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21 pages, 1830 KiB  
Article
Optimization Model of Express–Local Train Schedules Under Cross-Line Operation of Suburban Railway
by Jingyi Zhu, Xin Guo and Jianju Pan
Appl. Sci. 2025, 15(14), 7853; https://doi.org/10.3390/app15147853 - 14 Jul 2025
Viewed by 222
Abstract
Cross-line operation and express–local train coordination are both crucial for enhancing the efficiency of multi-level urban rail transit systems. Most studies address suburban railway operations in isolation, overlooking coordination and inducing supply–demand mismatches that weaken system efficiency. This study addresses the joint optimization [...] Read more.
Cross-line operation and express–local train coordination are both crucial for enhancing the efficiency of multi-level urban rail transit systems. Most studies address suburban railway operations in isolation, overlooking coordination and inducing supply–demand mismatches that weaken system efficiency. This study addresses the joint optimization of cross-line operation and express–local scheduling by proposing a novel train timetable model. The model determines train service plans and departure times to minimize total system cost, including train operating and passenger travel costs. A space–time network represents integrated train–passenger interactions, and an extended adaptive large neighborhood search (E-ALNS) algorithm is developed to solve the model efficiently. Numerical experiments verify the effectiveness of the proposed approach. The E-ALNS achieves near-optimal solutions with less than 4% deviation from Gurobi. Comparative analysis shows that the proposed hybrid operation mode reduces total passenger travel cost by 6% and improves the cost efficiency ratio by 13% compared to independent operations. Sensitivity analyses further confirm the model’s robustness to variations in transfer walking time, passenger penalties, and waiting thresholds. This study provides a practical and scalable framework for optimizing train timetables in complex cross-line transit systems, offering insights for enhancing system coordination and passenger service quality. Full article
(This article belongs to the Section Transportation and Future Mobility)
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23 pages, 1794 KiB  
Article
Dynamic Rescheduling Strategy for Passenger Congestion Balancing in Airport Passenger Terminals
by Yohan Lee, Seung Chan Choi, Keyju Lee and Sung Won Cho
Mathematics 2025, 13(13), 2208; https://doi.org/10.3390/math13132208 - 7 Jul 2025
Viewed by 404
Abstract
Airports are facing significant challenges due to the increasing number of air travel passengers. After a significant downturn during the COVID-19 pandemic, airports are implementing measures to enhance security and improve their level of service in response to rising demand. However, the rising [...] Read more.
Airports are facing significant challenges due to the increasing number of air travel passengers. After a significant downturn during the COVID-19 pandemic, airports are implementing measures to enhance security and improve their level of service in response to rising demand. However, the rising passenger volume has led to increased congestion and longer waiting times, undermining operational efficiency and passenger satisfaction. While most previous studies have focused on static modeling or infrastructure improvements, few have addressed the problem of dynamically allocating passengers in real-time. To tackle this issue, this study proposes a mathematical model with a dynamic rescheduling framework to balance the workload across multiple departure areas where security screening takes place, while minimizing the negative impact on passenger satisfaction resulting from increased walking distances. The proposed model strategically allocates departure areas for passengers in advance, utilizing data-based predictions. A mixed integer linear programming (MILP) model was developed and evaluated through discrete event simulation (DES). Real operational data provided by Incheon International Airport Corporation (IIAC) were used to validate the model. Comparative simulations against four baseline strategies demonstrated superior performance in balancing workload, reducing waiting passengers, and minimizing walking distances. In conclusion, the proposed model has the potential to enhance the efficiency of the security screening stage in the passenger departure process. Full article
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27 pages, 1599 KiB  
Article
Optimization of Combined Urban Rail Transit Operation Modes Based on Intelligent Algorithms Under Spatiotemporal Passenger Imbalance
by Weisong Han, Zhihan Shi, Xiaodong Lv and Guangming Zhang
Sustainability 2025, 17(13), 6178; https://doi.org/10.3390/su17136178 - 5 Jul 2025
Viewed by 433
Abstract
With increasing attention to sustainability and energy efficiency in transportation systems, advanced intelligent algorithms provide promising solutions for optimizing urban rail transit operations. This study addresses the challenge of optimizing train operation plans for urban rail transit systems characterized by spatiotemporal passenger flow [...] Read more.
