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Mathematical Optimization in Transportation Engineering
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Mathematical Optimization in Transportation Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 29098

Special Issue Editors

Prof. Dr. Jin Qin

E-Mail Website
Guest Editor
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China
Interests: optimization; transportation engineering
Dr. Yuche Chen

E-Mail Website
Guest Editor
Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA
Interests: transportation and sustainability; AI-augmented simulation and optimization of transportation and urban infrastructure systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gang Ren

E-Mail Website
Guest Editor
School of Transportation, Southeast University, 2 Sipailou, Nanjing 210096, China
Interests: multimodal transportation system simulation; traffic behavior and safety analysis; emergency traffic management; active transport optimization; transportation resilience
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical tools are used routinely in many areas of transportation engineering as an effective way of providing optimal solutions to real-world problems. This Special Issue is devoted to “Mathematical Optimization in Transportation Engineering” and focuses on areas that involve the application of mathematics and numerical methods to problems in transportation/traffic/logistics/supply chain.

The main purposes of this Special Issue are to present recent advances in utilizing the innovative mathematical technologies and provide real-world applications in the field of transportation engineering.

Editors invite authors to contribute original research papers and high-quality review papers related to mathematical optimization in transportation engineering, which include traffic planning and design, transportation scheme, traffic flow, travel behavior, forecasting, public transport management, multimodal transport, cold chain transportation, traffic signal control, vehicle routing, supply chain, logistics network, revenue management, and optimization techniques, simulation analysis, and decision analysis related to transportation engineering.

Prof. Dr. Jin Qin
Dr. Yuche Chen
Prof. Dr. Gang Ren
Guest Editors

Manuscript Submission Information

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Keywords

  • mathematical model
  • optimization
  • planning and design
  • transportation scheme
  • transportation network
  • traffic flow
  • forecasting
  • public transport
  • passenger transport
  • freight transport
  • multimodal transport

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Related Special Issue

Published Papers (12 papers)

