Yahan Lu
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1
Integrated demand-side management and timetabling for an urban rail transit line
A Benders decomposition approach
The intelligent upgrading of metropolitan rail transit systems has made it feasible to implement demand-side management policies that integrate multiple operational strategies in practical operations. However, the tight interdependence between supply and demand necessitates a coordinated approach combining demand-side management policies and supply-side resource allocations to enhance the urban rail transit ecosystem. In this study, we propose a mathematical and computational framework that optimizes train timetables, passenger flow control strategies, and trip-shifting plans through the pricing policy. Our framework incorporates an emerging trip-booking approach that transforms waiting at the stations into waiting at home, thereby mitigating station overcrowding. Additionally, it ensures service fairness by maintaining an equitable likelihood of delays across different stations. We formulate the problem as an integer linear programming model, aiming to minimize passengers’ waiting time and government subsidies required to offset revenue losses from fare discounts used to encourage trip shifting. To improve the computational efficiency, we develop a Benders decomposition-based algorithm within the branch-and-cut method, which decomposes the model into train timetabling with partial passenger assignment and passenger flow control subproblems. We propose valid inequalities based on our model's properties to strengthen the linear relaxation bounds at each node of the branch-and-bound tree. Computational results from proof-of-concept and real-world case studies on the Beijing metro show that our solution method outperforms commercial solvers in terms of computational efficiency. We can obtain high-quality solutions, including optimal ones, at the root node with reduced branching requirements thanks to our novel decomposition framework and valid inequalities. Our integrated optimization approach reduces the fleet size for operators by at least 8.33 % and decreases the waiting time of passengers on the tested instances, thereby validating the effectiveness of our proposed methods.
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The intelligent upgrading of metropolitan rail transit systems has made it feasible to implement demand-side management policies that integrate multiple operational strategies in practical operations. However, the tight interdependence between supply and demand necessitates a coordinated approach combining demand-side management policies and supply-side resource allocations to enhance the urban rail transit ecosystem. In this study, we propose a mathematical and computational framework that optimizes train timetables, passenger flow control strategies, and trip-shifting plans through the pricing policy. Our framework incorporates an emerging trip-booking approach that transforms waiting at the stations into waiting at home, thereby mitigating station overcrowding. Additionally, it ensures service fairness by maintaining an equitable likelihood of delays across different stations. We formulate the problem as an integer linear programming model, aiming to minimize passengers’ waiting time and government subsidies required to offset revenue losses from fare discounts used to encourage trip shifting. To improve the computational efficiency, we develop a Benders decomposition-based algorithm within the branch-and-cut method, which decomposes the model into train timetabling with partial passenger assignment and passenger flow control subproblems. We propose valid inequalities based on our model's properties to strengthen the linear relaxation bounds at each node of the branch-and-bound tree. Computational results from proof-of-concept and real-world case studies on the Beijing metro show that our solution method outperforms commercial solvers in terms of computational efficiency. We can obtain high-quality solutions, including optimal ones, at the root node with reduced branching requirements thanks to our novel decomposition framework and valid inequalities. Our integrated optimization approach reduces the fleet size for operators by at least 8.33 % and decreases the waiting time of passengers on the tested instances, thereby validating the effectiveness of our proposed methods.
Coordinated scheduling and pricing for public transport-oriented MaaS systems
A passenger-centric approach
This paper studies a coordinated service planning problem for public transport-oriented Mobility-as-a-Service (MaaS) systems under time-varying passenger demand. We consider the integrated optimization of schedules, vehicle compositions, stop patterns, pricing, the rebalancing strategy of modular units, and passenger routing in a multi-modal public transport network with metro and modular bus services. A public transport-oriented MaaS platform is modeled as a planning and coordination tool that recommends scheduling and pricing decisions to operators, rather than directly operating services or setting fares. To capture the interaction between supply-side service design and demand-side time-dependent passenger routing, we formulate a bi-objective mixed-integer nonlinear programming model that balances public welfare and financial sustainability. The model is reformulated as a single-objective optimization formulation via the ε-constraint method, and solved using a hybrid algorithm that combines Adaptive Large Neighborhood Search (ALNS) with GUROBI. Computational experiments on both small-scale and real-world instances demonstrate the effectiveness of the proposed approaches in supporting scalable, coordinated, and sustainable public transport planning within the MaaS framework and provide managerial insights.