With increasing attention to sustainability and energy efficiency in transportation systems, advanced intelligent algorithms provide promising solutions for optimizing urban rail transit operations. This study addresses the challenge of optimizing train operation plans for urban rail transit systems characterized by spatiotemporal passenger flow imbalance. By exploring a combined short-turning and unpaired train operation mode, a three-objective optimization model was established, aiming to minimize operational costs, reduce passenger waiting times, and enhance load balancing. To effectively solve this complex problem, an Improved GOOSE (IGOOSE) algorithm incorporating elite opposition-based learning, probabilistic exploration based on elite solutions, and golden-sine mutation strategies were developed, significantly enhancing global search capability and solution robustness. A case study based on real operational data adjusted for confidentiality was conducted, and comparative analyses with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO) demonstrated the superiority of IGOOSE. Furthermore, an ablation study validated the effectiveness of each enhancement strategy within the IGOOSE algorithm. The optimized operation planning model reduced passenger waiting times by approximately 12.72%, improved load balancing by approximately 39.30%, and decreased the overall optimization objective by approximately 10.25%, highlighting its effectiveness. These findings provide valuable insights for urban rail transit operation management and indicate directions for future research, underscoring the significant potential for energy savings and emission reductions toward sustainable urban development. Full article
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26 pages, 1223 KiB  
Article
Genetic Algorithm and Mathematical Modelling for Integrated Schedule Design and Fleet Assignment at a Mega-Hub
by Melis Tan Tacoglu, Mustafa Arslan Ornek and Yigit Kazancoglu
Aerospace 2025, 12(6), 545; https://doi.org/10.3390/aerospace12060545 - 16 Jun 2025
Viewed by 438
Abstract
Airline networks are becoming increasingly complex, particularly at mega-hub airports characterized by high transit volumes. Effective schedule design and fleet assignment are critical for an airline, as they directly influence passenger connectivity and profitability. This study addresses the challenge of introducing a new [...] Read more.
Airline networks are becoming increasingly complex, particularly at mega-hub airports characterized by high transit volumes. Effective schedule design and fleet assignment are critical for an airline, as they directly influence passenger connectivity and profitability. This study addresses the challenge of introducing a new route from a mega-hub to a new destination, while maintaining the existing flight network and leveraging arrivals from spoke airports to ensure connectivity. First, a mixed-integer nonlinear mathematical model was formulated to produce a global optimal solution at a lower time granularity, but it became computationally intractable at higher granularities due to the exponential growth in constraints and variables. Second, a genetic algorithm (GA) was employed to demonstrate scalability and flexibility, delivering near-optimal, high-granularity schedules with significantly reduced computational time. Empirical validation using real-world data from 37 spoke airports revealed that, while the exact model minimized waiting times and maximized profit at lower granularity, the GA provided nearly comparable profit at higher granularity. These findings guide airline managers seeking to optimize passenger connectivity and cost efficiency in competitive global markets. Full article
(This article belongs to the Section Air Traffic and Transportation)
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25 pages, 1240 KiB  
Article
An Intelligent Heuristic Algorithm for a Multi-Objective Optimization Model of Urban Rail Transit Operation Plans
by Weisong Han, Zhihan Shi, Xiaodong Lv and Guangming Zhang
Sustainability 2025, 17(10), 4617; https://doi.org/10.3390/su17104617 - 18 May 2025
Viewed by 441
Abstract
Urban rail transit (URT) systems frequently face operational challenges arising from temporal and spatial imbalances in passenger demand, resulting in inefficiencies in train scheduling and resource utilization. To address these issues, this study proposes a multi-objective optimization model that jointly plans short-turn and [...] Read more.