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Research

Jump to: Review

27 pages, 5209 KiB  
Article
Designing Flexible-Bus System with Ad-Hoc Service Using Travel-Demand Clustering
by Xuekai Cen, Kanghui Ren, Yiying Cai and Qun Chen
Mathematics 2023, 11(4), 825; https://doi.org/10.3390/math11040825 - 6 Feb 2023
Cited by 2 | Viewed by 1660
Abstract
Providing direct and affordable transit services for travelers is the goal of the evolving flexible-bus (FB) system. In this study, we design an FB system with an ad-hoc service, to supplement traditional public transit and provide a better FB service. We first build [...] Read more.
Providing direct and affordable transit services for travelers is the goal of the evolving flexible-bus (FB) system. In this study, we design an FB system with an ad-hoc service, to supplement traditional public transit and provide a better FB service. We first build up a mathematical model to optimize bus-stop sites, routes, and schedules, where the unmet travel demand is served by an ad-hoc service with relatively high cost. Then, we cluster travel demand spatially and temporarily, using the ST-DBSCAN algorithm. We use the simulated-annealing algorithm, which has better convergence and diversity than other heuristic algorithms, to solve the suggested model in large-scale networks. To demonstrate the effectiveness of the proposed model, we run experiments on a small network and a large real-world network of Shenzhen airport, which shows that the FB system with ad-hoc service can reduce overall cost and improve social welfare, compared to taxies and FB only. In addition, it provides affordable transit services with shorter walking distances and lower waiting times, which can be deployed in airports or high-speed railway stations with massive, irregular travel demands. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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16 pages, 5290 KiB  
Article
A Game-Theory-Based Approach to Modeling Lane-Changing Interactions on Highway On-Ramps: Considering the Bounded Rationality of Drivers
by Weihan Chen, Gang Ren, Qi Cao, Jianhua Song, Yikun Liu and Changyin Dong
Mathematics 2023, 11(2), 402; https://doi.org/10.3390/math11020402 - 12 Jan 2023
Cited by 6 | Viewed by 2469
Abstract
In highway on-ramp sections, the conflictual interactions between a subject vehicle (merging vehicle) in the acceleration lane and a following vehicle (lagging vehicle) in the adjacent mainline can lead to traffic congestion, go–stop oscillations, and serious safety hazards. Human drivers combine their previous [...] Read more.
In highway on-ramp sections, the conflictual interactions between a subject vehicle (merging vehicle) in the acceleration lane and a following vehicle (lagging vehicle) in the adjacent mainline can lead to traffic congestion, go–stop oscillations, and serious safety hazards. Human drivers combine their previous lane-changing experience and their perception of surrounding traffic conditions to decide whether to merge. However, the decisions that they make are not always optimal in specific traffic scenarios due to fuzzy perception and misjudgment. That is, they make lane-changing decisions in a bounded rational way. In this paper, a game-theory-based approach is used to model the interactive behavior of mandatory lane-changing in a highway on-ramp section. The model comprehensively considers vehicle interactions and the bounded rationality of drivers by modeling lane-changing behavior on on-ramps as a two-person non-zero-sum non-cooperative game with incomplete information. In addition, the Logit QRE is used to explain the bounded rationality of drivers. In order to estimate the parameters, a bi-level programming framework is built. Vehicle trajectory data from NGSIM and an unmanned aerial vehicle survey were used for model calibration and validation. The validation results were rigorously evaluated by using various performance indicators, such as the mean absolute error, root mean square error, detection rate, and false-alarm rate. It can be seen that the proposed game theory-based model was able to effectively predict merging and yielding interactions with a high degree of accuracy. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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21 pages, 8165 KiB  
Article
A Heuristic Approach for Multi-Path Signal Progression Considering Traffic Flow Uncertainty
by Tianrui Hai, Gang Ren, Weihan Chen, Qi Cao and Changyin Dong
Mathematics 2023, 11(2), 377; https://doi.org/10.3390/math11020377 - 10 Jan 2023
Viewed by 1258
Abstract
The multi-path progression of an arterial signal model, generally, is applied to arterial traffic scenarios with large turning flows. However, existing methods generally fail to capture traffic flow uncertainty, which leads to high sensitivity to fluctuations in traffic flow. To bridge this gap, [...] Read more.
The multi-path progression of an arterial signal model, generally, is applied to arterial traffic scenarios with large turning flows. However, existing methods generally fail to capture traffic flow uncertainty, which leads to high sensitivity to fluctuations in traffic flow. To bridge this gap, in this study, a heuristic approach for multi-path signal progression is proposed to deal with the uncertainties of flow fluctuation by using distributionally flow scenarios. The model varies the phase sequence and the offsets of each intersection to achieve optimal progression with weighting of efficiency and stability. The preference degree of the efficiency and stability of the model is selected by adjusting the efficiency stability coefficient and solved by using a genetic algorithm. A case study and comparison experiment with benchmark models is presented and analyzed to prove the advantages of the proposed model. The results show that the standard deviation of the proposed model decreases by 45% as compared with conventional methods. It indicates that the model proposed in this paper can reduce congestion due to uncertainties, and can significantly improve stability, on the premise of ensuring that the efficiency index maintains a better value. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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16 pages, 4532 KiB  
Article
Differential Evolution Based Numerical Variable Speed Limit Control Method with a Non-Equilibrium Traffic Model
by Irena Strnad and Rok Marsetič
Mathematics 2023, 11(2), 265; https://doi.org/10.3390/math11020265 - 4 Jan 2023
Cited by 4 | Viewed by 1657
Abstract
This paper introduces a numerical variable speed limit (VSL) control method on a motorway, modeled by the system of partial differential equations (PDEs) of a non- equilibrium continuum traffic model. The method consists of a macroscopic simulation (i.e., numerical solution of the system [...] Read more.
This paper introduces a numerical variable speed limit (VSL) control method on a motorway, modeled by the system of partial differential equations (PDEs) of a non- equilibrium continuum traffic model. The method consists of a macroscopic simulation (i.e., numerical solution of the system of PDEs of the continuum model), introduction of the solution-based cost function and numerical optimization with a differential evolution algorithm (DE). Due to the numerical solution scheme, the method enables application of a wide range of continuum traffic models without prior discretization of PDEs. In this way, the method overcomes the limitations of the basic continuum models and represents a step towards more accurate traffic modelling in control strategies. In this paper, we determine optimal variable speed limits with the DE algorithm on a motorway section modeled by the modified switching curve model, which is a non-equilibrium continuum model consistent with the three-phase traffic flow theory. The effectiveness of the determined variable speed limits is validated using microsimulations of the test section, which show promising reductions of queue lengths and number of stops. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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19 pages, 8157 KiB  
