The volume of instant delivery has witnessed a significant growth in recent years. Given the involvement of numerous heterogeneous stakeholders, instant delivery operations are inherently characterized by dynamics and uncertainties. This study introduces two order dispatching strategies, namely task buffering and dynamic batching, as potential solutions to address these challenges. The task buffering strategy aims to optimize the assignment timing of orders to couriers, thereby mitigating demand uncertainties. On the other hand, the dynamic batching strategy focuses on alleviating delivery pressure by assigning orders to couriers based on their residual capacity and extra delivery distances. To model the instant delivery problem and evaluate the performances of order dispatching strategies, Adaptive Agent-Based Order Dispatching (ABOD) approach is developed, which combines agent-based modelling, deep reinforcement learning, and the Kuhn-Munkres algorithm. The ABOD effectively captures the system's uncertainties and heterogeneity, facilitating stakeholders learning in novel scenarios and enabling adaptive task buffering and dynamic batching decision-makings. The efficacy of the ABOD approach is verified through both synthetic and real-world case studies. Experimental results demonstrate that implementing the ABOD approach can lead to a significant increase in customer satisfaction, up to 275.42%, while simultaneously reducing the delivery distance by 11.38% compared to baseline policies. Additionally, the ABOD approach exhibits the ability to adaptively adjust buffering times to maintain high levels of customer satisfaction across various demand scenarios. As a result, this approach offers valuable support to logistics providers in making informed decisions regarding order dispatching in instant delivery operations.@en

Employing regenerative braking in trains contributes to reducing the amount of energy used, especially when applied to commuter trains and to those used on very dense suburban networks. This paper presents a method to fine-tune the periodic timetable to improve the utilization of regenerative energy and to shave power peaks while maintaining the structure and robustness of the original timetable. First, a mixed-integer linear programming model based on the periodic event scheduling framework is proposed. A set of feasible timetables is determined and optimized with the aim of increasing synchronized acceleration and braking events at the same station, and maintaining the timetable robustness at the specified level. Next, a local search algorithm is developed to optimize the timetable such that the power peak value is minimized. The max-plus system model is adopted to estimate the delay propagation. Monte Carlo simulation is used to evaluate the utilization of regenerative energy and power peaks in random delayed circumstances. The proposed method was adopted to fine-tune the 2019 timetable for a sub-network of the Dutch railway. In the case of on- time scenarios, the optimized timetable increases the regenerative energy usage by almost 290% and decreases the 15-minute power peaks by 8.5%. In the case of delay scenarios, the optimized timetable outperforms the original timetable in terms of using regenerative energy and shaving power peaks.@en

In the last decade, pseudospectral methods have become popular for solving optimal control problems. Pseudospectral methods do not need prior knowledge about the optimal control structure and are thus very flexible for problems with complex path constraints, which are common in optimal train control, or train trajectory optimization. Practical optimal train control problems are nonsmooth with discontinuities in the dynamic equations and path constraints corresponding to gradients and speed limits varying along the track. Moreover, optimal train control problems typically include singular solutions with a vanishing Hessian of the associated Hamiltonian. These characteristics make these problems hard to solve and also lead to convergence issues in pseudospectral methods. We propose a computational framework that connects pseudospectral methods with Pontryagin's Maximum Principle allowing flexible computations, verification and validation of the numerical approximations, and improvements of the continuous solution accuracy. We apply the framework to two basic problems in optimal train control: minimum-time train control and energy-efficient train control, and consider cases with short-distance regional trains and long-distance intercity trains for various scenarios including varying gradients, speed limits, and scheduled running time supplements. The framework confirms the flexibility of the pseudospectral method with regards to state, control and mixed algebraic inequality path constraints, and is able to identify conditions that lead to inconsistencies between the necessary optimality conditions and the numerical approximations of the states, costates, and controls. A new approach is proposed to correct the discrete approximations by incorporating implicit equations from the optimality conditions. In particular, the issue of oscillations in the singular solution for energy-efficient driving as computed by the pseudospectral method has been solved.@en

