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Distributed search in railway scheduling problems
Abstract
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.
... The performance of the railway companies is judged by various criteria. In The Netherlands, the NS (by far the largest Dutch passenger railway operating company) is judged by the percentage of trains that are more than 3 minutes late 4 . Other countries use other threshold values as the punctuality criterion. ...
... Two separated paths are called conflict-free since the trains that are assigned to them will never be in conflict unless they deviate from their paths. 4 Starting from the year 2010 the trains are regarded as being late if their delay exceeds 5 minutes [126]. ...
... The proposed algorithm is shown to be more efficient than the algorithms that search for one single solution in a whole search space. Constraint programming is also used by Salido et al. [106] and Abril et al. [4]. The authors divide the problem into a number of semi-independent subproblems to reduce the huge number of variables and constraints of the original problem. ...
At railways the capacity is scarce. An increasing demand challenges policy makers to think of innovative ways in which the current infrastructure might be used. The Program for High-Frequency Railway Transport (in Dutch: Programma Hoogfrequent Spoorvervoer), which has been launched recently by the Dutch government, is an example of such innovative movement. This program sets aside the traditional timetables, which characterize the railways nowadays, and paves the way for timetable-free railway operation. This new approach will result in a dynamic environment which requires conflict resolution methods that are dynamic and robust. But even in today’s railway system, the need for such resolution methods is evident. This thesis presents an innovative approach based on the theory of the Semi-Markovian Decision Processes and examines its potential as a dynamic delay management mechanism. The approach is compared to the resolution method used nowadays by ProRail (the Dutch railway infrastructure manager) and to a number of other heuristics. The research presented in this thesis shows promising results that reveal the potential of the approach.
... Tornquist and Persson (2007) presented an optimization approach to the problem of rescheduling railway traffic in an n-tracked network when a disturbance had occurred [2]. Abril et al. (2008) took railway scheduling problems as constraint satisfaction problems (CSPS) and designed a distributed and asynchronous search algorithm (DTS) to solve the problems [3]. Castillo et al. (2011) studied the timetabling problem for a mixed multiple-and single-tracked railway network [4]. ...
... Tornquist and Persson (2007) presented an optimization approach to the problem of rescheduling railway traffic in an n-tracked network when a disturbance had occurred [2]. Abril et al. (2008) took railway scheduling problems as constraint satisfaction problems (CSPS) and designed a distributed and asynchronous search algorithm (DTS) to solve the problems [3]. Castillo et al. (2011) studied the timetabling problem for a mixed multiple-and single-tracked railway network [4]. ...
Both train rescheduling and station track assignment have become hot topics in recent years. It is fundamentally important to do the rescheduling and track assignment work at the same time to avoid the feasibility risk of the re‐scheduled timetable. The purpose of this paper is to design an integrated model for train rescheduling and track assignment in order to provide an integrative plan for the trains to run on the railway sections and go through stations. Based on the existing train rescheduling model, the model is designed by adding the constraints and the optimization goal of track assignment. The goal of track assignment is to maximize the equilibrium of the track usage time, and the constraint is that two trains cannot occupy a same track at the same time. An artificial bee colony algorithm is used to solve the model to get the operation plan. A computing experiment was carried out to prove the effectiveness of the model and the efficiency of the algorithm. The approach presented in this paper can provide a reference for the developers of a railway dispatching system.
... The optimization literature on non-cyclic TTP is very wide, and we must also consider the works on Train Dispatching. It starts as early as the 1970s with the work of Szpigel [48], and it includes many dierent approaches (ranging from pure heuristic to exact methods based on integer programming) and hundreds of papers: only to mention a few of them, see [1,3,5,7,21,24,39,47]. ...
... track sidings, junctions etc.). Clearly, dierent routing decisions may involve dierent atomic movements, which in turn have an eect on the structure of the constraints and of the objective function in (1). In particular, the eect on the simple precedence constraints (1.i) can be modelled by considering the modied constraint 5 ...
When planning new railway infrastructures in order to enhance the network to meet future demand, the capacity departments of railway operators typically have to face a time consuming trial-and-error process. The process involves the computation of a new timetable which satisfies the demand and is feasible w.r.t. the enhanced network, and is typically carried out by expert personnel with little or no assistance by computer tools. The quality of the results is thus very dependent on the skills of the individual planner. In this paper, we describe an exact approach to produce train timetables in short computation time. The approach extends the models and decomposition algorithms previously developed for train dispatching, a deeply related operational problem. The problem is solved at the microscopic level and the final timetable, even if in general non-cyclic, can incorporate cyclicity constraints for any subset of trains. Results are presented for a feasibility study in the Oslo area commissioned by the capacity planning department at Jernbaneverket (Norway's infrastructure manager).
... Not later than 11 month before the new timetable is operated the infrastructure managers shall ensure that the international train slot requests have been allocated provisionally. 2 Four months after the deadline for submission of the annual train slot requests by railway undertakings, a draft timetable shall be prepared. ...
... For our type of problem, i.e., the Lagrangean dual of model (PCP), the parameter calibration of the the bundle method was rather uncomplicated and straight-forward. Figure 6 compares exemplary the effect of different choices for the size of the bundle (2,5,10,15,20,25) on the solution of the Lagrangean relaxation of some test instances. It can be seen that larger bundles lead in general to a reduction in the number of iterations to a certain limit. ...