Article
A Framework to Analyze Function Domains of Autonomous Transportation Systems Based on Text Analysis
by Xiangzhi Huang, Xuekai Cen, Ming Cai and Rui Zhou
Mathematics 2023, 11(1), 158; https://doi.org/10.3390/math11010158 - 28 Dec 2022
Cited by 1 | Viewed by 1482
Abstract
With the development of information and communication technologies, the current intelligent transportation systems (ITSs) will gradually become automated and connected, and can be treated as autonomous transportation systems (ATSs). Function, which unites cutting-edge technology with ATS services as a fundamental component of ATS [...] Read more.
With the development of information and communication technologies, the current intelligent transportation systems (ITSs) will gradually become automated and connected, and can be treated as autonomous transportation systems (ATSs). Function, which unites cutting-edge technology with ATS services as a fundamental component of ATS operation, should be categorized into function domains to more clearly show how ATS operates. Existing ITS function domains are classified mostly based on the experience of experts or the needs of practitioners, using vague classification criteria. To ensure tractability, we aim to categorize ATS functions into function domains based on text analysis, minimizing the reliance on subjective experience. First, we introduce the Latent Dirichlet Allocation (LDA) topic model to extract text features of functions into distribution weights, reflecting the semantics of the text data. Second, based on the LDA model, we categorize ATS functions into twelve function domains by the k-means method. The comparison between the proposed function domains and the existing counterparts of other ITS framework demonstrates the effectiveness of the LDA-based classification method. This study provides a reference for text processing and function classification of ATS architecture. The proposed functions and function domains reveal the objectives in future transportation systems, which could guide urban planners or engineers to better design control strategies when facing new technologies. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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21 pages, 2287 KiB  
Article
Neural Network-Based Hybrid Forecasting Models for Time-Varying Passenger Flow of Intercity High-Speed Railways
by Huanyin Su, Shuting Peng, Shanglin Mo and Kaixin Wu
Mathematics 2022, 10(23), 4554; https://doi.org/10.3390/math10234554 - 1 Dec 2022
Cited by 5 | Viewed by 1601
Abstract
Time-varying passenger flow is the input data in the optimization design of intercity high-speed railway transportation products, and it plays an important role. Therefore, it is necessary to predict the origin-destination (O-D) passenger flow at different times of the day in combination with [...] Read more.
Time-varying passenger flow is the input data in the optimization design of intercity high-speed railway transportation products, and it plays an important role. Therefore, it is necessary to predict the origin-destination (O-D) passenger flow at different times of the day in combination with the stable time-varying characteristics. In this paper, three neural network-based hybrid forecasting models are designed and compared, named Variational Mode Decomposition-Multilayer Perceptron (VMD-MLP), Variational Mode Decomposition-Gated Recurrent Unit Neural Network (VMD-GRU), and Variational Mode Decomposition-Bidirectional Long Short-Term Memory Neural Network (VMD-Bi-LSTM). First, the time-varying characteristics of passenger travel demand under different time granularities are analyzed and extracted by the VMD method. Second, three neural network prediction models are constructed to predict the passenger flow sequence after VMD decomposition and reconstruction. Experimental analysis is performed on the Guangzhou Zhuhai intercity high-speed railway in China, and the passenger flow at different time periods of the day under different time granularities is predicted. The following results were found: (i) The number of hidden neurons and the number of iterations of the hybrid forecasting model have a great impact on the prediction accuracy. The error of the VMD-MLP model fluctuates less and it performs more smoothly than both the VMD-GRU model and the VMD-Bi-LSTM model. (ii) The VMD-MLP, VMD-GRU, and VMD-Bi-LSTM models can basically reduce the MAPE error to less than 10%. With the increase of time granularity, RMSE and MAE errors tend to gradually increase, while the MAPE error tends to gradually decrease. (iii) For passenger flow under a smaller time granularity, the prediction accuracy of the VMD-MLP model is higher, while for passenger flow under a larger time granularity, the prediction accuracy of the VMD-GRU and VMD-Bi-LSTM models is higher. (iv) The proposed neural network-based hybrid models outperform the existing models and the hybrid models perform better than the single models. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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20 pages, 750 KiB  
Article
Analysis of the Accident Propensity of Chinese Bus Drivers: The Influence of Poor Driving Records and Demographic Factors
by Lili Zheng, Xinyu He, Tongqiang Ding, Yanlin Li and Zhengfeng Xiao
Mathematics 2022, 10(22), 4354; https://doi.org/10.3390/math10224354 - 19 Nov 2022
Cited by 3 | Viewed by 2048
Abstract
Previous studies have shown that bus drivers are a major contributing factor to bus accidents. The aim of this study is to explore the factors that contribute to the presence of accident propensity among bus drivers, as well as the relative importance of [...] Read more.
Previous studies have shown that bus drivers are a major contributing factor to bus accidents. The aim of this study is to explore the factors that contribute to the presence of accident propensity among bus drivers, as well as the relative importance of each influencing factor and the mechanism of influence. To this end, a C5.0 decision tree model was developed to determine the relative importance as well as rank the importance of the impact of poor driving records and demographic factors on accident propensity, and a binary logistic regression model was developed to analyze the relationship between accident propensity and the different values of each essential influencing factor. Based on our results, we found that: (1) the number of violations had the most significant effect on bus drivers’ accident propensity, followed by age, driving age, and number of alarms; (2) violations and alarms are positively related to bus driver accident propensity; age and driving age are inversely related to bus driver accident propensity; and (3) men have a higher accident risk probability than women. This study’s findings will help bus companies and traffic management authorities to implement more targeted improvements to their bus driver management programs. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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17 pages, 5004 KiB  
Article
On-Street Cruising for Parking Model in Consideration with Gaming Elements and Its Impact Analysis
by Wei Wang, Yuwei Zhou, Jianbin Liu and Baofeng Sun
Mathematics 2022, 10(19), 3423; https://doi.org/10.3390/math10193423 - 21 Sep 2022
Cited by 2 | Viewed by 1742
Abstract
On-street cruising by drivers impedes the effectiveness of road traffic conditions and increases energy consumption and environmental impact. Existing models of on-street cruising for parking mainly embody those intrinsic on-street parking factors and disregard the extrinsic impacts from off-street parking gaming factors. This [...] Read more.