This paper proposes a novel approach for energy-efficient timetabling by adjusting the running time allocation of given timetables using train trajectory optimization. The approach first converts the arrival and departure times to time window constraints in order to relax the given timetable. Then a train trajectory optimization method is developed to find optimal arrival/departure times and optimal energy-efficient speed profiles within the relaxed time windows. The proposed train trajectory optimization method includes two types, a single-train trajectory optimization (STTO), which focuses on optimizing individual train movements within the relaxed arrival and departure time windows, and a multi-train trajectory optimization (MTTO), which computes multi-train trajectories simultaneously with a shared objective of minimizing multi-train energy consumption and an additional target of eliminating conflicts between trains. The STTO and MTTO are re-formulated as a multiple-phase optimal control problem, which has the advantage of accurately incorporating varying gradients, curves and speed limits and different train routes. The multiple-phase optimal control problem is then solved by a pseudospectral method. The proposed approach is applied in case studies to fine-tune two timetables, for a single-track railway corridor and a double-track corridor of the Dutch railway. The results suggest that the proposed approach is able to improve the energy efficiency of a timetable.@en

Even though rail is more energy efficient than most other transport modes, the enhancement of energy efficiency is an important issue for railways to reduce their contributions to climate change further as well as to save costs and enlarge competition advantages involved. This thesis is motivated by the challenges in improving energy efficiency of train operations. The main objectives are to develop the modelling and solution methods for the train trajectory optimization problem to improve the model accuracy and the computation time, to apply the methods in a train driver advisory system development, and to develop a multi-train trajectory optimization method to solve the delay recovery and the energy-efficient timetabling problem. @en

Optimizing the railway timetable to increase synchronous accelerating and braking processes can lead to an improvement in the usage of regenerative energy. However, such a synchronized timetable might result in little or unsuitable transfer connections for the passengers. This paper focuses on the optimization of railway periodic timetables, to increase usage of regenerative energy while ensuring passenger satisfaction. We work by extending the traditional Periodic Event Scheduling Problem (PESP) formulation, to address the problem of synchronization of acceleration and braking phases, (and re-used energy) and including passenger-related events (and their satisfaction). Three objectives are identified, in a resulting Mixed Integer Linear Programming (MILP) model: maximizing the overlapping times of accelerating and braking trains to achieve increased usage of regenerative energy, minimizing the total passengers’ generalized travel times (global passenger dissatisfaction), and minimizing the maximum increase in individual's generalized travel time (local passenger dissatisfaction). A multi-step approach solves the trade-offs among three conflicting objectives. Results on a realistic case study show that the proposed approach can find optimized timetables, which compared to the currently-in-use timetable, can increase the usage of regenerative energy by over 1.5 times, save the average generalized travel time per passenger by 2 min, with only a minor increase on specific individual generalized travel time (up to 4 min). A detailed results analysis imply that to achieve a higher usage of regenerative energy, it is required to have a higher tolerance for the maximum increase in individual generalized travel time, while this is not necessary for the overall passenger generalized travel time, which can even be reduced when the maximum increase in individual generalized travel time becomes larger.@en