Diese Arbeit befasst sich mit der mathematischen Optimierung zur effizienten Nutzung der Eisenbahninfrastruktur. Wir behandeln die optimale Allokation der zur Verfügung stehenden Kapazität eines Eisenbahnschienennetzes - das Trassenallokationsproblem. Das Trassenallokationsproblem stellt eine wesentliche Herausforderung für jedes Bahnunternehmen dar, unabhängig, ob ein freier Markt, ein privates Monopol, oder ein öffentliches Monopol vorherrscht. Die Planung und der Betrieb eines Schienenverkehrssystems ist extrem schwierig aufgrund der kombinatorischen Komplexität der zugrundeliegenden diskreten Optimierungsprobleme, der technischen Besonderheiten, und der immensen Größen der Probleminstanzen. Mathematische Modelle und Optimierungstechniken können zu enormen Nutzen führen, sowohl für die Kunden der Bahn als auch für die Betreiber, z.B. in Bezug auf Kosteneinsparungen und Verbesserungen der Servicequalität.Wir lösen diese Herausforderung durch die Entwicklung neuartiger mathematischer Modelle und der dazughörigen innovativen algorithmischen Lösungsmethoden für sehr große Instanzen. Dadurch waren wir erstmals in der Lage zuverlässige ösungen für Instanzen der realen Welt, d.h. für den Simplon Korridor in der Schweiz, zu produzieren. Der erste Teil beschäftigt sich mit der Modellierung des Schienenbahnsystems unter Berücksichtigung von Kapazität und Ressourcen. Kapazität im Schienenverkehr hat grundsätzlich zwei Dimensionen, eine räumliche, welche der physischen Infrastruktur entspricht, und eine zeitliche, die sich auf die Zugbewegungen innerhalb dieser bezieht, d.h. die Belegung- und Blockierungszeiten. Sicherungssysteme im Schienenverkehr beruhen überall auf der Welt auf demselben Prinzip. Ein Zug muss Blöcke der Infrastruktur für die Durchfahrt reservieren. Das gleichzeitige Belegen eines Blockes durch zwei Züge wird Blockkonflikt genannt. Um eine konfliktfreie Belegung zu erreichen, beinhalten Modelle zur Kapazität im Schienenverkehr daher die Definition und Berechnung von angemessenen Fahrzeiten und dementsprechenden Reservierungs- oder Blockierungszeiten. Im zweiten und Hauptteil der Dissertation wird das Problem des Bestimmens optimaler Trassenallokationen für makroskopische Bahnmodelle betrachtet. Ein Literaturüberblick zu verwandten Problemen wird gegeben. Für das Trassenallokationsproblem wird ein graphentheoretisches Modell entwickelt, in dem optimale ösungen als maximal gewichtete konfliktfreie Menge von Pfaden in speziellen zeitexpandierten Graphen dargestellt werden können. Des Weiteren erreichen wir wesentliche Fortschritte beim Lösen von Trassenallokationsprobleme durch zwei Hauptbeiträge - die Entwickling einer neuartigen Modellformulierung des makroskopischen Trassenallokationsproblemes und algorithmische Verbesserungen basierend auf der Nutzung des Bündelverfahrens. Den Höhepunkt bilden Resultate für Praxisszenarios zum Simplon Korridor in der Schweiz. Nach bestem Wissen des Autors und bestätigt durch zahlreiche Eisenbahnpraktiker ist dies das erste Mal, dass auf einer makroskopischen Ebene automatisch erstellte Trassenallokationen die Bedingungen des ursprünglichen mikroskopischen Modells erfüllen und der Evaluierung innerhalb des mikroskopischen Simulationstools OpenTrack standhalten. Das dokumentiert den Erfolg unseres Ansatzes und den Nutzen and die Anwendbarkeit mathematischer Optimierung zur Allokation von Trassen im Schienenverkehr.
... As many problems need multiple solutions in practice, CP techniques have the capabilities to quickly generate high-quality solutions to meet this real-life requirement. Abril et al. [2] modelled train scheduling problems as constraint satisfaction problems (CSP). Abril et al. [2] presented a distributed tree-structure technique to solve the CSP model of train scheduling. ...
... Abril et al. [2] modelled train scheduling problems as constraint satisfaction problems (CSP). Abril et al. [2] presented a distributed tree-structure technique to solve the CSP model of train scheduling. Liebchen [23] reported that the optimised timetable of the periodic-event-scheduling problem was implemented in the Berlin railway. ...
Because of the bottlenecking operations in a complex coal rail system, millions of dollars are costed by mining companies. To handle this issue, this paper investigates a real-world coal rail system and aims to optimise the coal railing operations under constraints of limited resources (e.g., limited number of locomotives and wagons). In the literature, most studies considered the train scheduling problem on a single-track railway network to be strongly NP-hard and thus developed metaheuristics as the main solution methods. In this paper, a new mathematical programming model is formulated and coded by optimization programming language based on a constraint programming (CP) approach. A new depth-first-search technique is developed and embedded inside the CP model to obtain the optimised coal railing timetable efficiently. Computational experiments demonstrate that high-quality solutions are obtainable in industry-scale applications. To provide insightful decisions, sensitivity analysis is conducted in terms of different scenarios and specific criteria.
... Authors in [146] implement different Ant Colony Optimization (ACO) algorithms with immigrant schemes for the train rescheduling problem in a dynamic setting. Whereas the authors in [159] proposed a solution to TTP based on the formulation of a constrain satisfaction problem (CSP) in conjunction with a distributed search tree (DST). The studies presented in [151] and [152] proposed Evolutionary Algorithms (EA) to solve the TTP and rescheduling problem. ...
This Thesis project aims for a holistic overview of Artificial Intelligence
(AI) applications in the railway industry. Our research covers diverse
subdomains of railway systems such as traffic planning and scheduling,
logistics and optimization, maintenance, safety and security, passenger
experience, communication, and autonomous trains. The first part of this
work presents a taxonomy of different terms related to AI and the
railway industry. Then, we have analyzed the state of the art of AI
applied to the railway industry by conducting an extensive literature
review, summarizing different tasks and problems belonging to specific
domains and subdomains of the railway industry and common AI-based
models implemented for their solution. The existing literature reviews
typically cover a limited scope either regarding specific railway
subdomains or some certain aspects of AI. Within this study we present
an integrated overview with special emphasis on the data used to create
AI models. To achieve this, we have also conducted an extensive review
on publicly available AI-oriented datasets that can be used in the
different railway domains. Finally, we present a blueprint for the
implementation of AI within the railway industry based on our findings.