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This paper studies a coordinated service planning problem for public transport-oriented Mobility-as-a-Service (MaaS) systems under time-varying passenger demand. We consider the integrated optimization of schedules, vehicle compositions, stop patterns, pricing, the rebalancing strategy of modular units, and passenger routing in a multi-modal public transport network with metro and modular bus services. A public transport-oriented MaaS platform is modeled as a planning and coordination tool that recommends scheduling and pricing decisions to operators, rather than directly operating services or setting fares. To capture the interaction between supply-side service design and demand-side time-dependent passenger routing, we formulate a bi-objective mixed-integer nonlinear programming model that balances public welfare and financial sustainability. The model is reformulated as a single-objective optimization formulation via the ε-constraint method, and solved using a hybrid algorithm that combines Adaptive Large Neighborhood Search (ALNS) with GUROBI. Computational experiments on both small-scale and real-world instances demonstrate the effectiveness of the proposed approaches in supporting scalable, coordinated, and sustainable public transport planning within the MaaS framework and provide managerial insights.
Emerging reservation-based travel technologies offer a promising solution to mitigate supply-demand mismatches in metro systems. This paper presents a framework to support metro operators by optimizing time-varying reservation slot allocation plans, passenger flow control strategies, and train schedules. The proposed approach ensures that passengers with reservations can directly access platforms and board the first available train services, while those without reservations are managed through effective passenger flow control strategies to optimize train capacity utilization. To address this, an integer nonlinear programming model is formulated, incorporating constraints that capture interactions between passengers with and without reservations, with the objective of minimizing passengers’ waiting time and line congestion. A hybrid algorithm is developed to improve computational efficiency, combining the adaptive large neighborhood search method with a commercial solver and incorporating valid inequalities tailored to the properties of the model. The effectiveness of the proposed approaches is demonstrated through numerical experiments using real-world operational data from the Beijing metro Batong line. Computational results indicate that the integrated optimization approach reduces the objective value by 6.19 % compared to a step-by-step optimization method, achieving better alignment of capacity with dynamic passenger flows. In addition, the extreme unfairness between reserved and unreserved passengers, where passengers with reservations have a 100 % service ratio compared to less than 20 % for unreserved passengers, is mitigated by increasing passenger waiting times by 3.51 % and line congestion by 0.51 %. Furthermore, the proposed algorithm efficiently solves large-scale and real-world instances, outperforming the state-of-the-art commercial solver.
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Emerging reservation-based travel technologies offer a promising solution to mitigate supply-demand mismatches in metro systems. This paper presents a framework to support metro operators by optimizing time-varying reservation slot allocation plans, passenger flow control strategies, and train schedules. The proposed approach ensures that passengers with reservations can directly access platforms and board the first available train services, while those without reservations are managed through effective passenger flow control strategies to optimize train capacity utilization. To address this, an integer nonlinear programming model is formulated, incorporating constraints that capture interactions between passengers with and without reservations, with the objective of minimizing passengers’ waiting time and line congestion. A hybrid algorithm is developed to improve computational efficiency, combining the adaptive large neighborhood search method with a commercial solver and incorporating valid inequalities tailored to the properties of the model. The effectiveness of the proposed approaches is demonstrated through numerical experiments using real-world operational data from the Beijing metro Batong line. Computational results indicate that the integrated optimization approach reduces the objective value by 6.19 % compared to a step-by-step optimization method, achieving better alignment of capacity with dynamic passenger flows. In addition, the extreme unfairness between reserved and unreserved passengers, where passengers with reservations have a 100 % service ratio compared to less than 20 % for unreserved passengers, is mitigated by increasing passenger waiting times by 3.51 % and line congestion by 0.51 %. Furthermore, the proposed algorithm efficiently solves large-scale and real-world instances, outperforming the state-of-the-art commercial solver.