Optimizing the railway timetable to increase synchronous accelerating and braking processes can lead to an improvement in the usage of regenerative energy. However, such a synchronized timetable might result in little or unsuitable transfer connections for the passengers. This paper focuses on the optimization of railway periodic timetables, to increase usage of regenerative energy while ensuring passenger satisfaction. We work by extending the traditional Periodic Event Scheduling Problem (PESP) formulation, to address the problem of synchronization of acceleration and braking phases, (and re-used energy) and including passenger-related events (and their satisfaction). Three objectives are identified, in a resulting Mixed Integer Linear Programming (MILP) model: maximizing the overlapping times of accelerating and braking trains to achieve increased usage of regenerative energy, minimizing the total passengers’ generalized travel times (global passenger dissatisfaction), and minimizing the maximum increase in individual's generalized travel time (local passenger dissatisfaction). A multi-step approach solves the trade-offs among three conflicting objectives. Results on a realistic case study show that the proposed approach can find optimized timetables, which compared to the currently-in-use timetable, can increase the usage of regenerative energy by over 1.5 times, save the average generalized travel time per passenger by 2 min, with only a minor increase on specific individual generalized travel time (up to 4 min). A detailed results analysis imply that to achieve a higher usage of regenerative energy, it is required to have a higher tolerance for the maximum increase in individual generalized travel time, while this is not necessary for the overall passenger generalized travel time, which can even be reduced when the maximum increase in individual generalized travel time becomes larger.@en

Optimizing the railway timetable to increase synchronous accelerating and braking processes can lead to an improvement in the usage of regenerative energy. However, such a synchronized timetable might result in little or unsuitable transfer connections for the passengers. This paper focuses on the optimization of railway periodic timetables, to increase usage of regenerative energy while ensuring passenger satisfaction. We work by extending the traditional Periodic Event Scheduling Problem (PESP) formulation, to address the problem of synchronization of acceleration and braking phases, (and re-used energy) and including passenger-related events (and their satisfaction). Three objectives are identified, in a resulting Mixed Integer Linear Programming (MILP) model: maximizing the overlapping times of accelerating and braking trains to achieve increased usage of regenerative energy, minimizing the total passengers’ generalized travel times (global passenger dissatisfaction), and minimizing the maximum increase in individual's generalized travel time (local passenger dissatisfaction). A multi-step approach solves the trade-offs among three conflicting objectives. Results on a realistic case study show that the proposed approach can find optimized timetables, which compared to the currently-in-use timetable, can increase the usage of regenerative energy by over 1.5 times, save the average generalized travel time per passenger by 2 min, with only a minor increase on specific individual generalized travel time (up to 4 min). A detailed results analysis imply that to achieve a higher usage of regenerative energy, it is required to have a higher tolerance for the maximum increase in individual generalized travel time, while this is not necessary for the overall passenger generalized travel time, which can even be reduced when the maximum increase in individual generalized travel time becomes larger.@en

Virtual coupling technology was recently proposed in railways, which separates trains by a relative braking distance (or even shorter distance) and moves trains synchronously to increase capacity at bottlenecks. This study proposes a real-time cooperative train trajectory planning algorithm for coordinating train movements under virtual coupling by considering stochastic initial delays. The algorithm uses mixed-integer programming models to estimate the delay propagation among trains, detect feasible coupled-running locations, and optimize the trajectories of the two trains such that they coordinate their speeds to achieve energy-efficient, punctual movements, as well as a safe coupled-running process. A robust optimization method is proposed to capture the stochastic delays as an uncertainty set, which is reformulated to its dual problem. Case studies of planning train trajectories for the classical virtual-coupling scenario suggest that (1) the coupled-running distance is greatly affected by the coordination of train timetables, delays, and safe separation constraints at switches; (2) the coordination of train movements for a coupled-running process imposes extra energy costs; and (3) the proposed method can detect feasible coupled-running locations and produce cooperative speed profiles in short computational times.@en

Virtual coupling technology was recently proposed in railways, which separates trains by a relative braking distance (or even shorter distance) and moves trains synchronously to increase capacity at bottlenecks. This study proposes a real-time cooperative train trajectory planning algorithm for coordinating train movements under virtual coupling by considering stochastic initial delays. The algorithm uses mixed-integer programming models to estimate the delay propagation among trains, detect feasible coupled-running locations, and optimize the trajectories of the two trains such that they coordinate their speeds to achieve energy-efficient, punctual movements, as well as a safe coupled-running process. A robust optimization method is proposed to capture the stochastic delays as an uncertainty set, which is reformulated to its dual problem. Case studies of planning train trajectories for the classical virtual-coupling scenario suggest that (1) the coupled-running distance is greatly affected by the coordination of train timetables, delays, and safe separation constraints at switches; (2) the coordination of train movements for a coupled-running process imposes extra energy costs; and (3) the proposed method can detect feasible coupled-running locations and produce cooperative speed profiles in short computational times.@en