Urban rail transit (URT) systems frequently face operational challenges arising from temporal and spatial imbalances in passenger demand, resulting in inefficiencies in train scheduling and resource utilization. To address these issues, this study proposes a multi-objective optimization model that jointly plans short-turn and full-length train services. The objectives of the model are to minimize total passenger waiting time and train mileage while improving passenger load distribution across the rail line, subject to practical constraints such as departure frequency limitations, rolling stock availability, and coverage of short-turn services. To efficiently solve this model, an improved Pelican Optimization Algorithm (POA) is developed, incorporating techniques such as Tent chaotic mapping, nonlinear weight adjustment, Cauchy mutation, and the sparrow alert mechanism, significantly enhancing convergence accuracy and computational efficiency. A real-world case study based on Nanjing Metro Line 1 demonstrates that the proposed framework substantially reduces average passenger waiting times and overall train mileage, achieving a more balanced distribution of passenger loads. In addition, the study reveals that flexible-ratio dispatching strategies, representing theoretically optimal solutions, outperform integer-ratio dispatching schemes that reflect real-world operational constraints. This finding underscores that investigating the practical feasibility and optimization potential of flexible-ratio scheduling strategies constitutes a valuable direction for future research. The outcomes of this study provide a scalable and intelligent decision-support framework for train scheduling in URT systems, effectively contributing to the sustainable and intelligent development of rail operations. Full article
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18 pages, 1759 KiB  
Article
DHDRDS: A Deep Reinforcement Learning-Based Ride-Hailing Dispatch System for Integrated Passenger–Parcel Transport
by Huanwen Ge, Xiangwang Hu and Ming Cheng
Sustainability 2025, 17(9), 4012; https://doi.org/10.3390/su17094012 - 29 Apr 2025
Viewed by 1001
Abstract
Urban transportation demands are growing rapidly. Concurrently, the sharing economy continues to expand. These dual trends establish ride-hailing dispatch as a critical research focus for building sustainable smart transportation systems. Current ride-hailing systems only serve passengers. However, they ignore an important opportunity: transporting [...] Read more.
Urban transportation demands are growing rapidly. Concurrently, the sharing economy continues to expand. These dual trends establish ride-hailing dispatch as a critical research focus for building sustainable smart transportation systems. Current ride-hailing systems only serve passengers. However, they ignore an important opportunity: transporting packages. This limitation causes two issues: (1) wasted vehicle capacity in cities, and (2) extra carbon emissions from cars waiting idle. Our solution combines passenger rides with package delivery in real time. This dual-mode strategy achieves four benefits: (1) better matching of supply and demand, (2) 38% less empty driving, (3) higher vehicle usage rates, and (4) increased earnings for drivers in changing conditions. We built a Dynamic Heterogeneous Demand-aware Ride-hailing Dispatch System (DHDRDS) using deep reinforcement learning. It works by (a) managing both passenger and package requests on one platform and (b) allocating vehicles efficiently to reduce the environmental impact. An empirical validation confirms the developed framework’s superiority over conventional approaches across three critical dimensions: service efficiency, carbon footprint reduction, and driver profits. Specifically, DHDRDS achieves at least a 5.1% increase in driver profits and an 11.2% reduction in vehicle idle time compared to the baselines, while ensuring that the majority of customer waiting times are within the system threshold of 8 min. By minimizing redundant vehicle trips and optimizing fleet utilization, this research provides a novel solution for advancing sustainable urban mobility systems aligned with global carbon neutrality goals. Full article
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30 pages, 7693 KiB  
Article
Analyzing New Operation Strategy of Demand-Responsive Transports Using Discrete-Event Simulation Framework
by Seung-Wan Cho, Yeong-Hyun Lim, Seong-Hyeon Ju and Kyung-Min Seo
Systems 2025, 13(4), 303; https://doi.org/10.3390/systems13040303 - 21 Apr 2025
Viewed by 581
Abstract
Demand-responsive transport (DRT) provides flexible ride-sharing by dynamically adjusting routes based on real-time user demand, making it suitable for complex urban mobility needs. This study proposes a modular simulation framework based on the DEVS (Discrete Event System Specification) formalism and introduces an “express [...] Read more.