Periodic timetabling is a crucial but computationally challenging problem in the railway planning field. Existing approaches often overlook the interaction between passenger routes and timetables, leading to suboptimal solutions. In this paper, we propose a method that incorporates passenger routing into the optimization of periodic timetables. Our goal is to optimize the periodic timetable from the strategic planning perspective, aiming to minimize the total perceived passenger travel time. We propose an iterative heuristic approach that integrates an adaptive large neighborhood search algorithm with a mixed-integer linear programming solver. To improve the efficiency of the algorithm, we design tailored operators and an outer loop. We conduct realworld case studies on real-life instances of Netherlands Railways to illustrate the effectiveness of our approach. The computational results show that our solution method is capable of addressing real-life problems.
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Periodic timetabling is a crucial but computationally challenging problem in the railway planning field. Existing approaches often overlook the interaction between passenger routes and timetables, leading to suboptimal solutions. In this paper, we propose a method that incorporates passenger routing into the optimization of periodic timetables. Our goal is to optimize the periodic timetable from the strategic planning perspective, aiming to minimize the total perceived passenger travel time. We propose an iterative heuristic approach that integrates an adaptive large neighborhood search algorithm with a mixed-integer linear programming solver. To improve the efficiency of the algorithm, we design tailored operators and an outer loop. We conduct realworld case studies on real-life instances of Netherlands Railways to illustrate the effectiveness of our approach. The computational results show that our solution method is capable of addressing real-life problems.
Journal article
(2024)
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Lei Mi, Yahan Lu, Lixing Yang, Jianguo Qi
The novel mixed passengers and freights transportation mode has brought both opportunities and challenges to the operation and management of high-speed railway in China. This paper proposes an integer linear programming model for the collaborative optimization problem of train schedules and freight allocation on a shared freight and passenger high-speed railway system to minimize the train dwell time, the number of detained freight, and operating costs, where the arrival and departure times of trains, the formation of trains, and the freight allocation are the decision variables. Then, extensive numerical experiments based on the operational data of the Beijing-Shanghai high-speed railway line are conducted to verify the effectiveness of the model, and the CPLEX optimization solver is used to solve the problem. The results show that the proposed method can improve the train capacity by flexibly deciding the train schedule and increasing the train composition while minimizing the impact on the quality of passenger service. Compared to the optimization method with fixed train timetables, the integrated optimization method can significantly improve the freight transportation capacity while only a slight increase in stopping time, providing theoretical support for the relevant operational departments to make mixed transportation plans.
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The novel mixed passengers and freights transportation mode has brought both opportunities and challenges to the operation and management of high-speed railway in China. This paper proposes an integer linear programming model for the collaborative optimization problem of train schedules and freight allocation on a shared freight and passenger high-speed railway system to minimize the train dwell time, the number of detained freight, and operating costs, where the arrival and departure times of trains, the formation of trains, and the freight allocation are the decision variables. Then, extensive numerical experiments based on the operational data of the Beijing-Shanghai high-speed railway line are conducted to verify the effectiveness of the model, and the CPLEX optimization solver is used to solve the problem. The results show that the proposed method can improve the train capacity by flexibly deciding the train schedule and increasing the train composition while minimizing the impact on the quality of passenger service. Compared to the optimization method with fixed train timetables, the integrated optimization method can significantly improve the freight transportation capacity while only a slight increase in stopping time, providing theoretical support for the relevant operational departments to make mixed transportation plans.