Virtual coupling technology was recently proposed in railways, which separates trains by a relative braking distance (or even shorter distance) and moves trains synchronously to increase capacity at bottlenecks. This study proposes a real-time cooperative train trajectory planning algorithm for coordinating train movements under virtual coupling by considering stochastic initial delays. The algorithm uses mixed-integer programming models to estimate the delay propagation among trains, detect feasible coupled-running locations, and optimize the trajectories of the two trains such that they coordinate their speeds to achieve energy-efficient, punctual movements, as well as a safe coupled-running process. A robust optimization method is proposed to capture the stochastic delays as an uncertainty set, which is reformulated to its dual problem. Case studies of planning train trajectories for the classical virtual-coupling scenario suggest that (1) the coupled-running distance is greatly affected by the coordination of train timetables, delays, and safe separation constraints at switches; (2) the coordination of train movements for a coupled-running process imposes extra energy costs; and (3) the proposed method can detect feasible coupled-running locations and produce cooperative speed profiles in short computational times.@en

This paper studies the train trajectory optimization problem of two opposite trains on single-Track railway lines. A two-Train trajectory optimization problem is formulated using the multiple-phase optimal control model, where the timetable as well as train performance parameters, track gradients, curves, speed limits and energy-saving requirements are taken into account. Multiple-Tracks at stations are reflected in the model, so that trains may use different tracks at stations. A meeting constraint is developed to avoid head-on conflicts between opposite trains on open tracks. The trajectories of the two opposite trains are optimized simultaneously by a pseudospectral method with minimizing energy consumption as the objective function. In addition, an optimization method is developed for energy-efficient time-distance paths for two opposite trains based on the two-Train trajectory optimization model. The method is applied in case studies of two opposite trains running on a Dutch single-Track railway corridor. The results show that our method is able to produce optimal trajectories and time-distance paths for both trains within a short time.@en

This paper proposes a novel multi-train trajectory optimization for single-track lines. We restrict our attention to delay cases aiming at finding optimal speed profiles, which reduce delays and save energy consumption. A multi-train trajectory optimization method is proposed to find optimal meeting locations, arrival/departure times, and speed trajectories of multiple trains within the time and speed windows. The proposed method first finds timetable constraint sets for trains under delayed situations. The timetable constraint sets provide drivable, feasible, and energy-efficient time and speed windows along the trains’ routes. The multi-train trajectory optimization method uses minimizing energy consumption and reducing delays as the objective functions, and takes into account each train's operational constraints as well as constraints to avoid conflicts between adjacent trains. Three driving strategies of delay-recovery, energy-efficient and on-time driving, are proposed and combined in the optimization objective selection for different delay scenarios. The multi-train trajectory optimization is formulated as a multiple-phase optimal control problem and solved by a pseudospectral method. The proposed method is applied in case studies of opposite trains running on a Dutch single-track railway corridor with different initial delay scenarios. The results show that our method is able to produce a feasible schedule with energy-efficient speed trajectories for all interacting trains.@en

