Train unit scheduling guided by historic capacity provisions and passenger count surveys

Train unit scheduling concerns the assignment of train unit vehicles to cover all the journeys in a fixed timetable. Coupling and decoupling activities are allowed in order to achieve optimal utilization while satisfying passenger demands. While the scheduling methods usually assume unique and well-defined train capacity requirements, in practice most UK train operators consider different levels of capacity provisions. Those capacity provisions are normally influenced by information such as passenger count surveys, historic provisions and absolute minimums required by the authorities. In this paper, we study the problem of train unit scheduling with bi-level capacity requirements and propose a new integer multicommodity flow model based on previous research. Computational experiments on real-world data show the effectiveness of our proposed methodology

A railway timetable rescheduling approach for handling large scale disruptions

On a daily basis, relatively large disruptions require infrastructure managers and railway operators to reschedule their railway timetables together with their rolling stock and crew schedules. This research focuses on timetable rescheduling for passenger trains at a macroscopic level in a railway network. An integer programming model is formulated for solving the timetable rescheduling problem, which minimizes the number of cancelled and delayed trains while adhering to infrastructure and rolling stock capacity constraints. The possibility of rerouting trains in order to reduce the number of cancelled and delayed trains is also considered. In addition, all stages of the disruption management process (from the start of the disruption to the time the normal situation is restored) are taken into account. Computational tests of the described model on a heavily used part of the Dutch railway network show that we are able to find optimal solutions in short computation times. This makes the approach applicable for use in practice

Optimization over time of reliable 5G-RAN with network function migrations

Resource optimization in 5G Radio Access Networks (5G-RAN) has to face the dynamics over time in networks with increasing numbers of nodes and virtual network functions. In this context, multiple objectives need to be jointly optimized, and key application requirements such as latency must be enforced. In addition, virtual network functions realizing baseband processing are subject to failures of the cloud infrastructure, requiring an additional level of reliability. Overall, this is a complex problem to solve, requiring fast algorithms to cope with dynamic networks while avoiding resource overprovisioning. This paper considers the problem of optimal virtual function placement in 5G-RAN with reliability against a single DU Hotel failure and proposes a solution that takes service dynamics into account. Firstly, the joint optimization of the total number of DU Hotels, of the RU–DU latency and of the backup DU sharing in a static traffic scenario is considered, and the DUOpt algorithm, based on Lexicographic Optimization, is proposed for solving efficiently this multi- objective problem. DUOpt splits the multi-objective problem into smaller Integer Linear Programming (ILP) subproblems that are sequentially solved, adopting for each one the most effective methodology to reduce the total execution time. The proposed DUOpt algorithm is extensively benchmarked to show its effectiveness in optimization of medium to large size networks: in particular, it is shown to greatly outperform an aggregate multi-objective approach, being able to compute optimal or close to optimal solutions for networks of several tens of nodes in computing times of a few seconds. Then, the problem is extended to a dynamic traffic scenario in which optimization is performed over time. In this context, in addition to the aforementioned objectives, the total number of network function migrations induced by multiple reoptimizations must be kept to the minimum. For solving efficiently this problem the DUMig algorithm is proposed, which extends and improves DUOpt. Reoptimization over a time horizon of one day in an illustrative dynamic traffic scenario is performed to evaluate the proposed DUMig algorithm against DUOpt, the latter being oblivious of the traffic dynamics. DUMig shows remarkable savings in the total number of migrations (above 86.1% for primary virtual functions and 83% for backup virtual functions) compared to DUOpt, while preserving near-optimal resource assignment

A matheuristic algorithm for the pollution and energy minimization traveling salesman problems

The pollution traveling salesman problem (PTSP) and the energy minimization traveling salesman problem (EMTSP) generalize the well-known asymmetric traveling salesman problem by including environmental issues and the goal of reducing carbon emissions. Both problems call for determining a Hamiltonian tour that, in the PTSP, minimizes a function of fuel consumption and driver cost (where the fuel consumption depends on the distance traveled, the vehicle speed, and the vehicle load), while, in the EMTSP, minimizes a function depending on the vehicle load and the traveled distances. For both PTSP and EMTSP, we propose a matheuristic algorithm that uses the solution of the linear programming relaxation of a mixed integer linear programming model for the considered problem to determine good initial feasible solutions, applies a multioperator genetic algorithm to improve these solutions, and refines the best solution found through an iterated local search procedure. In order to evaluate the performance of the proposed matheuristics, we compare them with exact and heuristic algorithms from the literature on benchmark instances of both problems

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

An iterative heuristic for passenger-centric train timetabling with integrated adaption times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes average perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging. The described periodic timetabling problem can be modelled as an extension of a Peri- odic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that mini- mizes the average perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infras- tructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting average per- ceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one

A two-phase approach for real-world train unit scheduling

A two-phase approach for the train unit scheduling problem is proposed. The first phase assigns and sequences train trips to train units temporarily ignoring some station infrastructure details. Real-world scenarios such as compatibility among traction types and banned/restricted locations and time allowances for coupling/ decoupling are considered. Its solutions would be near-operable. The second phase focuses on satisfying the remaining station detail requirements, such that the solutions would be fully operable. The first phase is modeled as an integer fixed-charge multicommodity flow (FCMF) problem. A branch-and-price approach is proposed to solve it. Experiments have shown that it is only capable of handling problem instances within about 500 train trips. The train company collaborating in this research operates over 2400 train trips on a typical weekday. Hence, a heuristic has been designed for compacting the problem instance to a much smaller size before the branch-and-price solver is applied. The process is iterative with evolving compaction based on the results from the previous iteration, thereby converging to near-optimal results. The second phase is modeled as a multidimensional matching problem with a mixed integer linear programming (MILP) formulation. A column-and-dependentrow generation method for it is under development