Journal article
(2024)
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Xiangjiang Li, Yahan Lu, Lixing Yang
With the advantages of high speed and punctuality, urban rail transit has become the preferred choice for many commuters. However, overcrowding of urban rail transit lines during peak hours is a common problem in megacities owing to the excessive passenger demand. To address this problem, this study proposes an integrated optimization method that combines passenger flow control and bus-bridging services. An integer nonlinear optimization model is developed to minimize the weighted passenger waiting time and operating cost of bus-bridging services by considering the coupling relationships between passenger movements on both the metro and buses. Then, the proposed model is equivalently transformed into a linear form with better mathematical properties, and variants of this model are further formulated to extend the usability. Finally, real-world case studies based on the operational data of the Beijing Metro Batong line are conducted to verify the effectiveness of the proposed methods. The computational results indicate that the proposed approach can effectively alleviate overcrowding and reduce passengers' waiting time, thereby improving the operational efficiency and safety of the urban rail transit system.
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With the advantages of high speed and punctuality, urban rail transit has become the preferred choice for many commuters. However, overcrowding of urban rail transit lines during peak hours is a common problem in megacities owing to the excessive passenger demand. To address this problem, this study proposes an integrated optimization method that combines passenger flow control and bus-bridging services. An integer nonlinear optimization model is developed to minimize the weighted passenger waiting time and operating cost of bus-bridging services by considering the coupling relationships between passenger movements on both the metro and buses. Then, the proposed model is equivalently transformed into a linear form with better mathematical properties, and variants of this model are further formulated to extend the usability. Finally, real-world case studies based on the operational data of the Beijing Metro Batong line are conducted to verify the effectiveness of the proposed methods. The computational results indicate that the proposed approach can effectively alleviate overcrowding and reduce passengers' waiting time, thereby improving the operational efficiency and safety of the urban rail transit system.
Robust collaborative passenger flow control on a congested metro line
A joint optimization with train timetabling
Journal article
(2023)
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Y. Lu, Lixing Yang, Hai Yang, Housheng Zhou, Ziyou Gao
With the rapid increase in residents in megacities, the passenger demand of metro systems is rising sharply and steadily, bringing immense pressure to train operations. To improve the service quality, this paper discusses systematically investigating a joint optimization of the robust passenger flow control strategy and train timetable on a congested metro line. A deterministic model for train timetabling and passenger flow control at each station is first developed to make a trade-off between operation efficiency and service fairness. Then, the uncertain passenger demand is further considered at each station, and three integer linear programming models are formulated to derive the robust passenger flow control strategies. The first two models are related to the technique of Light Robustness, in which the uncertainty is handled by inserting expected protection levels at stations or on trains. In addition, with a stochastic scenario set that characterizes the uncertain passenger information, the last model aims to find a solution that is feasible for all involved scenarios, and thus, reduces the impact of the uncertainty in metro systems. To improve the computational efficiency of large-scale instances, a customized decomposition-based algorithm is developed. Finally, some real-world case studies based on the operation data of the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.
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With the rapid increase in residents in megacities, the passenger demand of metro systems is rising sharply and steadily, bringing immense pressure to train operations. To improve the service quality, this paper discusses systematically investigating a joint optimization of the robust passenger flow control strategy and train timetable on a congested metro line. A deterministic model for train timetabling and passenger flow control at each station is first developed to make a trade-off between operation efficiency and service fairness. Then, the uncertain passenger demand is further considered at each station, and three integer linear programming models are formulated to derive the robust passenger flow control strategies. The first two models are related to the technique of Light Robustness, in which the uncertainty is handled by inserting expected protection levels at stations or on trains. In addition, with a stochastic scenario set that characterizes the uncertain passenger information, the last model aims to find a solution that is feasible for all involved scenarios, and thus, reduces the impact of the uncertainty in metro systems. To improve the computational efficiency of large-scale instances, a customized decomposition-based algorithm is developed. Finally, some real-world case studies based on the operation data of the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.