The train trajectory optimization problem aims at finding the optimal speed profiles and control regimes for a safe, punctual, comfortable, and energy-efficient train operation. This paper studies the train trajectory optimization problem with consideration of general operational constraints as well as signalling constraints. Operational constraints refer to time and speed restrictions from the actual timetable, while signalling constraints refer to the influences of signal aspects and automatic train protection on train operation. A railway timetable provides each train with a train path envelope, which consists of a set of positions on the route with a specified target time and speed point or window. The train trajectory optimization problem is formulated as a multiple-phase optimal control model and solved by a pseudospectral method. This model is able to capture varying gradients and speed limits, as well as time and speed constraints from the train path envelope. Train trajectory calculation methods under delay and no-delay situations are discussed. When the train follows the planned timetable, the train trajectory calculation aims at minimizing energy consumption, whereas in the case of delays the train trajectory is re-calculated to track the possibly adjusted timetable with the aim of minimizing delays as well as energy consumption. Moreover, the train operation could be affected by yellow or red signals, which is taken into account in the train speed regulation. For this purpose, two optimization policies are developed with either limited or full information of the train ahead. A local signal response policy ensures that the train makes correct and quick responses to different signalling aspects, while a global green wave policy aims at avoiding yellow signals and thus proceed with all green signals. The method is applied in a case study of two successive trains running on a corridor with various delays showing the benefit of accurate predictive information of the leading train on energy consumption and train delay of the following train.@en

This paper proposes an approach to facilitate smooth merging of freight trains into a stream of passenger trains with short headways, to help drivers better control freight trains and avoid red signals. An algorithm architecture is proposed for Driver Advisory Systems (DASs) to compute time/speed advice for freight train drivers. The framework includes four parts: buffer stairway prediction, freight train movement prediction, merging window detection and merging optimization. The basic idea is to predict the traffic state in the merging area regularly and find the feasible merging time window. Proper advice can be presented to freight train drivers and help them to merge smoothly, by comparing the freight train movement to the feasible merging window. The performance of the proposed algorithms is illustrated on examples of merging freight trains in the Meteren and Kijfhoek areas on the Dutch railway network. The experimental results show the efficiency and quality of the proposed algorithms on real world size problems.@en

This paper proposes an approach to facilitate smooth merging of freight trains into a stream of passenger trains with short headways, to help drivers better control freight trains and avoid red signals. An algorithm architecture is proposed for Driver Advisory Systems (DASs) to compute time/speed advice for freight train drivers. The framework includes four parts: buffer stairway prediction, freight train movement prediction, merging window detection and merging optimization. The basic idea is to predict the traffic state in the merging area regularly and find the feasible merging time window. Proper advice can be presented to freight train drivers and help them to merge smoothly, by comparing the freight train movement to the feasible merging window. The performance of the proposed algorithms is illustrated on examples of merging freight trains in the Meteren and Kijfhoek areas on the Dutch railway network. The experimental results show the efficiency and quality of the proposed algorithms on real world size problems.@en

The railway systems are affected by unexpected disturbances on a daily basis causing delays to trains and passengers. Real-time traffic management is necessary and is currently handled by human traffic controllers who mainly focus on minimizing train delays. In the past two decades, extensive research has been done to improve railway traffic management by shifting the focus to passengers (generally called delay management) using optimization or heuristics. The existing optimization-based models are difficult to solve efficiently. The existing heuristics perform well in terms of computational efficiency but are based on simplified passenger behaviours. In this paper, we propose an efficient method including complex passenger behaviours. That is a Reinforcement Learning (RL) framework for delay management (at a network-level for mainline railways) aiming to minimize passenger destination delays. In our method, passengers re-plan their travels when actually miss their transfers (i.e. reactive behaviour) or when they are aware of better path choices than their current planned ones (i.e. proactive behaviour), whichever happens first. The re-plan behaviour is allowed to happen multiple times during a single journey of a passenger as long as it is beneficial. We tested the proposed RL approach on a real-world railway network and compared it to three benchmarks: the first-in-first-out (FIFO) dispatching rule that is widely adopted in practice, and the train-centric and passenger-centric optimization models (TcOM and PcOM) on timetable rescheduling. Results show the ability of our RL approach to obtain better rescheduling solutions (in terms of total passenger delays) than the FIFO and TcOM, and better computational efficiency (43 seconds on average after training) than the PcOM (4572 seconds on average). With sufficient training, 74% of the trained RL agents can solve all other new delay scenarios designed in our case study, implying good generalization performance of the proposed method.@en

