Container reloading in international railway transport involves transferring containers to trains compatible with the destination’s railway gauge. The duration depends on factors like port facilities, staff proficiency, and customs clearance. Accurate forecasting is crucial for efficient planning and railway efficiency, including predicting train travel times and informing consignment customers about arrivals. However, current prediction methods cannot handle fluctuating nonlinear container reloading times and are too subjective in forest learner selection. Therefore, this paper proposes a novel structure-optimized deep learning model named the intelligent Bayesian deep forest (IBDF) model, which combines the deep forest and Bayesian optimization methods to handle complex datasets in predicting the railway port container reloading times. In this model, a combinatorial optimization algorithm incorporating an integer programming model and the Hungarian algorithm is first proposed to identify the optimal types of forest learners. Then, hyperparameter optimization technique is designed to obtain the optimal number of forest learners per type selected. Based on the container reloading time data from the Alataw Pass border station of China Railway Express (Chengdu-Europe) from 2017 to 2020, the performance of the IBDF model is systematically compared with ten benchmark models. This model averagely reduces the values of MSE, RMSE, MAE, and MAPE by 68.62%, 51.90%, 67.41%, and 59.52%, respectively. The prediction results show that the IBDF model provides high quality predictions, which can support the container reloading operations at the Alataw Pass border station, compressing the customs clearance time, and boosting the quality and speed of China Railway Express trains.

Unexpected disruptions in urban rail transit systems cause the infeasibility of the initial train schedule and delays or cancelations of a lot of trains. Even though some recent studies begun to address the rolling stock and timetable optimization problem (RSTO), there is still a large gap between theoretical models and practical applications due to the real-time requirements of train rescheduling decisions. In this work, we first model RSTO using a path-based formulation, in which each path refers to a spatial-temporal trajectory of a rescheduled train in the considered network. The optimal set of paths can minimize the expected cost of train cancelation and train delay time. Our formulation also considers a series of operational constraints, such as train headway constraints, short-turning constraints and rolling stock constraints. We develop an efficient branch-and-price framework that decomposes the problem into a restricted master problem and a set of pricing subproblems, where we iteratively generate promising paths with negative reduce costs. We show that each subproblem is a resource-constrained shortest path problem and can be solved efficiently by an improved label setting algorithm by proving its optimality conditions. We compare the tightness of our new path-based formulation with state-of-art formulations and test our branch-and-price approach on real-world instances from Beijing rail transit. The results show that our approach can generate near-optimal solutions in less than three minutes with small duality gap, which evidently outperforms existing formulations and fulfills the requirement of rail managers in practical applications. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72288101 and 72322022]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0391 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0391 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

In this article, a fixed-time deep reinforcement learning (DRL) formation hunting control problem is investigated for a multi-marine surface vehicle (MSV) system. First, considering the lack of dynamic adaptability caused by the conventional deep neural network (DNN) framework, an online adaptive DNN method is proposed for the high-dimensional multi-MSV system. Second, a novel DRL framework is developed for designing fixed-time formation hunting controllers, which integrates the online adaptive DNNs method with the actor–critic-based reinforcement learning (RL) algorithm. Finally, a nonsmooth fixed-time stability analysis is established for the nonsmooth closed-loop system induced by the DRL-based structure, which rigorously demonstrates that all signals converge within a fixed-time interval independent of initial states. The simulation example demonstrates the practical viability of the presented scheme.