On-street cruising by drivers impedes the effectiveness of road traffic conditions and increases energy consumption and environmental impact. Existing models of on-street cruising for parking mainly embody those intrinsic on-street parking factors and disregard the extrinsic impacts from off-street parking gaming factors. This research focused on both the intrinsic and extrinsic elements, especially gaming factors, of off-street parking, i.e., the price of off-street parking, the waiting time of off-street parking, and the difference in walking time between their parking lots to their destinations. On-street cruising for a parking model is reconstructed in this paper in consideration with the equilibrium cruising time, i.e., the maximum tolerable cruise time after evaluating the cost of on-street and off-street parking. Correlation analysis showed that the off-street parking gaming factors were all positively related with the maximum tolerable cruise time. A simulation model was further presented for on-street cruising for the parking model by the cellular automata approach with real-world data. Simulation experiments demonstrated that the average speed of vehicles on the street increases by 9.858 km/h, the average delay decreases by 44.934 s, and the price of on-street parking increases by 4.5 CNY/h. The proposed on-street cruising for parking model proved effective by decreasing the maximum tolerable cruising time to bring significant improvements in average speed, average delay, and on-street cruising vehicles in road traffic flow. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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18 pages, 3778 KiB  
Article
Developing a Variable Speed Limit Control Strategy for Mixed Traffic Flow Based on Car-Following Collision Avoidance Theory
by Chen Yuan, Yuntao Shi, Bin Pan and Ye Li
Mathematics 2022, 10(16), 2987; https://doi.org/10.3390/math10162987 - 18 Aug 2022
Cited by 1 | Viewed by 2586
Abstract
Variable speed limit (VSL) control is an effective technology to improve safety near freeway bottlenecks. This study aims to develop a control strategy for mixed traffic flow consisting of both human-driven vehicles (HDVs) and connected and automated vehicles (CAVs) based on collision avoidance [...] Read more.
Variable speed limit (VSL) control is an effective technology to improve safety near freeway bottlenecks. This study aims to develop a control strategy for mixed traffic flow consisting of both human-driven vehicles (HDVs) and connected and automated vehicles (CAVs) based on collision avoidance theory. A microscopic simulation platform is first established, and four vehicle longitudinal dynamic models including Cruising model, Intelligent Driver Model (IDM), Adaptive Cruise Control model (ACC), Cooperative Cruise Control model (CACC) and one vehicle lateral dynamic model Minimizing Overall Braking Induced by Lane Changes model (MOBIL) are incorporated into the simulation platform. Then, a new VSL control strategy derived from collision avoidance theory is proposed for mixed traffic flow at the initial stage of CAVs’ popularization. Extensive simulation experiments are conducted, and surrogate safety measures and total travel time indicators are utilized to evaluate the safety and efficiency performances of the proposed VSL control. Results indicate that the proposed VSL control strategy can effectively improve the safety performance near freeway bottlenecks with an acceptable efficiency level. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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16 pages, 729 KiB  
Article
Improving the Road and Traffic Control Prediction Based on Fuzzy Logic Approach in Multiple Intersections
by Sadiqa Jafari, Zeinab Shahbazi and Yung-Cheol Byun
Mathematics 2022, 10(16), 2832; https://doi.org/10.3390/math10162832 - 9 Aug 2022
Cited by 14 | Viewed by 3696
Abstract
Traffic congestion is a significant issue in many countries today. The suggested method is a novel control method based on multiple intersections considering the kind of traffic light and the duration of the green phase to determine the optimal balance at intersections by [...] Read more.
Traffic congestion is a significant issue in many countries today. The suggested method is a novel control method based on multiple intersections considering the kind of traffic light and the duration of the green phase to determine the optimal balance at intersections by using fuzzy logic control, for which the balance should be adaptable to the unchanging behavior of time. It should reduce traffic volume in transport, average waits for each vehicle, and collisions between cars by controlling this balance in response to the typical behavior of time and randomness in traffic conditions. The proposed method is investigated at intersections using a sampling multi-agent system to set traffic light timings appropriately. The program is provided with many intersections, each of which is an independent entity exchanging information with the others. The stability per entity is proven separately. Simulation results show that Takagi–Sugeno (TS) fuzzy modeling performs better than Takagi–Sugeno (TS) fixed-time scheduling in decreasing the length of queueing times for vehicles. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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18 pages, 2630 KiB  
Article
Enhancing Model-Based Anticipatory Traffic Signal Control with Metamodeling and Adaptive Optimization
by Wei Huang, Yang Hu and Xuanyu Zhang
Mathematics 2022, 10(15), 2640; https://doi.org/10.3390/math10152640 - 27 Jul 2022
Cited by 4 | Viewed by 1608
Abstract
Traffic signal control is one effective way to alleviate traffic congestion. Anticipatory traffic signal control determines signal settings from a network planning perspective, which takes into account the influence of travelers’ route choice response and triggers better equilibrium flow patterns for better network [...] Read more.
Traffic signal control is one effective way to alleviate traffic congestion. Anticipatory traffic signal control determines signal settings from a network planning perspective, which takes into account the influence of travelers’ route choice response and triggers better equilibrium flow patterns for better network performance. For the route choice response, it is usually predicted by a response function known as traffic assignment model. However, the response behavior can never be precisely modeled, leading to a mismatch between the modeled and real traffic flow patterns. This model-reality mismatch generally contributes to suboptimal control performance and hence brings unexpected congestion in real-life traffic operations. This study aims to address the model-reality mismatch and proposes an effective anticipatory traffic control for real operations. A metamodel is introduced that serves as a surrogate of the unknown structural model bias. Then an iterative optimizing control scheme is applied to correct the model bias by learning from observations. By integrating the model-based control design with data-driven learning techniques, the metamodeling framework is able to enhance the control performance. Moreover, the analytical model bias formulation allows theoretical investigation of the model approximation error. To further improve the control performance, a joint traffic model parameter estimation is developed, hence achieving a better model calibration jointly with the model bias correction. The proposed control method is examined on a test network. Numerical examples confirm the effectiveness of the proposed method in improving control performance despite the model-reality mismatch. Comparison results show that the proposed method outperforms the traditional model-based control method and an improvement of 14.8% in total travel time is achieved in the example network. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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Review