Demand-responsive transport (DRT) provides flexible ride-sharing by dynamically adjusting routes based on real-time user demand, making it suitable for complex urban mobility needs. This study proposes a modular simulation framework based on the DEVS (Discrete Event System Specification) formalism and introduces an “express service” strategy that enables direct trips without intermediate stops. The framework supports scenario-based analysis using key performance indicators (KPIs) and allows for flexible testing of operational strategies. Two experiments were conducted: the first validated the simulation model under varying demand and fleet conditions; and the second assessed the impact of the express service. Results showed that express passengers experienced significantly shorter waiting and riding times, while standard passenger service remained stable. The strategy also improved operational efficiency under constrained resources. This study contributes to a configurable simulation platform for evaluating differentiated DRT services and provides practical insights for adaptive service planning, especially in urban settings where tiered mobility solutions are increasingly needed. Full article
(This article belongs to the Special Issue Modelling and Simulation of Transportation Systems)
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19 pages, 3446 KiB  
Article
Hybrid Model for Motorway EV Fast-Charging Demand Analysis Based on Traffic Volume
by Bojan Rupnik, Yuhong Wang and Tomaž Kramberger
Systems 2025, 13(4), 272; https://doi.org/10.3390/systems13040272 - 9 Apr 2025
Cited by 1 | Viewed by 592
Abstract
The expected growth of electric vehicle (EV) usage will not only increase the energy demand but also bring the requirement to provide the necessary electrical infrastructure to handle the load. While charging infrastructure is becoming increasingly present in urban areas, special attention is [...] Read more.
The expected growth of electric vehicle (EV) usage will not only increase the energy demand but also bring the requirement to provide the necessary electrical infrastructure to handle the load. While charging infrastructure is becoming increasingly present in urban areas, special attention is required for transit traffic, not just for passengers but also for freight transport. Differences in the nature of battery charging compared to that of classical refueling require careful planning in order to provide a resilient electrical infrastructure that will supply enough energy at critical locations during peak hours. This paper presents a hybrid simulation model for analyzing fast-charging demand based on traffic flow, projected EV adoption, battery characteristics, and environmental conditions. The model integrates a probabilistic model for evaluating the charging requirements based on traffic flows with a discrete-event simulation (DES) framework to analyze charger utilization, waiting queues, and energy demand. The presented case of traffic flow on Slovenian motorways explored the expected power demands at various seasonal traffic intensities. The findings provide valuable insight for planning the charging infrastructure, the electrical grid, and also the layout by anticipating the number of vehicles seeking charging services. The modular design of the model allowed replacing key parameters with different traffic projections, supporting a robust scenario analysis and adaptive infrastructure planning. Replacing the parameters with real-time data opens the path for integration into a digital twin framework of individual EV charging hubs, providing the basis for development of an EV charging hub network digital twin. Full article
(This article belongs to the Special Issue Modelling and Simulation of Transportation Systems)
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16 pages, 2854 KiB  
Article
Evaluating the Level of Balance Between Demand and Supply at Bus Stops Using Smartcard Data
by Shin-Hyung Cho
Sustainability 2025, 17(7), 3278; https://doi.org/10.3390/su17073278 - 7 Apr 2025
Cited by 1 | Viewed by 495
Abstract
The efficient operation of urban bus systems necessitates the alignment of service supply with passenger demand. An inadequate supply of services results in passenger inconvenience, whereas excessive supply leads to inefficiencies for operators. This study introduces a performance measure to evaluate the equilibrium [...] Read more.