The results of our research show that the possible applications of AI in
the railway sector are vast and there are many problems and tasks that
can greatly benefit from it. Moreover, very different types of data are
implemented to feed AI models: including not only numerical, label and
image data but a wide variety of data types ranging from sound, GPS
coordinates, track geometry, speed and acceleration data, data from
rolling stock vibrations, knowledge from experts, log data, temperature
and geological data and more. Data can also be harvested using different
technologies such as IoT devices, wireless networks, smart sensors,
computer-based simulations and digital twins. These and more insights
are discussed in detail within this project.
With this study, we want to stress that the existence of available data is
one of the critical aspects of AI applications in the railway industry, and
we hope to benefit researchers in the fields of computer science and the
transport industry alike by providing an insight into these valuable data
and information on how it can be accessed and utilized.
... The eco-driving problem is usually stated as the search of the speed profile with the minimum energy consumption for a target running time between stations. Target running times are obtained after solving the capacity allocation problem [20] and the design of the timetable that distributes the time margins among stations [21] and coordinates train starts and stops [22]. The techniques applied to solve the problem can be classified as analytical methods and numerical methods [23]. ...
The new Automatic Train Operation (ATO) system over the standard European Rail Traffic Management System (ERTMS) will specify the requirements that an automatic train driving system must fulfil in order to be interoperable. The driving is defined by target times located along the journey that are received from the trackside system. Then, the on-board equipment drives the train with the objective of meeting all of the target times. The use of eco-driving methods to calculate the train driving is necessary, as one of the main goals of modern train driving systems is to increase the energy efficiency. This paper presents a simulation-based optimisation algorithm to solve the eco-driving problem constrained by multiple target times. This problem aims to minimize the energy consumption subject to a commercial running time, as the classical eco-driving problem, and also to meet intermediate target times during the journey between stations to enable automatic traffic regulation, especially at junctions. The algorithm proposed combines a Differential Evolution procedure to generate possible solutions with a detailed train simulation model to evaluate them. The use of this algorithm makes possible to find accurate speed profiles that meet the requirements of multiple time objectives. The proposed Differential Evolution algorithm is capable of finding the feasible speed profile with the minimum energy consumption, obtaining a 7.7% of energy variation in the case of a journey with one intermediate target time and 3.1% in the case of two intermediate targets.
... The problem of energy reduction in railways has been widely studied in the literature. The methods proposed can be divided in three general groups : methods related to the rolling stock (Beusen, Degraeuwe, and Debeuf 2013;Matsuoka and Kondo 2014), methods related to infrastructure (Liu et al. 2018;Sousa, Alçada-Almeida, and Coutinho-Rodrigues 2019) and methods related to the traffic operation (Abril, Salido, and Barber, 2008;Fay 2000;Huang and Li 2017;Peña-Alcaraz et al. 2012;Su et al. 2019;. The methods related to the traffic operation are popular since they allow great energy reduction results to be achieved in the short term, being applicable to railways lines that have already been built, and using low levels of investment. ...
Eco-driving is one of the most promising methods to reduce the energy consumption of existing railways. Considering the practical situation in complex railway lines, this article proposes a new multi-objective searching algorithm to obtain the set of most efficient speed profiles in train journey for each combination of arrival and intermediate times. This algorithm makes use of the particle swarm optimization principles. However, a criterion of minimum energy consumption for a combination of objective arrival and passing times is applied to avoid the gaps that could appear in Pareto fronts. The multi-dimensional set of speed profiles obtained by means of the proposed algorithm can help railway operators to make better decisions when designing timetables. In the simulation, variations of 25% can be observed in the energy consumption of two speed profiles with the same arrival time but with different passing times.
... Yuan and Hansen studied optimization of capacity of trains at train stations and their scheduling [27]. Abril et al proposed a distributed search method in the form of tree to solve a train scheduling problem [1]. Chung et al studied the Korean railway system and proposed a genetic algorithm based technique for train sequencing [10]. ...
Search and optimization problems are a major arena for the practical application of Artificial Intelligence. However, when supply chain optimization and scheduling is tackled, techniques based on linear or non-linear programming are often used in preference to Evolutionary Computation such as Genetic Algorithms (GAs). It is important to analyse whether GA are suitable for continuous real-world supply chain scheduling tasks which need regular updates. We analysed a practical situation involving iron ore train networks which is indeed one of significant economic importance. In addition, iron ore train networks have some interesting and distinctive characteristics so analysing this situation is an important step toward understanding the performance of GA in real-world supply chain scheduling. We compared the performance of GA with Nonlin-ear programming heuristics and existing industry scheduling approaches. The main result is that our comparison of techniques here produce an example in which GAs perform well and is a cost effective approach.
... A. Fernández-Rodríguez et al. / Simulation Modelling Practice and Theory 84 (2018) 50-68 51 The main energy efficiency actions that can be taken in the field of traffic operation are focused on: traffic design [1,27,35,55,62] , on-line traffic regulation [25,42,50,58,59,72] , maximization of the use of regenerative energy [21,24,53] and eco-driving. ...
Eco-driving is a traffic operation measure that may lead to important energy savings in high speed railway systems. Eco-driving optimization has been applied offline in the design of commercial services. However, the benefits of the efficient driving can also be applied on-line in the regulation stage to recover train delays or in general, to adapt the driving to the changing conditions in the line. In this paper the train regulation problem is stated as a dynamic multi-objective optimization model to take advantage in real time of accurate results provided by detailed train simulation. If the simulation model is realistic, the railway operator will be confident on the fulfillment of punctuality requirements. The aim of the optimization model is to find the Pareto front of the possible speed profiles and update it during the train travel. It continuously calculates a set of optimal speed profiles and, when necessary, one of them is used to substitute the nominal driving. The new speed profile is energy efficient under the changing conditions of the problem. The dynamic multi-objective optimization algorithms DNSGA-II and DMOPSO combined with a detailed simulation model are applied to solve this problem. The performance of the dynamic algorithms has been analyzed in a case study using real data from a Spanish high speed line. The results show that dynamic algorithms are faster tracking the Pareto front changes than their static versions. In addition, the chosen algorithms have been compared with the typical delay recovery strategy of drivers showing that DMOPSO provides 7.8% of energy savings.
