An exact decomposition approach for the real-time Train Dispatching problem (v.2)

-Trains movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast re-scheduling and re-routing decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic ""holistic"" approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. The decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two subproblems are modeled as mixed integer linear programs, with their specific sets of variables and constraints. Similarly to the classical Bender's decomposition approach, the slave and the master communicate through suitable feasibility cuts in the variables of the master. By applying our approach to a number of real-life instances from single and double-track lines in Italy, we were able to (quickly) find optimal or near-optimal solutions, with impressive improvements over the performances of the current operating control systems. The new approach will be put in operation in such lines for an extensive on-field test-campaign as of April 2013. Follows SINTEF Technical Report A2327

The Tick Formulation for deadlock detection and avoidance in railways traffic control

Wrong dispatching decisions may lead to deadlocks, where trains reciprocally block resources necessary to reach their destinations. It is crucial to develop tools to detect such potential deadlocks on time, in order to reverse the decisions previously taken by dispatchers or to take recovery actions. In this paper we present a new 0,1 linear formulation for detecting deadlocks and optimally park the involved trains to reduce congestion around the affected area. We discuss computational results on some realistic randomly generated instances to show the validity of the approach, as well as its limits.acceptedVersio

Easy Cases of Deadlock Detection in Train Scheduling

A deadlock occurs when two or more trains are preventing each other from moving forward by occupying the required tracks. Deadlocks are rare but pernicious events in railroad operations and, in most cases, are caused by human errors. Recovering is a time-consuming and costly operation, producing large delays and often requiring crew rescheduling and complex switching moves. In practice, most deadlocks involve only two long trains missing their last potential meet location. In this paper, we prove that, for any network configuration, the identification of two-train deadlocks can be performed in polynomial time. This is the first exact polynomial algorithm for such a practically relevant combinatorial problem. We also develop a pseudo-polynomial but efficient oracle that allows real-time early detection and prevention of any (potential) two-train deadlock in the Union Pacific (a U.S. class 1 rail company) railroad network. A deadlock prevention module based on the work in this paper will be put in place at Union Pacific to prevent all deadlocks of this kind.acceptedVersio

Timing of initiation of oral anticoagulants in patients with acute ischemic stroke and atrial fibrillation comparing posterior and anterior circulation strokes

Background: The aim of this study in patients with acute posterior ischemic stroke (PS) and atrial fibrillation (AF) were to evaluate the risks of recurrent ischemic event and severe bleeding and these risks in relation with oral anticoagulant therapy (OAT) and its timing. Methods: Patients with PS were prospectively included; the outcome events of these patients were compared with those of patients with anterior stroke (AS) which were taken from previous registries. The primary outcome was the composite of: stroke recurrence, TIA, symptomatic systemic embolism, symptomatic cerebral bleeding and major extracranial bleeding occurring within 90 days from acute stroke. Results: A total of 2,470 patients were available for the analysis: 473 (19.1%) with PS and 1,997 (80.9%) AS. Over 90 days, 213 (8.6%) primary outcome events were recorded: 175 (8.7%) in patients with AS and 38 (8.0%) in those with PS. In patients who initiated OAT within 2 days, the primary outcome occurred in 5 out of 95 patients (5.3%) with PS compared to 21 out of 373 patients (4.3%) with AS (OR 1.07; 95% CI 0.39-2.94). In patients who initiated OAT between days 3 and 7, the primary outcome occurred in 3 out of 103 patients (2.9%) with PS compared to 26 out of 490 patients (5.3%) with AS (OR 0.54; 95% CI 0.16-1.80). Conclusions: Patients with posterior or anterior stroke and AF appear to have similar risks of ischemic or hemorrhagic events at 90 days with no difference concerning the timing of initiation of OAT

An exact decomposition approach for the real-time Train Dispatching problem (v.2)

Trains movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast re-scheduling and re-routing decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic ""holistic"" approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. The decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two subproblems are modeled as mixed integer linear programs, with their specific sets of variables and constraints. Similarly to the classical Bender's decomposition approach, the slave and the master communicate through suitable feasibility cuts in the variables of the master. By applying our approach to a number of real-life instances from single and double-track lines in Italy, we were able to (quickly) find optimal or near-optimal solutions, with impressive improvements over the performances of the current operating control systems. The new approach will be put in operation in such lines for an extensive on-field test-campaign as of April 2013. Follows SINTEF Technical Report A2327

An exact decomposition approach for the real-time train dispatching problem

Trains movement on a railway network are regulated by the official timetables. Deviations and delays occur quite often in practice, asking for fast rescheduling and rerouting decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic ""holistic"" approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. This decomposition allows for the application of suitable simplified models,  which in turn makes it possible to apply Mixed Integer Linear Programming to quickly find optimal or near-optimal solutions to a number of real-life instances from single-track lines in Italy

Integer Programming Techniques for Train Dispatching in Mass Transit and Main Line

Trains moving in railway systems are often affected by delays or cancellations. This in turn may produce knock-on effects and propagate to other trains and other regions of the network. These undesired effects may be alleviated by suitably rerouting and rescheduling trains in real time. Train dispatching is thus a central task in managing railway systems because it allows recovery from undesirable deviations from the timetable and a better exploitation of railway resources. With few exceptions, dispatching is still almost entirely in the hands of human operators, despite the fact that it is a large and complex optimization problem that does not lend itself to manual solution. In this chapter, we describe how integer programming (IP) can be exploited to quickly find optimal solutions to large dispatching problems and describe real-life implementations of these ideas.acceptedVersio

An exact decomposition approach for the real-time train dispatching problem

Trains’ movements on a railway network are regulated by official timetables. Deviations and delays occur quite often in practice, demanding fast rescheduling and rerouting decisions in order to avoid conflicts and minimize overall delay. This is the real-time train dispatching problem. In contrast with the classic “holistic” approach, we show how to decompose the problem into smaller subproblems associated with the line and the stations. This decomposition is the basis for a master-slave solution algorithm, in which the master problem is associated with the line and the slave problem is associated with the stations. The two subproblems are modeled as mixed integer linear programs, with specific sets of variables and constraints. Similarly to the classical Benders’ decomposition approach, slave and master communicate through suitable feasibility cuts in the variables of the master. Extensive tests on real-life instances from single and double-track lines in Italy showed significant improvements over current dispatching performances. A decision support system based on this exact approach has been in operation in Norway since February 2014 and represents one of the first operative applications of mathematical optimization to train dispatching

The track formulation for the train dispatching problem

With few exceptions, train movements are still controlled by human operators, the dispatchers. They establish routes and precedence between trains in real-time in order to cope with normal operations but also to recover from deviations from the timetable, and minimize overall delays. Implicitly they tackle and solve repeatedly a hard optimization problem, the Train Dispatching Problem. We recently developed a decomposition approach which allowed us to solve real-life instances to optimality or near optimality in times acceptable for dispatchers. We present here some new ideas which appear to significantly reduce computational times while solving to optimality even large instances. © 2013 Elsevier B.V