L. Ingolotti

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.

Robustness in railway transportation scheduling

Railway scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to compute railway scheduling. However, robust solutions are necessary to absorb short disruptions. In this paper, we present the robustness problem from the point of view of railway operators and we give some guidelines to measure robustness in timetabling. We have developed some formulae to compare robustness between two timetables based on the study of railway infrastructure topology and buffer times. Thus, each buffer time is pondered by some factors such as tightest tracks, number of subsequent trains, remaining stations, etc. This method is inserted in MOM1, which is a project in collaboration with the Spanish Railway Infrastructure Manager (ADIF).

Robustness for a single railway line: Analytical and simulation methods

Railway scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to compute railway scheduling. However, robust solutions are necessary to absorb short disruptions. In this paper, we present the robustness problem from the point of view of railway operators and we propose analytical and simulation methods to measure robustness in a single railway line. In the analytical approach, we have developed some formulas to measure robustness based on the study of railway line infrastructure topology and buffer times. In the simulation approach, we have developed a software tool to assess the robustness for a given schedule. These methods have been inserted in MOM (More information can be found at the MOM web page http://www.dsic.upv.es/users/ia/gps/MOM), which is a project in collaboration with the Spanish Railway Infrastructure Manager (ADIF).

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.

A genetic algorithm for robust berth allocation and quay crane assignment

Scheduling problems usually obtain the optimal solutions assuming that the environment is deterministic. However, actually the environment is dynamic and uncertain. Thus, the initial data could change and the initial schedule obtained might be unfeasible. To overcome this issue, a proactive approach is presented for scheduling problems without any previous knowledge about the incidences that can occur. In this paper, we consider the berth allocation problem and the quay crane assignment problem as a representative example of scheduling problems where a typical objective is to minimize the service time. The robustness is introduced within this problem by means of buffer times that should be maximized to absorb possible incidences or breakdowns. Therefore, this problem becomes a multi-objective optimization problem with two opposite objectives: minimizing the total service time and maximizing the robustness or buffer times.

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.

Intelligent train scheduling on a high-loaded railway network

We present an interactive application to assist planners in adding new trains on a complex railway network. It includes many trains with different characteristics, whose timetables cannot be modified because they are already in circulation. The application builds the timetable for new trains linking the available time slots to trains to be scheduled. A very flexible interface allows the user to specify the parameters of the problem. The resulting problem is formulated as a CSP and efficiently solved. The solving method carries out the search assigning values to variables in a given order verifying the satisfaction of constraints where these are involved. When a constraint is not satisfied, a guided backtracking is done. Finally, the resulting timetable is delivered to the user who can interact with it, guaranteeing the traffic constraint satisfaction.