Conference paper
(2023)
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Xiangjiang Li, Yahan Lu
Due to the advantages of high punctuality and speed, urban rail transit systems are attracting more and more commuters. In consequence, overcrowding during peak periods has become the norm in megacities, which poses a great challenge to operations. To address this challenge, this paper investigates the integrated optimization of passenger flow control and bus-bridging on oversaturated urban rail transit lines. Based on the time-dependent passenger demand, we propose an integer nonlinear programming model that aims to minimize the overall system cost. Then, to cope with the solving difficulty due to nonlinearity, the proposed formulation is further transformed into an equivalent mixed-integer linear programming model. Finally, real-world case studies based on the operating data of Beijing metro Batong line are applied to verify the effectiveness of our proposed approach. The computational results illustrate that our proposed method can significantly reduce the average passenger waiting time and improve operational safety.
...
Due to the advantages of high punctuality and speed, urban rail transit systems are attracting more and more commuters. In consequence, overcrowding during peak periods has become the norm in megacities, which poses a great challenge to operations. To address this challenge, this paper investigates the integrated optimization of passenger flow control and bus-bridging on oversaturated urban rail transit lines. Based on the time-dependent passenger demand, we propose an integer nonlinear programming model that aims to minimize the overall system cost. Then, to cope with the solving difficulty due to nonlinearity, the proposed formulation is further transformed into an equivalent mixed-integer linear programming model. Finally, real-world case studies based on the operating data of Beijing metro Batong line are applied to verify the effectiveness of our proposed approach. The computational results illustrate that our proposed method can significantly reduce the average passenger waiting time and improve operational safety.
Journal article
(2023)
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Yahan Lu, Kai Yang, Lixing Yang, Dongyang Xia, Duo Wang
With the rapid development and expansion of the urban rail transit network in China, the coordination between different lines brings great challenges to the operation due to its high complexity. In order to minimize the unsuccessful transfer-passenger flows of last-train under the worse case with the given level of tolerance, a distributionally robust chance-constrained programming model is proposed for the last-train connection planning problem in urban rail transit networks under uncertain transfer-passenger demand. In particular, the probability distribution of uncertain parameters is only partially known. By analyzing the relationship between the distributionally robust optimization model and the corresponding robust optimization model, it is proved that the former is an extension of the latter. Furthermore, the original model can be reformulated into a second-order mixed-integer conic programming form under the Gaussian perturbations ambiguity set based on the limited information of expectation and variance, which can be solved by CPLEX. The results of numerical examples indicate that the proposed model can be solved to optimality quickly by CPLEX on a small network, and can effectively avoid over-conservative solutions compared to the robust optimization model and reduce unsuccessful transfer-passenger flows in the extreme situation compared with the stochastic programming model, which exhibits more robust performance.
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With the rapid development and expansion of the urban rail transit network in China, the coordination between different lines brings great challenges to the operation due to its high complexity. In order to minimize the unsuccessful transfer-passenger flows of last-train under the worse case with the given level of tolerance, a distributionally robust chance-constrained programming model is proposed for the last-train connection planning problem in urban rail transit networks under uncertain transfer-passenger demand. In particular, the probability distribution of uncertain parameters is only partially known. By analyzing the relationship between the distributionally robust optimization model and the corresponding robust optimization model, it is proved that the former is an extension of the latter. Furthermore, the original model can be reformulated into a second-order mixed-integer conic programming form under the Gaussian perturbations ambiguity set based on the limited information of expectation and variance, which can be solved by CPLEX. The results of numerical examples indicate that the proposed model can be solved to optimality quickly by CPLEX on a small network, and can effectively avoid over-conservative solutions compared to the robust optimization model and reduce unsuccessful transfer-passenger flows in the extreme situation compared with the stochastic programming model, which exhibits more robust performance.
