A Fast Heuristic Algorithm for the Train Unit Assignment Problem

In this paper we study a railway optimization problem known as the Train Unit Assignment Problem. A train unit consists of a self-contained train with an engine and a set of wagons with passenger seats. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for the best assignment of the train units to the trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. We propose a heuristic algorithm based on the computation of a lower bound obtained by solving an Integer Linear Programming model that gives the optimal solution in a "peak period" of the day. The performance of the heuristic algorithm is computationally evaluated on real-world instances provided by a regional Italian Train Operator. The results are compared with those of existing methods from the literature, showing that the new method is able to obtain solutions of good quality in much shorter computing times

A branch-and-price approach for solving the train unit scheduling problem

We propose a branch-and-price approach for solving the integer multicommodity flow model for the network-level train unit scheduling problem (TUSP). Given a train operator’s fixed timetable and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled train units. The TUSP is challenging due to its complex nature. Our branch-and-price approach includes a branching system with multiple branching rules for satisfying real-world requirements that are difficult to realize by linear constraints, such as unit type coupling compatibility relations and locations banned for coupling/decoupling. The approach also benefits from an adaptive node selection method, a column inheritance strategy and a feature of estimated upper bounds with node reservation functions. The branch-and-price solver designed for TUSP is capable of handling instances of up to about 500 train trips. Computational experiments were conducted based on real-world problem instances from First ScotRail. The results are satisfied by rail practitioners and are generally competitive or better than the manual ones

Passenger train unit scheduling optimisation

This thesis deals with optimisation approaches for the train unit scheduling problem (TUSP). Given a train operator’s fixed timetables and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled units, with certain objectives achieved and certain constraints respected. From the perspective of a train unit, scheduling assigns a sequence of trains to it as its daily workload. The TUSP also includes some auxiliary activities such as empty-running generation, coupling/decoupling control, platform assignment, platform/siding/depot capacity control, re-platforming, reverse, shunting movements from/to sidings or depots and unit blockage resolution. It is also relevant with activities like unit overnight balance, maintenance provision and unit rostering. In general, it is a very complex planning process involving various aspects. Current literature on optimisation methods for the TUSP is very scarce, and for those existing ones they are generally unsuitable for the UK railway industry, either due to different problem settings and operational regulations or simplifications on some critical factors in practice. Moreover, there is no known successful commercial software for automatically optimising train unit scheduling in the world as far as the author is aware, in contrast with bus vehicle scheduling, crew scheduling and flight scheduling. This research aims at taking an initial step for filling the above gaps. A two-level framework for solving the TUSP has been proposed based on the connection-arc graph representation. The network-level as an integer multicommodity flow model captures the essence of the rail network and allocates the optimum amount of train unit resources to each train globally to ensure the overall optimality, and the station-level process (post-processing) resolves the remaining local issues like unit blockage. Several ILP formulations are presented to solve the network-level model. A local convex hull method is particularly used to realise difficult requirements and tighten LP relaxation and some further discussions over this method is also given. Dantzig-Wolfe decomposition is used to convert an arc formulation to a path formulation. A customised branch-and-price solver is designed to solve the path formulation. Extensive computational experiments have been conducted based on real-world problem instances from ScotRail. The results are satisfied by rail practitioners from ScotRail and are generally competitive or better than the manual ones. Experiments for fine-tuning the branch-and-price solver, solution quality analysis, demand estimation and post-processing have also been carried out and the results are reported. This research has laid a promising foundation leading to a continuation EPSRC funded project (EP/M007243/1) in collaboration with FirstGroup and Tracsis plc

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

Applying Operations Research techniques to planning of train shunting

In this paper, we discuss a model-based algorithmic approach for supporting planners in the creation of shunt plans for passenger trains. The approach provides an example of a mathematical model and a corresponding solution approach for model based support. We introduce a four-step solution approach and we discuss how the planners are supported by this approach. Finally, we present computational results for these steps and give some suggestions for further research.A* search;railway optimization;real world application;routing

Shunting of Passenger Train Units in a Railway Station

In this paper we introduce the problem of shunting passenger trainunits in a railway station. Shunting occurs whenever train units aretemporarily not necessary to operate a given timetable. We discussseveral aspects of this problem and focus on two subproblems. Wepropose mathematical models for these subproblems together with asolution method based on column generation. Furthermore, a newefficient and speedy solution technique for pricing problems in columngeneration algorithms is introduced. Finally, we present computationalresults based on real life instances from Netherlands Railways.logistics;column generation;railway optimization;real world application

Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table