In the stockyard of dry bulk materials such as coal and iron ore, multiple stacker-reclaimers operate collaboratively to enhance stockyard productivity. However, effectively planning the routes for these interconnected machines presents a significant challenge. We propose a new modeling framework for this conflict-free routing problem in which the reclaiming process is modeled in a so-called time-space network (TSN) framework. The formulated optimization problem is mixed integer programming (MIP), which has been proven NP-hard. To address its computational efficiency, we develop a two-level metaheuristic algorithm to simplify the encoding complexity of the original problem. In the developed two-level algorithm, a task priority ordering candidate is listed at the top level, while the detailed conflict-free routes are constructed at the bottom level using an insertion-based conflict-free reclaiming and customized route improvement. The developed metaheuristic is tested on a large number of instances in comparison with the Gurobi solver and three commonly used methods for such a routing problem. The experimental results show that the proposed algorithm outperforms the other four methods regarding the solution quality and the computation time. Note to Practitioners—This study is motivated by the need for efficient route planning of interconnected reclaimers in the stockyard of dry bulk materials such as coal and iron ore. To address this problem, we present a novel modeling framework for addressing the conflict-free routing problem, wherein the reclaiming process is intricately modeled within a so-called time-space network framework. Solving the resulting mixed-integer programming is of high computational complexity; therefore, we have engineered a two-level metaheuristic framework to reduce its complexity. The developed methodology has been extensively tested on instances featuring real-world stockyard operations and contributes to terminal operators by improving productivity and resulting in more economic benefits. Future research will integrate real-time data and dynamic optimization techniques to facilitate routing decisions that can adapt to evolving operational conditions and stockyard configurations.

Train breakdowns have significant negative impacts on metro systems and passengers. In this context, the implementation of a train-to-train rescue serves as a crucial mechanism to restore operations promptly. This paper proposes a train rescheduling approach in the case of a train breakdown, incorporating a train-to-train rescue on a metro line. The train-to-train rescue procedure is formulated into two sub-models according to the depot position and the operating direction of the faulty train. The train timetable rescheduling and the rolling stock rescheduling problems are simultaneously considered in this paper by leveraging advanced rescheduling strategies such as the flexible short-turning and adding backup trains. Subsequently, a two-stage approach is developed to solve the model. Additionally, some valid inequalities are proposed to improve the lower bound of the model. Simulations are carried out using a case study based on the real-world data from the Beijing metro Yizhuang line to verify the effectiveness of the train rescheduling model. The proposed algorithms achieve high-quality solutions within a reasonable timeframe, surpassing the efficiency of the CPLEX optimizer.

This paper investigates a novel routing problem of a multi-robot station in a manufacturing cell. In the existing literature, the objective is to minimize the cycle time or energy consumption separately. The routing problem considered in this paper aims to reduce the cycle time and energy consumption jointly for each robot while avoiding collisions between these robots. For this routing problem, we propose a new flexible time-space network model that allows us to reduce energy consumption while minimizing the cycle time. The corresponding optimization problem is Mixed-Integer Nonlinear Programming (MINLP). For addressing its computational complexity, this paper designs a metaheuristic algorithm tailored to the studied problem and proposes an$\varepsilon $-constraint algorithm to study the trade-off between these two objectives. We conduct industrially relevant simulation experiments of case studies to show its effectiveness, in comparison to a conventional method, two state-of-the-art solvers, and two commonly-used metaheuristics. The results show that the proposed methodology can reduce energy consumption by up to 30% without compromising the cycle time. Meanwhile, the proposed algorithm can provide efficient solutions within a reasonable computation time.Note to Practitioners—This paper is motivated by the problem of improving energy efficiency when routing cooperative robots in a manufacturing station. In current approaches for routing multi-robot stations, the cycle time and energy consumption are minimized separately. This paper focuses on the movement of the robot end-effector and its connected joint and suggests a new approach to minimize these two objectives jointly by proposing a new mathematical model. The resulting planning problem is computationally intractable. A customized metaheuristic algorithm is thus designed for efficiently solving this planning problem. Our meta-heuristic algorithm is integrated with the$\varepsilon $-constraint method to study the relationship between these two objectives. Simulation experiments suggest that this approach can reduce energy consumption considerably, for the shortest cycle time, compared with the current approaches. In future research, the movements of multi-joints will be investigated whereby 3-D collision-free trajectory planning will be considered.

