrastructure, user requirements and traffic constraints, and we propose a method to solve it efficiently. This method carries out the search by assigning values to variables in a given order and verifying the satisfaction of constraints where these are involved. When a constraint is not satisfied, a guided backtracking is done. The technique reduces the search space allowing us to solve real and complex problems efficiently.

Distributed Constraint Satisfaction Problems to Model Railway Scheduling Problems

This paper describes how railway scheduling is considered to be a difficult and time-consuming task. Despite real railway networks being modeled as Constraint Satisfaction Problems (CSPs), they require a huge number of variables and constraints. The general CSP is known to be NP-complete; however, distributed models may reduce the exponential complexity by dividing the problem into a set of sub-problems. This paper presents several proposals to distribute the railway scheduling problem into a set of sub-problems as independently as possible. The first technique carries out a partition over the constraint network, meanwhile the second distributes the problem by trains and the third technique divides the problem by means of contiguous stations.

A Decision Support System for Railway Timetabling (MOM): the Spanish Case

This paper describes how, given the complexity and number of constraints to be taken into account, train timetabling is a difficult and time-consuming task. A feasible train timetable should specify the departure and arrival time of each train to each location of its journey so that the line capacity and other operational constraints are met. Traditionally, train timetables have been generated manually by drawing trains on the time-distance diagram, where train schedules are manually adjusted so that all constraints are fulfilled. This process can take a long time and it usually stops once a feasible timetable is found. The difficulty of the process increases in complex and high-loaded networks and the resulting timetabling may be far from optimal. This paper presents MOM: a friendly, flexible, computer-based Decision Support System (DSS) whose main goal is to support the railway planner to efficiently obtain optimized train timetables. The system generates feasible and high quality timetables by considering the set of constraints of the problem and optimization criteria related to the use of railway infrastructures and operator requirements. The railway planner can obtain several solutions automatically, by modifying certain parameters (departure interval, frequencies, among others). Hence, the user can analyze them and take decisions about conditions related to railway traffic and infrastructure. Furthermore, an important feature of the DSS is the consideration of hard and soft constraints which makes the search process more flexible and reaches better solutions. The developed DSS offers assistance in train scheduling, conclusions about the maximum capacity of the network, identifying bottlenecks, determining the consequences of changes, providing support in the resolution of incidents, and alternative planning in on-line scheduling for real traffic control. This DSS software is being successfully used by the Spanish Manager of Railway Infrastructure (ADIF).

A Decision Support System (DSS) for the Railway Scheduling Problem

The recent deregulation occurred in the public railway sector in many parts of the world has increased the awareness of this sector of the need for quality service that must be offered to its customers. In this paper, we present a software system for solving and plotting the Single-Track Railway Scheduling Problem efficiently and quickly. The problem is formulated as a Constraint Satisfaction Problem (CSP), which must be optimized. The solving process uses different stages to translate the problem into mathematical models, which are solved to optimality by means of mixed integer programming tools. The Decision Support System (DSS) we present allows the user to interactively specify the parameters of the problem, guarantees that constraints are satisfied and plots the optimized timetable obtained.

Nogood-FC for solving partitionable constraint satisfaction problems

Many real problems can be naturally modelled as constraint satisfaction problems (CSPs). However, some of these problems are of a distributed nature, which requires problems of this kind to be modelled as distributed constraint satisfaction problems (DCSPs). In this work, we present a distributed model for solving CSPs. Our technique carries out a partition over the constraint network using a graph partitioning software; after partitioning, each sub-CSP is arranged into a DFS-tree CSP structure that is used as a hierarchy of communication by our distributed algorithm. We show that our distributed algorithm outperforms well-known centralized algorithms solving partitionable CSPs.