... The strong pressure to protect the environment and the upcoming liberalization of railway markets, lead to the need to find new procedures that will increase efficiency and competitiveness (González-Gil et al., 2014). Ecodriving is one of the main strategies used to save energy and therefore reduce a railway company's operational costs (Abril et al., 2008;Ceraolo and Lutzemberger, 2014;Conti et al., 2015;Fay, 2000;Feng et al., 2013aFeng et al., , 2013bZhang et al., 2005). Ecodriving consists in optimization of the driving profile to reduce the associated energy consumption. ...
In CBTC (Communications-Based Train Control) operated metro lines, headway can be reduced by taking advantage of the system's train-track continuous communication, thus increasing transport capacity. When a train runs close enough to the preceding one, a tracking algorithm is triggered to control the distance between the trains. The following train receives the LMA (limit of movement authority) via radio, which is updated periodically as the preceding train runs. Besides transport capacity, one of railway operators' main goals is the reduction of energy consumption, for environmental and economic reasons. This paper firstly shows that the existing basic CBTC tracking algorithm is not energy efficient, due to the application of short braking-traction cycles. It then proposes a new efficient algorithm that makes use of coast (null traction) command, and models the uncertainty associated with the speed of the preceding train. This fuzzy algorithm is compared to the basic one in terms of energy consumption, running time and steady state interval (resulting tracking interval). Simulation results show that the proposed fuzzy tracking algorithm provides important energy savings with minor influence on running time and steady state interval. This algorithm is suitable for implementation in on-board CBTC equipment to reduce the energy consumption of traffic operation.
... Joaquin et al [4] presented a constraint programming model for the routing and scheduling of trains running through a junction. Montserrat et al [5] focused research on the railway scheduling problem which can be distributed by tree structures. X Zhou et al [6] proposed a generalized resource-constrained project scheduling formulation and presented a branch-and-bound solution procedure to obtain feasible schedules with guaranteed optimality. ...
Scheduling trains in a railway network is a fundamental operational problem in the railway industry. This paper sets up multi-objective optimal model of train operation adjustment, whose optimization objective is to reduce the train delay time and the numbers of delay train. Since the model is established as an NP complete problem, a multi-objective particle swarm optimization algorithm (MPSO) is proposed to solve the complex problem. Considering the strategy of dispatcher’ preference, MPSO can get a set of Pareto solutions in the actual train operation adjustment problems. The actual experiment, taking Beijing-Shanghai high-speed railway as example, is conducted to validate the feasibility of the algorithm compared with the basic particle swarm optimization algorithm (PSO). Results demonstrate that the model can capture the characteristics of the practical dispatching problem. MPSO is efficient for train operation adjustment and provides better solutions than the traditional approaches.
... A wide range of meta-heuristic algorithms were used to solve the train scheduling problem. Abril et al. [1] presented distributed and asynchronous search algorithms with application to the train scheduling problem based on an innovative meta-tree Constraint Satisfaction Problem (CSP) structure. Cucala et al. [16] addressed the optimal train operation model with the aim of minimizing the energy consumption subject to the uncertain delays caused by the driver response in high speed rail. ...
... As a consequence, new strategies are being implemented to reduce energy consumption. Some of these efficiency strategies are focused on improving the traffic management from the point of view of traffic design [2]- [6] and regulation [7]- [12], on the optimal use of regenerative braking [13]- [15] and on eco-driving [16]- [18]. These actions can be implemented in the short term with low investments compared with other energy efficiency actions as the renewal of trains [19] or the improvement of the infrastructure. ...
Metropolitan railway operators’ strategic plans include nowadays actions to reduce energy consumption. The application of ecodriving initiatives in lines equipped with automatic train operation (ATO) systems can provide important savings with low investments. Previous studies carried out under the ATO framework have not considered the main uncertainties in the traffic operation: the train load and delays in the line. This paper proposes a method to design robust and efficient speed profiles to be programmed in the ATO equipment of a metro line. First, an optimal Pareto front for ATO speed profiles that are robust to changes in train load is constructed. There are two objectives: running time and energy consumption. A robust optimization technique and an alternative method based on the conservation of the shape of the speed profiles (pattern robustness) are compared. Both procedures make use of a multi objective particle swarm optimization algorithm. Then, the set of speed profiles to be programmed in the ATO equipment is selected from the robust Pareto front by means of an optimization model. This model is a particle swarm optimization algorithm (PSO) to minimize the total energy consumption considering the statistical information about delays in the line. This procedure has been applied to a case study. The results showed that the pattern robustness is more restrictive and meaningful than the robust optimization technique as it provides information about shapes that are more comfortable
for passengers. In addition, the use of statistical information about delays provides additional energy savings between 3% and 14%.
... Second, short or mid-term strategies related to traffic operation increase energy efficiency without high investment. Related to the traffic operation strategies, different approaches are being researched from the point of view of traffic management (Abril et al., 2008;Fay, 2000;Feng et al., 2013aFeng et al., , 2013bJia and Zhang, 1994), the efficient use of regenerative energy Falvo et al., 2011) and efficient driving also called ecodriving. ...
One of the main priorities for metro line operators is the reduction of energy consumption, due to the environmental impact and economic cost. The new moving block signalling system CBTC (Communication Based Train Control) is being installed in order to increase the transport capacity of new metro lines, and to upgrade lines equipped with the former fixed block signalling systems. In addition, this new technology could be used to improve energy efficiency in the traffic operation, due to its capability to update the ATO (Automatic Train Operation) driving commands not only at stations but also along the journey.
In this paper a new optimization algorithm is proposed to design ATO CBTC speed profiles to minimize energy consumption, generating the Pareto optimal curve. The algorithm is a multi-objective NSGA-II-F based on simulation of the train motion under uncertainty. The main source of uncertainty in the consumption calculation is the mass of the train, which is dependent on the passenger load, and it is modeled as a fuzzy number. In addition, a new method is proposed to fill running time gaps with dominated points, providing a pseudo-Pareto curve.
