Federico Barber

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 CSPs by graph partitioning

Nowadays, many real problems in artificial intelligence can be modelled as constraint satisfaction problems (CSPs). A general CSP is known to be NP-complete. Nevertheless, distributed models may reduce the exponential complexity by partitioning the problem into a set of subproblems. In this paper, we present a preprocess technique to break a single large problem into a set of smaller loosely connected ones. These semi-independent CSPs can be efficiently solved and, furthermore, they can be solved concurrently.

A metric time-point and duration-based temporal model

Constraint-based formalisms are a useful and common way to deal with temporal reasoning tasks. Assertions represent temporal constraints between temporal objects, time-points or intervals: Metric temporal constraints between time points permit us to express a minimum and maximum temporal distance between two time points and to define a valid temporal interval for each one. However, existing approaches have limited expressiveness for representing non-disjunctive qualitative constraints of point algebra and the empirical results do not seem very adequate for managing a great number of time points or when the time for management is limited.In this paper, an efficient and expressive time point and duration-based temporal representation model with metric constraints is presented. The main features of the model refer to the formal properties of the internal time model and the specific representation of temporal constraints, which integrates constraints on time-points and on durations and is more adequate for their computational management. Sound and complete management processes are specified on the basis of model properties. From this specification, two choices for management are proposed: (i) with neither propagation nor preprocessing techniques, complete management algorithms have an O(e*n) complexity, but a linear empirical cost is obtained; (ii) with complete propagation an O(n2) complexity is achieved.

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).

A decision support system for managing combinatorial problems in container terminals

A container terminal is a facility where cargo containers are transshipped between different transport vehicles. We focus our attention on the transshipment between vessels and land vehicles, in which case the terminal is described as a maritime container terminal. In these container terminals, many combinatorial related problems appear and the solution of one of the problems may affect to the solution of other related problems. For instance, the berth allocation problem can affect to the crane assignment problem and both could also affect to the Container Stacking Problem. Thus, terminal operators normally demand all containers to be loaded into an incoming vessel should be ready and easily accessible in the yard before vessels arrival. Similarly, customers (i.e., vessel owners) expect prompt berthing of their vessels upon arrival. However the efficiency of the loading/unloading tasks of containers in a vessel depends on the number of assigned cranes and the efficiency of the container yard logistic. In this paper, we present a decision support system to guide the operators in the development of these typical tasks. Due to some of these problems are combinatorial, some analytical formulas are presented to estimate the behavior of the container terminal.

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.

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).

Reasoning on interval and point-based disjunctive metric constraints in temporal contexts

We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defines labeled disjunctive metric point-based constraints, where each disjunct in each input disjunctive constraint is univocally associated to a label. Reasoning algorithms manage labeled constraints, associated label lists, and sets of mutually inconsistent disjuncts. These algorithms guarantee consistency and obtain a minimal network. Additionally, constraints can be organized in a hierarchy of alternative temporal contexts. Therefore, we can reason on context-dependent disjunctive metric constraints on intervals and points. Moreover, the model is able to represent non-binary constraints, such that logical dependencies on disjuncts in constraints can be handled. The computational cost of reasoning algorithms is exponential in accordance with the underlying problem complexity, although some improvements are proposed.

Temporal Reasoning in REAKT: An Environment for Real-Time Knowledge-Based Systems

Temporal representation and reasoning, as the ability of reasoning about temporal data, representing past, current and expected application states, is an important function to be accomplished by Real-Time Knowledge-Based Systems RTKBS, since these systems are usually applied in dynamic time-dependent problem domains. However, this feature is not completely nor usually addressed in current RTKBS tools. In this paper, a RTKBS architecture is presented, with special emphasis on its temporal reasoning function, which is integrated in a RTKBS environment with a multi-agent blackboard architecture. Representation and management of temporal data, representing past, current and future problem states and reasoning processes within these contexts are detailed.