The efficient operation of urban bus systems necessitates the alignment of service supply with passenger demand. An inadequate supply of services results in passenger inconvenience, whereas excessive supply leads to inefficiencies for operators. This study introduces a performance measure to evaluate the equilibrium between demand and supply at bus stops. The methodology involves deriving cumulative distribution functions (CDFs) of passenger waiting times during peak (High Ridership Period, HRP) and non-peak hours (Non-High Ridership Period, NHRP) using smartcard data. The maximum vertical distance between these CDFs, along with their definite integrals, serves as the basis for the performance metric. Using a reference threshold of 0.16, bus stops are categorized into three groups: those experiencing excessive demand, those operating in a balanced state, and those with insufficient supply during non-peak hours. This method was applied to 1785 bus stops in Seoul, demonstrating that balanced stops exhibited the shortest average waiting times. The analysis also revealed that stops with excessive demand had significantly higher ridership, whereas stops with lower supply showed ambiguous boundaries between the HRP and NHRP. The proposed performance measure offers a valuable tool for assessing and enhancing the service levels of public transport systems. Full article
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20 pages, 4397 KiB  
Article
Ridesharing Methods for High-Speed Railway Hubs Considering Path Similarity
by Wendie Qin, Liangjie Xu, Di Zhu, Wanheng Liu and Yan Li
Sustainability 2025, 17(7), 2975; https://doi.org/10.3390/su17072975 - 27 Mar 2025
Viewed by 312
Abstract
We propose a hub ridesharing method that considers path similarity to swiftly evacuate high volumes of passengers arriving at a high-speed railway hub. The technique aims to minimize total mileage and the number of service vehicles, considering the characteristics of hub passengers, such [...] Read more.
We propose a hub ridesharing method that considers path similarity to swiftly evacuate high volumes of passengers arriving at a high-speed railway hub. The technique aims to minimize total mileage and the number of service vehicles, considering the characteristics of hub passengers, such as the constraints of large luggage, departure times, and arrival times. Meanwhile, to meet passengers’ expectations, a path morphology similarity indicator combining directional and locational features is developed and used as a crucial criterion for passenger matching. A two-stage algorithm is designed as a solution. Passenger requests are clustered based on path vector similarity in the first stage using a heuristic approach. In the second stage, we employ an adaptive large-scale neighborhood search to form passenger matches and shared routes. The experiments demonstrate that this method can reduce operational costs, enhance computational efficiency, and shorten passenger wait times. Taking path similarity into account significantly decreases passenger detour distances. It improves the Jaccard coefficient (JAC) of post-ridesharing paths, fulfilling the passenger’s psychological expectation that the shared route will closely resemble the original one. Full article
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25 pages, 7009 KiB  
Article
Modular Scheduling Optimization of Multi-Scenario Intelligent Connected Buses Under Reservation-Based Travel
by Wei Shen, Honglu Cao and Jiandong Zhao
Sustainability 2025, 17(6), 2645; https://doi.org/10.3390/su17062645 - 17 Mar 2025
Viewed by 646
Abstract
In the context of big data and intelligent connectivity, optimizing scheduled bus dispatch can enhance urban transit efficiency and passenger experience, which is vital for the sustainable development of urban transportation. This paper, based on existing fixed bus stops, integrates traditional demand-responsive transit [...] Read more.