The NSGA-II-F algorithm has been applied to design ATO CBTC optimal speed profiles in a case study of Metro de Madrid, providing additional energy savings up to 7.3% compared to former fixed block signalling systems and a well time-distributed pseudo-Pareto curve for the running times required by the traffic regulation system.
... Some of the early efforts in this area include Petersen (1974), Petersen and Taylor (1982), Ceder (1991), Jovanovic and Harker (1991), and Kraay, Harker, and Chen (1991). More recent studies include Carey and Lockwood (1995), Higgins, Kozan, and Ferreira (1996), Brännlund, Lindberg, Nõu, and Nilsson (1998), Caprara, Fischetti, and Toth (2002, Zhou and Zhong (2005), Caprara, Monaci, Toth, and Guida (2006), Dessouky, Liu, Zhao, and Leachman (2006), Carey and Crawford (2007), Zhong (2007), D'Ariano, Pacciarelli, andPranzo (2007), Abril, Salido, and Barber (2008b), Castillo, Gallego, Ureña, and Coronado (2009), Burdett and Kozan (2009a), Burdett and Kozan (2009b), Liu and Kozan (2009), Burdett and Kozan (2010a), Burdett and Kozan (2010b), Cacchiani, Caprara, and Toth (2010), Castillo, Gallego, Ureña, and Coronado (2011), Liu and Kozan (2011), Harrod (2011), and Narayanaswami and Rangaraj (2013. ...
In this paper we extend the work of Bergmann (1975) to investigate the capacity of a single track, unidirectional rail line that adheres to a cyclic timetable. A set of intermediate stations lies between an origin and destination with one siding at each station. Two types of trains-express and local-are dispatched from the origin in alternating fashion. The local stops at every intermediate station and the express stops at no intermediate stations. A mixed integer linear program is developed in order to minimize the length of the dispatching cycle and minimize the total stopping (dwell) time of the local train at all stations combined. Constraints include a minimum dwell time for the local train at each station, a maximum total dwell time for the local train, and headway considerations on the main line and in stations. Hundreds of randomly generated problem instances with up to 70 stations are considered and solved to optimality in a reasonable amount of time using IBM ILOG CPLEX.
... It has become a global concern to reduce the energy consumption and costs in railway systems (Feng et al., 2013b). Different technologies, developments or strategies are being researched and tested from the point of view of traffic management (Jia and Zhang, 1994;Fay, 2000;Abril et al., 2008;Feng et al., 2013a;Feng et al., 2013b), optimal use of regenerative braking in order to improve the energy efficiency (Domínguez et al., 2012;Falvo et al., 2011) and driving optimization. ...
One of the strategies for the reduction of energy consumption in railways systems is to execute efficient drivings (eco-driving). This eco-driving is the speed profile that requires the minimum energy consumption without degrading commercial running times or passenger comfort. When the trains are equipped with Automatic Train Operation systems (ATO) additional difficulties are involved. Their particular features make it necessary to develop accurate models that optimize the combination of the ATO commands of each speed profile to be used by the traffic regulation system. These commands are transmitted to the train via encoded balises on the track with little channel capacity (bandwidth). Thus, only a few and discrete values of the commands can be sent and the solution space of every interstation is made up of a relatively small set of speed profiles. However, the new state-of-the-art of signalling technologies permit a better bandwidth resulting in an exponential solution space. This calls for new methods for the optimal design of the ATO speed profiles without an exhaustive simulation of all the combinations. A MOPSO algorithm (Multi Objective Particle Swarm Optimization) to obtain the consumption/time Pareto front based on the simulation of a train with a real ATO system is proposed. The algorithm is able even to take into account only the comfortable speed profiles of the solution space. The fitness of the Pareto front is verified by comparing it with a NSGA-II algorithm (non-dominated sorting genetic algorithm II) and with the real Pareto front. Further, it has been used to obtain the optimal speed profiles in a real line of the Madrid Underground.
... In Golshani and Thomas (1981), different heuristic procedures are proposed to distribute slack time along a route to design the train timetable, and a search technique based on Genetic Algorithms is presented in Babar Kan (2006) to solve the train scheduling problem. In Abril et al. (2008), the problem of railway scheduling is The earliest work based on mathematical programming to solve the train scheduling problem was Amit and Goldfarb (1971). Then, many mathematical programming models and algorithms were developed as heuristic algorithm in Carey and Lockwood (1995), Kraay and Harker (1995), Higgins et al. (1997) and Sahin (1999). ...
Energy efficiency is an important concern in for railway administrations and operators. Strategies focused on traffic operation can achieve energy savings in short term and with associated low investments. For that purpose the main strategies are the design of efficient timetables and driving (ecodriving). The ecodriving applies coasting commands (null traction force) to reduce energy consumption, taking into account downhill slopes, speed reductions, etc. (Acikbas and Soylemez, 2008). However, timetable models in literature do not typically consider energy minimization as a goal, and punctuality requirements under uncertainty. In this paper a model for the joint design of ecodriving and timetable under uncertainty for high speed lines is proposed where the railway operator and administrator requirements are incorporated. Uncertainty in delays is modeled as fuzzy numbers and punctuality constraints, and the timetable optimization model is a fuzzy linear programming model, in which the objective function includes the consumptions of delayed scenarios and the behavioral response of the driver that will affect the consumption. The ecodriving design is based on a Genetic Algorithm that makes use of a detailed simulation model, taking into account the specific characteristics of high speed lines and trains. The proposed method is applied to a real Spanish high speed line to optimize the operation and it is compared to the current commercial service in order to evaluate the potential energy savings.
... Salido [35] modelled train scheduling problems as constraint satisfaction problems (CSP). Abril et al. [3] presented a technique to solve the CSPs modelling for train scheduling problems by distributing the constraint network in tree structures. Liebchen [28] reported that the optimised timetable based on the results of the periodic-event-scheduling problem had been implemented in Berlin railway. ...