Journal article
(2022)
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Y. Lu, Lixing Yang, Kai Yang, Ziyou Gao, Housheng Zhou, Fanting Meng, Jianguo Qi
Regular coronavirus disease 2019 (COVID-19) epidemic prevention and control have raised new requirements that necessitate operation-strategy innovation in urban rail transit. To alleviate increasingly serious congestion and further reduce the risk of cross-infection, a novel two-stage distributionally robust optimization (DRO) model is explicitly constructed, in which the probability distribution of stochastic scenarios is only partially known in advance. In the proposed model, the mean-conditional value-at-risk (CVaR) criterion is employed to obtain a tradeoff between the expected number of waiting passengers and the risk of congestion on an urban rail transit line. The relationship between the proposed DRO model and the traditional two-stage stochastic programming (SP) model is also depicted. Furthermore, to overcome the obstacle of model solvability resulting from imprecise probability distributions, a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form. A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming (MILP) solver is developed to improve the computational efficiency of large-scale instances. Finally, a series of numerical examples with real-world operation data are executed to validate the proposed approaches.
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Regular coronavirus disease 2019 (COVID-19) epidemic prevention and control have raised new requirements that necessitate operation-strategy innovation in urban rail transit. To alleviate increasingly serious congestion and further reduce the risk of cross-infection, a novel two-stage distributionally robust optimization (DRO) model is explicitly constructed, in which the probability distribution of stochastic scenarios is only partially known in advance. In the proposed model, the mean-conditional value-at-risk (CVaR) criterion is employed to obtain a tradeoff between the expected number of waiting passengers and the risk of congestion on an urban rail transit line. The relationship between the proposed DRO model and the traditional two-stage stochastic programming (SP) model is also depicted. Furthermore, to overcome the obstacle of model solvability resulting from imprecise probability distributions, a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form. A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming (MILP) solver is developed to improve the computational efficiency of large-scale instances. Finally, a series of numerical examples with real-world operation data are executed to validate the proposed approaches.
Journal article
(2021)
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Kai Yang, Yahan Lu, Lixing Yang, Ziyou Gao
Aiming to increase successful transfers at stations for late-night passengers, we first propose an efficient dwell time adjustment strategy for the last-train coordination planning problem under transfer-passenger flows uncertainty. Unlike the traditional robust optimization model, we present a novel distributionally robust chance-constrained program to model this problem, where the probability distributions of the uncertain parameters are only partially available. By introducing a pessimistic ambiguous chance constraint, the proposed distributionally robust model guarantees that the probability of satisfying the service-oriented objective, i.e., maximum successful transfer-passenger flows in the whole subway system is larger than a predetermined confidence level in the worst case. We then draw the connection of the distributionally robust model with the traditional robust optimization model, and show that the proposed model can be interpreted as a generalized version of the robust optimization model. We further propose a safe tractable approximation method to reformulate the original model as a mixed-integer second-order conic programming under the bounded-perturbation ambiguous set, which can be solved to optimality on only small instances by the CPLEX. Hence, we develop a tabu search heuristic algorithm to obtain high-quality solutions for large-sized instances. We also use local search as a baseline algorithm to observe the improvements of the tabu search algorithm. Finally, we illustrate the superiority of the developed model on the Nanjing and Beijing subway networks and compare the performance of the proposed algorithms.
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Aiming to increase successful transfers at stations for late-night passengers, we first propose an efficient dwell time adjustment strategy for the last-train coordination planning problem under transfer-passenger flows uncertainty. Unlike the traditional robust optimization model, we present a novel distributionally robust chance-constrained program to model this problem, where the probability distributions of the uncertain parameters are only partially available. By introducing a pessimistic ambiguous chance constraint, the proposed distributionally robust model guarantees that the probability of satisfying the service-oriented objective, i.e., maximum successful transfer-passenger flows in the whole subway system is larger than a predetermined confidence level in the worst case. We then draw the connection of the distributionally robust model with the traditional robust optimization model, and show that the proposed model can be interpreted as a generalized version of the robust optimization model. We further propose a safe tractable approximation method to reformulate the original model as a mixed-integer second-order conic programming under the bounded-perturbation ambiguous set, which can be solved to optimality on only small instances by the CPLEX. Hence, we develop a tabu search heuristic algorithm to obtain high-quality solutions for large-sized instances. We also use local search as a baseline algorithm to observe the improvements of the tabu search algorithm. Finally, we illustrate the superiority of the developed model on the Nanjing and Beijing subway networks and compare the performance of the proposed algorithms.