In the context of big data and intelligent connectivity, optimizing scheduled bus dispatch can enhance urban transit efficiency and passenger experience, which is vital for the sustainable development of urban transportation. This paper, based on existing fixed bus stops, integrates traditional demand-responsive transit and travel booking models, considering the spatiotemporal variations in scheduled travel demands and passenger flows and addressing the combined scheduling issues of fixed-capacity bus models and skip-stop strategies. By leveraging intelligent connected technologies, it introduces a dynamic grouping method, proposes an intelligent connected bus dispatching model, and optimizes bus timetables and dispatch control strategies. Firstly, the inherent travel characteristics of potential reservation users are analyzed based on actual transit data, subsequently extracting demand data from reserved passengers. Secondly, a two-stage optimization program is proposed, detailing passenger boarding and alighting at each stop and section passenger flow conditions. The first stage introduces a precise bus–traveler matching dispatch model within a spatial–temporal–state framework, incorporating ride matching to minimize parking frequency in scheduled travel scenarios. The second stage addresses spatiotemporal variations in passenger demand and station congestion by employing a skip-stop and bus operation control strategy. This strategy enables the creation of an adaptable bus operation optimization model for temporal dynamics and station capacity. Finally, a dual-layer optimization model using an adaptive parameter grid particle swarm optimization algorithm is proposed. Based on Beijing’s Route 300 operational data, the simulation-driven study implements contrasting scenarios of different bus service patterns. The results demonstrate that this networked dispatching system with dynamic vehicle grouping reduces operational costs by 29.7% and decreases passenger waiting time by 44.15% compared to baseline scenarios. Full article
(This article belongs to the Special Issue Innovative and Sustainable Development of Transportation)
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16 pages, 13024 KiB  
Article
Edge Computing Based on Convolutional Neural Network for Passenger Counting: A Case Study in Guadalajara, Mexico
by Roxana Sánchez Laguna, Ulises Davalos-Guzman and Lina M. Aguilar-Lobo
Sensors 2025, 25(6), 1695; https://doi.org/10.3390/s25061695 - 9 Mar 2025
Viewed by 1042
Abstract
One of the most common deficiencies in the public transport system is long waiting times. Currently, in the Guadalajara Metropolitan Area, Mexico, the frequencies of routes are fixed, making it impossible to satisfy a demand with a dynamic variation. An intelligent public transport [...] Read more.
One of the most common deficiencies in the public transport system is long waiting times. Currently, in the Guadalajara Metropolitan Area, Mexico, the frequencies of routes are fixed, making it impossible to satisfy a demand with a dynamic variation. An intelligent public transport system is required. The first step to solve this problem is knowing the number of users so that we can respond appropriately to each scenario. In this context, this work focuses on the design and implementation of an embedded system module for passenger counting that can be used to improves public transport service quality. This work presents three contributions. First, a design and experimental validation of the passenger counting system is presented to determine the number of users in an image and send this information to a server suitable for the public transportation system in Guadalajara, Mexico. Second, the generation of two new datasets is reported for training and testing the CSRNet algorithm with images of public transportation systems in Mexican cities. Finally, we make the hardware implementation of the passenger counting system in a Jetson Nano development board. Full article
(This article belongs to the Special Issue Cloud and Edge Computing for IoT Applications)
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23 pages, 2713 KiB  
Article
Mathematical Modeling of Ride-Hailing Matching Considering Uncertain User and Driver Preferences: Interval-Valued Fuzzy Approach
by Sudradjat Supian, Subiyanto Subiyanto, Sisilia Sylviani, Tubagus Robbi Megantara, Abdul Talib Bon and Vasile Preda
Mathematics 2025, 13(3), 371; https://doi.org/10.3390/math13030371 - 23 Jan 2025
Viewed by 1152
Abstract
This study introduces a fuzzy interval-valued approach using multi-objective linear programming to optimize passenger–driver matching in ride-hailing systems, addressing uncertainties in waiting times and fare preferences. The model aims to minimize total waiting times, balance job allocations among drivers, and reduce deviations in [...] Read more.
This study introduces a fuzzy interval-valued approach using multi-objective linear programming to optimize passenger–driver matching in ride-hailing systems, addressing uncertainties in waiting times and fare preferences. The model aims to minimize total waiting times, balance job allocations among drivers, and reduce deviations in fare expectations between passengers and drivers. The proposed framework effectively manages operational uncertainties by incorporating interval-valued fuzzy parameters, including traffic variability and fluctuating demand patterns. Numerical experiments using real-world data demonstrate that the interval-valued fuzzy model significantly outperforms deterministic methods in reducing average waiting times, achieving higher request fulfillment rates, and ensuring a more equitable distribution of assignments among drivers. The results highlight the model’s robustness and adaptability, particularly under high uncertainty scenarios, and its ability to maintain service reliability and user satisfaction. While computational complexity remains a limitation, integrating the model with AI and IoT technologies offers promising avenues for scalability and real-time applications. These findings contribute to advancing optimization frameworks in ride-hailing systems, emphasizing uncertainty management’s importance in enhancing operational efficiency and fairness. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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21 pages, 2215 KiB  
Article
Optimizing Modular Vehicle Public Transportation Services with Short-Turning Strategy and Decoupling/Coupling Operations
by Honglu Cao and Jiandong Zhao
Sustainability 2025, 17(3), 870; https://doi.org/10.3390/su17030870 - 22 Jan 2025
Viewed by 1079
Abstract
In public transportation systems, the passenger demand during peak hours is characterized by over-saturation at intermediate stops and directional imbalances, and the traditional single scheduling strategy and fixed capacity cannot solve the contradiction between the demand and capacity mismatch. In order to accurately [...] Read more.