In this paper, a demand-responsive decision support system is proposed by integrating the operations of coal shipment, coal stockpiles and coal railing within a whole system. A generic and flexible scheduling optimisation methodology is developed to identify, represent, model, solve and analyse the coal transport problem in a standard and convenient way. As a result, the integrated train-stockpile-ship timetable is created and optimised for improving overall efficiency of coal transport system. A comprehensive sensitivity analysis based on extensive computational experiments is conducted to validate the proposed methodology. The mathematical proposition and proof are concluded as technical and insightful advices for industry practice. The proposed methodology provides better decision making on how to assign rail rolling-stocks and upgrade infrastructure in order to significantly improve capacity utilisation with the best resource-effectiveness ratio. The proposed decision support system with train-stockpile-ship scheduling optimisation techniques is promising to be applied in railway or mining industry, especially as a useful quantitative decision making tool on how to use more current rolling-stocks or whether to buy additional rolling-stocks for mining transportation.
... Burdett and Kozan (2006) developed capacity analysis techniques for estimating the absolute traffic carrying ability for a railway system under a wide range of defined operational conditions, which include the proportional mix of trains, the directions, the length of trains, the planned dwelling times of trains, the presence of crossing loops and intermediate signals in corridors. Abril et al. (2008) reviewed the main concepts and methods to perform capacity analyses, and presented an automated tool that is able to perform several capacity analyses. In addition, an indepth study was performed on several Spanish railway infrastructures. ...
The paper investigates train scheduling problems when prioritised trains and nonprioritised trains are simultaneously traversed in a single-line rail network. In this case, no-wait conditions arise because the prioritised trains such as express passenger trains should traverse continuously without any interruption. In comparison, nonprioritised trains such as freight trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available, which is thought of as a relaxation of no-wait conditions. With thorough analysis of the structural properties of the No-Wait Blocking ParallelMachine Job-Shop Scheduling (NWBPMJSS) problem that is originated in this research, an innovative generic constructive algorithm (called NWBPMJSS_Liu-Kozan) is proposed to construct the feasible train timetable in terms of a given order of trains. In particular, the proposed NWBPMJSS_Liu-Kozan constructive algorithm comprises several recursively used subalgorithms (i.e., Best-Starting-Time-Determination Procedure, BlockingTime-Determination Procedure, Conflict-Checking Procedure, Conflict-Eliminating Procedure, Tune-Up Procedure, and Fine-Tune Procedure) to guarantee feasibility by satisfying the blocking, no-wait, deadlock-free, and conflict-free constraints. A two-stage hybrid heuristic algorithm (NWBPMJSS_Liu-Kozan-BIH) is developed by combining the NWBPMJSS_Liu-Kozan constructive algorithm and the Best-Insertion-Heuristic (BIH) algorithm to find the preferable train schedule in an efficient and economical way. Extensive computational experiments show that the proposed methodology is promising because it can be applied as a standard and fundamental toolbox for identifying, analysing, modelling, and solving real-world scheduling problems.
In Australia, railway systems play a vital role in transporting the sugarcane crop
from farms to mills. The sugarcane transport system is very complex and uses daily
schedules, consisting of a set of locomotives runs, to satisfy the requirements of the
mill and harvesters. The total cost of sugarcane transport operations is very high;
over 35% of the total cost of sugarcane production in Australia is incurred in cane
transport. Efficient schedules for sugarcane transport can reduce the cost and limit
the negative effects that this system can have on the raw sugar production
system. There are several benefits to formulating the train scheduling problem as a
blocking parallel-machine job shop scheduling (BPMJSS) problem, namely to
prevent two trains passing in one section at the same time; to keep the train activities
(operations) in sequence during each run (trip) by applying precedence constraints;
to pass the trains on one section in the correct order (priorities of passing trains) by
applying disjunctive constraints; and, to ease passing trains by solving rail conflicts
by applying blocking constraints and Parallel Machine Scheduling. Therefore, the
sugarcane rail operations are formulated as BPMJSS problem.
A mixed integer programming and constraint programming approaches are used to
describe the BPMJSS problem. The model is solved by the integration of constraint
programming, mixed integer programming and search techniques. The optimality
performance is tested by Optimization Programming Language (OPL) and CPLEX
software on small and large size instances based on specific criteria. A real life
problem is used to verify and validate the approach. Constructive heuristics and new
metaheuristics including simulated annealing and tabu search are proposed to solve
this complex and NP-hard scheduling problem and produce a more efficient
scheduling system. Innovative hybrid and hyper metaheuristic techniques are
developed and coded using C# language to improve the solutions quality and CPU
time. Hybrid techniques depend on integrating heuristic and metaheuristic techniques
consecutively, while hyper techniques are the complete integration between different
metaheuristic techniques, heuristic techniques, or both
Eco-driving is a keystone in energy reduction in railways and a fundamental tool to contribute to the Sustainable Development Goals in the transport sector. However, its results in real applications are subject to uncertainties such as climatological factors that are not considered in the train driving optimisation. This paper aims to develop an eco-driving model to design efficient driving commands considering the uncertainty of climatological conditions. This uncertainty in temperature, pressure, and wind is modelled by means of fuzzy numbers, and the optimisation problem is solved using a Genetic Algorithm with fuzzy parameters making use of an accurate railway simulator. It has been applied to a realistic Spanish high-speed railway scenario, proving the importance of considering the uncertainty of climatological parameters to adapt driving commands to them. The results obtained show that the energy savings expected without considering climatological factors account for 29.76%, but if they are considered, savings can rise up to 34.7% in summer conditions. With the proposed model, a variation in energy of 5.32% is obtained when summer and winter scenarios are compared while punctuality constraints are fulfiled. In conclusion, the model allows the operator to estimate better energy by obtaining optimised driving adapted to the climate.
As an important part of the railway train dispatching, train operation adjustment is the key guarantee for increasing the efficiency of rail transport and improving the quality of transport service. According to the characteristics of the High-speed train operation organization, the model is set up. Immune Genetic Algorithm, which is the effective combination of the artificial immune algorithm and genetic algorithm, is adopted to solve the model. During the model solving process, the introduction of vaccination, immune operator and immune balance operator could reduce the solving blindness, guide the individual towards a better direction development, avoid the degeneracy which general evolution algorithms may encounter and improve the algorithm efficiency. Finally, according to the simulation example which is based on the background of JinQin high-speed railway, the feasibility, validity and practicability of the model and algorithm are validated.