Journal article
(2021)
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Yahan Lu, Lixing Yang, Fanting Meng, Dongyang Xia, Jianguo Qi
Considering the continuous arrival characteristics of outside arrival passenger flow and the impulsive feature of transferring passengers, this paper investigates the metro train timetabling and passenger flow control strategy under the influence of transferring passengers. This paper formulates an integer nonlinear collaborative optimization model for the metro train timetabling and passenger flow control strategy, which aims to minimize the number of detained passengers. The proposed model is reformulated into an integer linear programming model by introducing the 0-1 decision variables. A case study of a real-world urban rail transit line is performed to verify the effectiveness of the proposed approach, which is solved by the CPLEX software. The results reveal that, the proposed approach has good optimization quality and computational efficiency. Compared to the plan only optimize timetables, the obtained plan reduced the number of detained passengers by 17.69% and the service level was significantly improved. This study provides theoretical support for the high-quality operation of the urban rail transit system.
...
Considering the continuous arrival characteristics of outside arrival passenger flow and the impulsive feature of transferring passengers, this paper investigates the metro train timetabling and passenger flow control strategy under the influence of transferring passengers. This paper formulates an integer nonlinear collaborative optimization model for the metro train timetabling and passenger flow control strategy, which aims to minimize the number of detained passengers. The proposed model is reformulated into an integer linear programming model by introducing the 0-1 decision variables. A case study of a real-world urban rail transit line is performed to verify the effectiveness of the proposed approach, which is solved by the CPLEX software. The results reveal that, the proposed approach has good optimization quality and computational efficiency. Compared to the plan only optimize timetables, the obtained plan reduced the number of detained passengers by 17.69% and the service level was significantly improved. This study provides theoretical support for the high-quality operation of the urban rail transit system.
Journal article
(2021)
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Fanting Meng, Lixing Yang, Yahan Lu, Rongge Guo
To relieve severe traffic congestion and the over- saturation of rail transit system, this study integrates the service and demand from the perspective of system optimization, and considers the continuous arrival characteristics of passenger flow in the analysis. A collaborative optimization method is developed for the train operation schedule and passenger flow control at stations using the skip-stop pattern strategy. By introducing the train schedule and passenger flow control decision variables, a bi-objective integer nonlinear collaborative optimization model is formulated to improve the train operation efficiency and to reduce the number of delayed passengers. Then, the nonlinear constraints are linearized by time reconstruction and big-M method with 0-1 variables to solve the proposed model. The model is reconstructed into an integer linear programming model, which can be easily solved by the CPLEX solver. The numerical examples are executed to verify the effectiveness of the proposed model. The results show that compared to the single objective optimization method and only with the train service time，the proposed model significantly reduces the number of delayed passengers. Compared to only considering number of delayed passengers, the train running time is reduced by 2% to 3%.
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To relieve severe traffic congestion and the over- saturation of rail transit system, this study integrates the service and demand from the perspective of system optimization, and considers the continuous arrival characteristics of passenger flow in the analysis. A collaborative optimization method is developed for the train operation schedule and passenger flow control at stations using the skip-stop pattern strategy. By introducing the train schedule and passenger flow control decision variables, a bi-objective integer nonlinear collaborative optimization model is formulated to improve the train operation efficiency and to reduce the number of delayed passengers. Then, the nonlinear constraints are linearized by time reconstruction and big-M method with 0-1 variables to solve the proposed model. The model is reconstructed into an integer linear programming model, which can be easily solved by the CPLEX solver. The numerical examples are executed to verify the effectiveness of the proposed model. The results show that compared to the single objective optimization method and only with the train service time，the proposed model significantly reduces the number of delayed passengers. Compared to only considering number of delayed passengers, the train running time is reduced by 2% to 3%.