Most of the existing path planning methods of automated guided vehicles (AGVs) are static. This paper proposes a new methodology for the path planning of a fleet of AGVs to improve the flexibility, robustness, and scalability of the AGV system. We mathematically describe the transport process as a dynamical system using an ad hoc mixed logical dynamical (MLD) model. Based on our MLD model, model predictive control is proposed to determine the collision paths dynamically, and the corresponding optimization problem is formulated as 0–1 integer linear programming. An alternating direction method of multipliers (ADMM)-based decomposition technique is then developed to coordinate the AGVs and reduce the computational burden, aiming for real-time decisions. The proposed methodology is tested on industrial scenarios, and results from numerical experiments show that the proposed method can obtain high transport productivity of the multi-AGV system at a low computational burden and deal with uncertainties resulting from the industrial environment.

Railway traffic management focuses on regulating train movements and delivering improved service quality to passengers; however, such efforts are subject to many uncertainties in terms of disruptions and passenger demand on a rail transit line. In contrast to most existing studies, which focus on the rescheduling of passenger timetables in a deterministic framework, this study proposes a two-stage stochastic optimization model for allocating backup rolling stocks (BRS) to storage lines to reschedule the timetable and serve passengers delayed by disruptions. The first stage is an assignment problem to determine the optimal plan for the allocation of BRS to storage lines to achieve a good trade-off between the investment cost for the BRS and the expected travel time of delayed passengers across different stochastic scenarios. The second stage is explicitly formulated as a network flow model to optimize the timetable of the delayed trains on the tracks and the BRS from the storage lines such that the passenger travel time is minimized under each stochastic scenario. To improve the efficiency of convergence, we develop an improved L-shaped method with several accelerating techniques. Among these, we show that the classical integer L-shaped cut can be tightened given the property of the second-stage problem, which can also be generalized to other two-stage integer stochastic programs. Real-world case studies based on historical data from the Beijing metro verify the effectiveness of the proposed approach in reducing the travel time for passengers. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This research was supported by the National Natural Science Foundation of China [Grants 71621001, 71825004, and 71901016]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1233 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at [ http://dx.doi.org/10.5281/zenodo.6892548 ].

This paper investigates a new lane reservation problem with task merging that consists of optimally determining which lanes in a transportation network have to be reserved and designing reserved lane-based routes in the network for time-crucial transport tasks. Part of the tasks whose destinations are geographically close is merged to reduce the number of vehicles and transport costs. Reserved lanes can reduce the travel time of task vehicles passing through them, while they will generate negative impact on normal traffic, such as traffic delay to the vehicles on adjacent non-reserved lanes. The objective is to minimize the total negative impact of all reserved lanes. For this problem, two new integer linear programming (ILP) models are first developed. The complexity of the problem is proved to be NP-hard. Since commercial solver (like CPLEX) is time-consuming for solving it when the problem size increases, a fast and effective improved differential evolution algorithm (IDEA) is developed based on explored problem properties. Extensive experimental results for a real-life case and benchmark instances of up to 500 nodes in the network and 30 transport tasks show the favorable performance of the IDEA, as compared to CPLEX, differential evolution algorithm and genetic algorithm. Management insights are also drawn to support practical decision-making.

Energy consumption is expected to be reduced while maintaining high productivity for container handling. This paper investigates a new energy-efficient scheduling problem of automated container terminals, in which quay cranes (QCs) and lift automated guided vehicles (AGVs) cooperate to handle inbound and outbound containers. In our scheduling problem, operation times and task sequences are both to be determined. The underlying optimization problem is mixed-integer nonlinear programming (MINLP). To deal with its computational intractability, a customized and efficient genetic algorithm (GA) is developed to solve the studied MINLP problem, and lexicographic and weighted-sum strategies are further considered. An$\epsilon $-constraint algorithm is also developed to analyze the Pareto frontiers. Comprehensive experiments are tested on a container handling benchmark system, and the results show the effectiveness of the proposed lexicographic GA, compared to results obtained with two commonly-used metaheuristics, a commercial MINLP solver, and two state-of-the-art methods.