In this paper, a single machine scheduling model is used to schedule trains in order to minimize the total weighted delay time. The railway studied, is composed of a part of two joined railways in Brazil, which belongs to VALE company and to Ferrovia Centro-Atlântica (FCA). This railway is a single-track line composed by single-tracks and it is shared by these railways (VALE and FCA). The trains travel in both directions on this single-track line. These railways have a bottleneck caused by a heavy traffic. Therefore, mathematical equations are developed to determine the shortest time interval admissible between two trains, ensuring that they will not overlap. These equations enable us to simplify the mathematical representation of the problem and define it as a single machine scheduling problem. Later, two single machine scheduling formulations are proposed and analyzed; one based on “Arc-Time-Indexed” variables and other, on “Binary” variables. Each formulation reflects a specific concept on how the variables and parameters are defined and require particular settings and definitions. Extensive computational experiments are performed considering various instances to capture several aspects of practical situations. Based on the results of experiments, these mathematical formulations are evaluated as decision-support tools.
The purpose of this paper is to present a method of control synthesis f o r a given train station system and train set based on optimal resource scheduling. A Genetic Algorithm was designed to resolve the resource allocation problem in an example train traffic system with three stations. A method of controller synthesis based on Genetic Programming is also presented. This method synthetizes controllers that behaves according to the obtained resource allocation tables. These controllers are built based on Timed Petri Nets. The possibility of minimal environmental change was also added in order to obtain flexible and robust controllers. Solution methods were proposed f o r this extended problem.
The crew scheduling problem (CSP) is an important problem for the transportation enterprises, especially when crew's cost is increasing. This justifies the researcher's effort in order to create algorithms which obtain good solutions for this kind of problems. Particularly, hybrid algorithms appear as an efficient alternative in order to solve any combinatorial optimization problem. Tabu Search (TS) is a simple metaheuristic which has been applied in many combinatorial problems, obtaining very competitive solutions. Integer Programming (IP), in this case, allows to the TS algorithm to have a good level of diversification, avoiding that it's converge to local optimal solutions. In this article we presents an hybrid algorithm of Tabu Search and Integer Programming which is applied to the both CSP instances obtained from the literature and a real application case in Chile (MERVAL). The hybrid algorithm obtains good solutions in both cases, and obtains an important minimization in the execution time in the MERVAL case.
Train timetabling with minimum delays is the most important operating problem in any railway industry. This problem is considered to be one of the most interesting research topics in railway optimization problems. This paper deals with scheduling different types of trains in a single railway track. The primary focus of this paper is on the periodic aspects of produced timetables and the proposed modeling is based on the periodic event scheduling problem (PESP). To solve large-scale problems, a hybrid meta-heuristic algorithm based on simulated annealing (SA) and particle swarm optimization (PSO) is proposed and validated using some numerical examples and an Iranian case study that covers the railway line between two cities of Isfahan and Tehran.
This paper illustrates the results of an investigation into developing a new robust train-timetabling problem in a single-track railway line. The proposed model is formulated as a robust form of the mixed integer approach. A branch-and-bound (B&B) algorithm, along with a new heuristic beam search (BS) algorithm, is presented to solve the model for large-scale problems in reasonable time. We also propose two different methods to measure the required buffer times under the assumption of unknown and known distribution functions of disturbances. We have generated some random instances, and the efficiency of the B&B and BS algorithms are demonstrated by comparing the results with common software packages as well as a new lower bound method. The results demonstrate that the B&B algorithm can find optimum solutions in a shorter amount of time compared with common software packages such as Lingo. Moreover, the BS algorithm can effectively find a near-optimum solution in a rational amount of time.
In this paper we explore the number of tree search operations required to solve binary constraint satisfaction problems. We show analytically and experimentally that the two principles of first trying the places most likely to fail and remembering what has been done to avoid repeating the same mistake twice improve the standard backtracking search. We experimentally show that a lookahead procedure called forward checking (to anticipate the future) which employs the most likely to fail principle performs better than standard backtracking, Ullman's, Waltz's, Mackworth's, and Haralick's discrete relaxation in all cases tested, and better than Gaschnig's backmarking in the larger problems.
. When multiple agents are in a shared environment, there usually exist constraints among the possible actions of these agents. A distributed constraint satisfaction problem (distributed CSP) is a problem to find a consistent combination of actions that satisfies these inter-agent constraints. Various application problems in multi-agent systems can be formalized as distributed CSPs. This paper gives an overview of the existing research on distributed CSPs. First, we briefly describe the problem formalization and algorithms of normal, centralized CSPs. Then, we show the problem formalization and several MAS application problems of distributed CSPs. Furthermore, we describe a series of algorithms for solving distributed CSPs, i.e., the asynchronous backtracking, the asynchronous weak-commitment search, the distributed breakout, and distributed consistency algorithms. Finally,we showtwo extensions of the basic problem formalization of distributed CSPs, i.e., handling multiple local variables, and dealing with over-constrained problems. Keywords: Constraint Satisfaction, Search, distributed AI 1.
In this study, a new approach based on the consideration that electrocardiogram (ECG) signals are chaotic signals was presented for detection of electrocardiographic changes in patients with partial epilepsy. This consideration was tested successfully ...
Search algorithms on distributed constraints satisfactio n prob- lems, DisCSPs, are composed of agents performing computations concurrently. The most common abstract performance measure- ment that has been universally adopted for centralized CSPs algo- rithms is the number of constraints checks performed. However, when it comes to distributed search, constraints checks are per- formed concurrently by all agents on the network and therefore a simple measurement of constraints checks is not adequate any more. In order to be able to compare the behavior of different al- gorithms, there is a need for a new distributed method to measure the search effort of a DisCSP algorithm. A model for measuring concurrent constraints checks on dis- tributed constraints satisfaction problems (DisCSPs) is p resented. The advantages of the proposed model are clarified by a series of simple constraints network examples. An algorithm for comput- ing the proposed measure, the cumulative cost algorithm (CCA) , is presented. A formal correctness proof of the CCA algorith m, according to the proposed model for concurrent constraints checks (CCCs) is presented.