In public transportation systems, the passenger demand during peak hours is characterized by over-saturation at intermediate stops and directional imbalances, and the traditional single scheduling strategy and fixed capacity cannot solve the contradiction between the demand and capacity mismatch. In order to accurately match demand and capacity, this paper proposes a method to optimize the service of a public transportation system by using a short-turning strategy combined with decoupled/coupled operation of modular vehicles (MVs). The short-turning strategy is used to alleviate the heavy passenger flow at intermediate stations, and the decoupling/coupling operations of MVs are employed to flexibly adjust the capacity levels in different directions. Considering urban space limitations, depots for storing modular units (MUs) are only set up at the starting and ending stations of bidirectional lines. MVs can not only adjust the departure capacity at the starting station but also consider whether to decouple/couple at turnaround stations for short-turning trips to achieve a more effective supply–demand match, with the decoupled/coupled MUs being deadheaded from or provided by the depot. We formulated this problem as an integer nonlinear programming (INLP) model, jointly optimizing the departure intervals of each trip, the capacity of MVs, the turnaround scheme for short-turning trips, and the decoupling/coupling scheme for MVs at turnaround stations, with the aim of minimizing passenger waiting time costs and vehicle operating costs. To facilitate a solution, we equivalently transformed some nonlinear terms in the model, which was then solved by the commercial solver Gurobi. The numerical study shows that, compared with the traditional full-length strategy combined with conventional buses, the model proposed in this paper can reduce the total system cost by about 19.59%. In particular, it can achieve precise matching between passenger demand and transport capacity, thereby reducing the passenger waiting time cost by about 29.99%. Compared with the full-length strategy combined with MVs, the total system cost is also reduced by about 14.65%. The research results contribute to enhancing the service quality and efficiency of public transportation systems, which is of great significance to the sustainable development of these systems. Full article
(This article belongs to the Section Sustainable Transportation)
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18 pages, 2443 KiB  
Article
Integrated Optimization of Train Schedules and Transportation Plans for a Passenger–Freight Metro Line
by Zhen Di, Hanqi Zuo, Housheng Zhou, Jianguo Qi and Shenghu Zhang
Sustainability 2025, 17(2), 730; https://doi.org/10.3390/su17020730 - 17 Jan 2025
Viewed by 1228
Abstract
Against the backdrop of developing metro-based passenger and freight co-transportation plans, this study addresses the integrated optimization problem of train scheduling and flow control for a co-transportation metro line, where passengers and freight can share the same trains. Given a set of time-dependent [...] Read more.
Against the backdrop of developing metro-based passenger and freight co-transportation plans, this study addresses the integrated optimization problem of train scheduling and flow control for a co-transportation metro line, where passengers and freight can share the same trains. Given a set of time-dependent passenger and freight demands, the problem involves determining the space-time trajectories and passenger (or freight) capacities of trains while simultaneously assigning these demands to the trains. To tackle this, train selection variables, carriage arrangement variables, and flow assignment variables are introduced, and the problem is formulated as an integer linear programming model. The objective is to minimize the weighted sum of the number of freight carriages, the total waiting time of all passengers, and the total delay of all freight. The proposed model is equivalent to a mixed-integer linear programming model, which allows a commercial solver to efficiently find the exact solution. To validate the effectiveness of the proposed method, several numerical examples of varying scales are tested. The results demonstrate that integrating the optimization of train schedules and co-transportation plans significantly enhances the efficiency of the entire co-transportation system. Full article
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