The railway systems are affected by unexpected disturbances on a daily basis causing delays to trains and passengers. Real-time traffic management is necessary and is currently handled by human traffic controllers who mainly focus on minimizing train delays. In the past two decades, extensive research has been done to improve railway traffic management by shifting the focus to passengers (generally called delay management) using optimization or heuristics. The existing optimization-based models are difficult to solve efficiently. The existing heuristics perform well in terms of computational efficiency but are based on simplified passenger behaviours. In this paper, we propose an efficient method including complex passenger behaviours. That is a Reinforcement Learning (RL) framework for delay management (at a network-level for mainline railways) aiming to minimize passenger destination delays. In our method, passengers re-plan their travels when actually miss their transfers (i.e. reactive behaviour) or when they are aware of better path choices than their current planned ones (i.e. proactive behaviour), whichever happens first. The re-plan behaviour is allowed to happen multiple times during a single journey of a passenger as long as it is beneficial. We tested the proposed RL approach on a real-world railway network and compared it to three benchmarks: the first-in-first-out (FIFO) dispatching rule that is widely adopted in practice, and the train-centric and passenger-centric optimization models (TcOM and PcOM) on timetable rescheduling. Results show the ability of our RL approach to obtain better rescheduling solutions (in terms of total passenger delays) than the FIFO and TcOM, and better computational efficiency (43 seconds on average after training) than the PcOM (4572 seconds on average). With sufficient training, 74% of the trained RL agents can solve all other new delay scenarios designed in our case study, implying good generalization performance of the proposed method.@en

The railway systems are affected by unexpected disturbances on a daily basis causing delays to trains and passengers. Real-time traffic management is necessary and is currently handled by human traffic controllers who mainly focus on minimizing train delays. In the past two decades, extensive research has been done to improve railway traffic management by shifting the focus to passengers (generally called delay management) using optimization or heuristics. The existing optimization-based models are difficult to solve efficiently. The existing heuristics perform well in terms of computational efficiency but are based on simplified passenger behaviours. In this paper, we propose an efficient method including complex passenger behaviours. That is a Reinforcement Learning (RL) framework for delay management (at a network-level for mainline railways) aiming to minimize passenger destination delays. In our method, passengers re-plan their travels when actually miss their transfers (i.e. reactive behaviour) or when they are aware of better path choices than their current planned ones (i.e. proactive behaviour), whichever happens first. The re-plan behaviour is allowed to happen multiple times during a single journey of a passenger as long as it is beneficial. We tested the proposed RL approach on a real-world railway network and compared it to three benchmarks: the first-in-first-out (FIFO) dispatching rule that is widely adopted in practice, and the train-centric and passenger-centric optimization models (TcOM and PcOM) on timetable rescheduling. Results show the ability of our RL approach to obtain better rescheduling solutions (in terms of total passenger delays) than the FIFO and TcOM, and better computational efficiency (43 seconds on average after training) than the PcOM (4572 seconds on average). With sufficient training, 74% of the trained RL agents can solve all other new delay scenarios designed in our case study, implying good generalization performance of the proposed method.@en

The problem of train trajectory optimization of two successive trains on the same line is studied in this paper. The two-train optimal control problem is formulated by using the multiple-phase method of optimal control, in which the train schedules as well as train performance parameters and track gradients, curves and speed limits are taken into account. The objective is to ensure a smooth, safe, punctual, and energy-efficient train operation. A green-wave (GW) policy is adopted to ensure that the trains proceed safely under all green signals. Special objective functions and constraints are developed in case of train delays. The method is applied in a case study of two successive trains running on a railway line with various input delays showing the benefit of the GW policy and the ability of delay recovery.@en