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.
Many AI tasks can be formulated as constraint-satisfaction problems (CSP), i.e., the assignment of values to variables subject to a set of constraints. While some CSPs are hard, those that are easy can often be mapped into sparse networks of constraints which, in the extreme case, are trees. This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally. The paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simplified subproblem, and comparing these counts to decide among the choices pending in the original problem.
This paper describes the development and implementation of an optimization model used to resolve disruptions to an operating schedule in the rail industry. Alterations to the existing train timetable and crewing roster are made simultaneously in real time—previous treatments in the literature have always decoupled these two problems and solved them in series. An integer programming model is developed that constructs a train timetable and crew roster. This model contains two distinct blocks, with separate variables and constraints for the construction of the train timetable and crew roster, respectively. These blocks are coupled by piece of work sequencing constraints and shift length constraints, which involve variables from both blocks. This unique parallel construction process is then used as the basis of a method to deal with the resolution of train disruptions in realtime. Favourable results are presented for both the combined train/driver scheduling model and the real-time disruption recovery model.
We show that every 2-connected triangulated planar graph with n vertices has a simple cycle C of length at most 2√2 · n which separates the interior vertices A from the exterior vertices B such that neither A nor B contain more than vertices. The method also gives a linear time sequential algorithm for finding this simple cycle and an NC parallel algorithm. In general, if the maximum face size is d then we exhibit a cycle C as above of size at most 2√d · n.
We show that every 2-connected triangulated planar graph with n vertices has a simple cycle C of length at most 4@@@@n which separates the interior vertices A from the exterior vertices B such that neither A nor B contains more than 2/3n vertices. The method also gives a linear time algorithm for finding the simple cycle. In general, if the maximum face size is d then we exhibit a cycle C as above of size at most 2@@@@2d•n.
A mathematical model is proposed for scheduling activities of periodic type. First a model is proposed for scheduling periodic events with particular time constraints. This problem, which could be considered an extension to periodic phenomena of ordinary scheduling with precedence constraints, is shown to be NP-complete. An algorithm for it of implicit enumeration type is designed based on network flow results, and its average complexity is discussed. Some extensions of the model are considered. The results of this first part serve as a basis in modelling periodic activities using resources. Several cases are considered. Finally some applications are presented for which the proposed model can be a useful tool.
A constraint satisfaction problem revolves finding values for a set of variables subject to a set of constraints (relations) on those variables Backtrack search is often used to solve such problems. A relationship involving the structure of the constraints is described which characterizes to some degree the extreme case of mimmum backtracking (none) The relationship involves a concept called "width," which may,provide some guidance in the representation of constraint satisfaction problems and the order m which they are searched The width concept is studied and applied, in particular, to constraints which form tree structures. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]' Nonnu-
The aim of this paper is to present a survey of recent optimization models for the most commonly studied rail transportation problems. For each group of problems, we propose a classification of models and describe their important characteristics by focusing on model structure and algorithmic aspects. The review mainly concentrates on routing and scheduling problems since they represent the most important portion of the planning activities performed by railways. Routing models surveyed concern the operating policies for freight transportation and railcar fleet management, whereas scheduling models address the dispatching of trains and the assignment of locomotives and cars. A brief discussion of analytical yard and line models is also presented. The emphasis is on recent contributions, but several older yet important works are also cited.
Search algorithms on distributed constraints satisfaction problems, DisCSPs, are composed of agents performing computations concurrently. The most common abstract performance measurement that has been universally adopted for centralized CSPs algorithms is the number of constraints checks performed. However, when it comes to distributed search, constraints checks are performed concurrently by all agents on the network and therefore a simple measurement of constraints checks is not adequate any more. In order to be able to compare the behavior of different algorithms, there is a need for a new distributed method to measure the search effort of a DisCSP algorithm.
Contents 0.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.2 Modeling Mesh-based Computations as Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.3 Static Graph Partitioning Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.3.1 Geometric Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0.3.2 Combinatorial Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0.3.3 Spectral Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 0.3.4 Multilevel Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 0.3.5 Combined Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 0.3.6 Qualitative Comparison of Graph Partitioning Schemes . . . . . . . . . . . . . . . . . 16 0.4 Load Balancing of Adaptive Computations . . . . . .
The Single-Track Railway Scheduling Problem can be modelled as a special case of the Job-Shop Scheduling Problem. This can be achieved by considering the train trips as jobs, which will be scheduled on tracks regarded as resources. A train trip may have many tasks that consist of traversing from one point to another on a track. Each of these distinct points can be a station or a signal placed along the track. Conicts may occur when the desired timetable would result in two trains occupying the same section of the track at the same time. The mapping of the problem we have proposed in this thesis is a more realistic approach when modelling the physical representation of a track railway. This is because we take into account the actual signals placed along the track delimiting each track segment. These signals control whether a train can or cannot go on that particular track segment, avoiding thus the possibility of trains running into each other. Previous authors adopted an approximation to what is found in practice by adding minimum headway constraints between trains into their model. Two strategies for resolving the conicts in a desired timetable are presented. The two strategies have their applicability in practice. For instance, resolving a conict in the rst strategy stems from the observed practice of train operators: in the rst strategy a conict is resolved by re-timing one of the trips at its departure time up to the point the conict is resolved. Train operating companies do not typically want to plan for passenger trains being delayed after their departure. On the other hand, the second strategy resolves a conict by delaying only the conicting piece of one of the two trips (and subsequent pieces of that trip). In this way, the section of the trip before...
Constraint networks (survey). Encyclopedia Artificial Intelli-gence
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Timetable construction for railned
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Schrijver, A., Steenbeek, A., 1994. Timetable construction for railned. Technical Report, CWI, Amsterdam, The Netherlands.
Constraint networks (survey)
- Dechter