Jump to: Research

17 pages, 932 KiB  
Review
A Literature Review of Railway Pricing Based on Revenue Management
by Xueyi Guan, Jin Qin, Chenghui Mao and Wenliang Zhou
Mathematics 2023, 11(4), 857; https://doi.org/10.3390/math11040857 - 8 Feb 2023
Cited by 2 | Viewed by 4827
Abstract
In recent decades, railway passenger transport enterprises have been exploring numerous operation and management strategies to improve service quality and market competitiveness of railway passenger transport so as to ensure that the interests of railway passenger transport enterprises are maximized when taking social [...] Read more.
In recent decades, railway passenger transport enterprises have been exploring numerous operation and management strategies to improve service quality and market competitiveness of railway passenger transport so as to ensure that the interests of railway passenger transport enterprises are maximized when taking social welfare into account. However, there are still shortcomings in the current research with respect to determining the pricing mechanism and formulating a reasonable price. This paper systematically reviews the scientific literature related to railway pricing, focusing on the application of basic price methods, mathematical programming methods, and data-driven methods in railway pricing, with the hope of proposing an innovative direction to solve existing problems. The main subjects involved in the formulation of railway pricing are passenger groups and transportation companies. The research can be conducted from four broad aspects: passenger demand, passenger time value, market segmentation, and the equilibrium relationship between rail service supply and passenger demand. On the basis of absorbing and summarizing the strengths and weaknesses of previous studies, this paper puts forward suggestions for improvement and innovative directions which will help promote railway passenger transport services from the perspective of pricing, thereby enhancing the sustainability of railway transport. Full article
(This article belongs to the Special Issue Mathematical Optimization in Transportation Engineering)
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