In metro systems, a tactical train schedule with the rolling stock circulation plan aims to determine the movements of all physical trains. To utilize the regenerative energy as much as possible, this paper proposes an integrated model to simultaneously generate the optimal train schedule and rolling stock circulation plan, in which the brake-traction overlapping time at stations is maximized. In particular, our model rigorously considers the train turn-around constraints, train circulation constraints, and dynamic passenger demands to tackle the train loading capacity constraints. To eliminate the effect of non-linear constraints, we reformulate the original model into its equivalent linear model that can be efficiently solved by linear programming solvers. Finally, the numerical experiments based on Beijing Yizhuang Metro Line are implemented to demonstrate the effectiveness of our proposed model.

The aircraft scheduling problem (ASP) is the real‐time problem of scheduling takeoff and landing operations at a congested airport in a given time horizon, taking into account the runways and the air segments in the terminal maneuvering area . The ASP can be viewed as a job shop scheduling problem with additional real‐world constraints. Compared with the current literature based on job shop scheduling applied to solve the ASP, we enrich the existing models by including new formulations of relevant practical constraints. We introduce and analyze three alternative ASP formulations, in which the objective function is the minimization of delay propagation with respect to the off‐line timetable. Scheduling rules, heuristic and exact methods are implemented and tested on instances from the Roma Fiumicino airport, in Italy. Computational experiments show that practical‐size instances are solved to near‐optimality by our branch and bound algorithm in a few seconds of computation. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(3), 212–227 2015

Railway dispatchers reschedule trains in real-time in order to limit the propagation of disturbances and to regulate traffic in their respective dispatching areas by minimizing the deviation from the off-line timetable. However, the decisions taken in one area may influence the quality and even the feasibility of train schedules in the other areas. Regional control centers coordinate the dispatchers' work for multiple areas in order to regulate traffic at the global level and to avoid situations of global infeasibility. Differently from the dispatcher problem, the coordination activity of regional control centers is still underinvestigated, even if this activity is a key factor for effective traffic management. This paper studies the problem of coordinating several dispatchers with the objective of driving their behavior towards globally optimal solutions. With our model, a coordinator may impose constraints at the border of each dispatching area. Each dispatcher must then schedule trains in its area by producing a locally feasible solution compliant with the border constraints imposed by the coordinator. The problem faced by the coordinator is therefore a bilevel programming problem in which the variables controlled by the coordinator are the border constraints. We demonstrate that the coordinator problem can be solved to optimality with a branch and bound procedure. The coordination algorithm has been tested on a large real railway network in the Netherlands with busy traffic conditions. Our experimental results show that a proven optimal solution is frequently found for various network divisions within computation times compatible with real-time operations.

During rail operations, unforeseen events may cause timetable perturbations, which ask for the capability of traffic management systems to reschedule trains and to restore the timetable feasibility. Based on an accurate monitoring of train positions and speeds, potential conflicting routes can be predicted in advance and resolved in real time. The adjusted targets (location-time-speed) would be then communicated to the relevant trains by which drivers should be able to anticipate the changed traffic circumstances and adjust the train's speed accordingly. We adopt a detailed alternative graph model for the train dispatching problem. Conflicts between different trains are effectively detected and solved. Adopting the blocking time model, we ascertain whether a safe distance headway between trains is respected, and we also consider speed coordination issues among consecutive trains. An iterative rescheduling procedure provides an acceptable speed profile for each train over the intended time horizon. After a finite number of iterations, the final solution is a conflict-free schedule that respects the signaling and safety constraints. A computational study based on a hourly cyclical timetable of the Schiphol railway network has been carried out. Our automated dispatching system provides better solutions in terms of delay minimization when compared to dispatching rules that can be adopted by a human traffic controller