Journal articles: 'Timetable optimization'

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Yusop, Noorrezam. "A Systematic Literature Review: Optimization Timetable in Education to Support Work-Life Balance (WLB)." Journal of Computing Research and Innovation 7, no. 2 (September 30, 2022): 316–26. http://dx.doi.org/10.24191/jcrinn.v7i2.324.

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Scheduling academic staff timetables is crucial and necessary to avoid redundancy and clash of class between teacher and student timetables. A good timetable allows students and teachers to manage their time and support a good and healthy lifestyle. However, with the scheduling, academic staff timetable may use many procedures to get efficient results. Therefore, this paper provides a gap of study for existing work on Optimization Timetable to support Work-Life Balance (WLB) regarding their market commercial and research purposes. The methodology of this study was conducted using a Systematic Literature Review (SLR). Result: two findings investigate 1) relevant optimization timetable scheduling used and 2) the method for timetable optimization to support WLB. The strengths and weaknesses of the features and utilities behind each study are also presented to provide a further understanding of the gaps and weaknesses of each body of research. We conclude that these studies are still insufficient and require further evaluation and improvement.

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Chen, Dingjun, Sihan Li, Junjie Li, Shaoquan Ni, and Xiaolong Liu. "Optimal High-Speed Railway Timetable by Stop Schedule Adjustment for Energy-Saving." Journal of Advanced Transportation 2019 (December 8, 2019): 1–9. http://dx.doi.org/10.1155/2019/4213095.

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Timetable optimization techniques offer opportunity for saving energy and hence reducing operational costs for high-speed rail services. The existing energy-saving timetable optimization is mainly concentrated on the train running state adjustment and the running time redistribution between two stations. Not only the adjustment space of timetables is limited, but also it is hard for the train to reach the optimized running state in reality, and it is difficult to get feasible timetable with running time redistribution between two stations for energy-saving. This paper presents a high-speed railway energy-saving timetable based on stop schedule optimization. Under the constraints of safety interval and stop rate, with the objective of minimizing the increasing energy consumption of train stops and the shortest travel time of trains, the high-speed railway energy-saving timetable optimization model is established. The fuzzy mathematics programming method is used to design an efficient algorithm. The proposed model and algorithm are demonstrated in the actual operation data of Beijing-Shanghai high-speed railway. The results show that the total operating energy consumption of the train is reduced by 3.7%, and the total travel time of the train is reduced by 11 minutes.

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Zhang, Renjie, Shisong Yin, Mao Ye, Zhiqiang Yang, and Shanglu He. "A Timetable Optimization Model for Urban Rail Transit with Express/Local Mode." Journal of Advanced Transportation 2021 (April 19, 2021): 1–15. http://dx.doi.org/10.1155/2021/5589185.

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Nowadays, an express/local mode has be studied and applied in the operation of urban rail transit, and it has been proved to be beneficial for the long-distance travel. The optimization of train patterns and timetables is vital in the application of the express/local mode. The former one has been widely discussed in the various existing works, while the study on the timetable optimization is limited. In this study, a timetable optimization model is proposed by minimizing the total passenger waiting time at platforms. Further, a genetic algorithm is used to solve the minimization problems in the model. This study uses the data collected from Guangzhou Metro Line 14 and finds that the total passenger waiting time at platforms is reduced by 9.3%. The results indicate that the proposed model can reduce the passenger waiting time and improve passenger service compared with the traditional timetable.

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Yuan, Yu, Pengcheng Wang, and Minghui Wang. "Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm." Mathematical Problems in Engineering 2022 (August 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/9222636.

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The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.

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LEE, HSIN-YUN. "A DECISION SUPPORT SYSTEM FOR EXPOSITION TIMETABLING USING ANT COLONY OPTIMIZATION." International Journal of Information Technology & Decision Making 11, no. 03 (May 2012): 609–26. http://dx.doi.org/10.1142/s0219622012500137.

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The exposition industry has developed rapidly in recent years. For exposition centers, exposition timetabling is a complicated problem. The timetables arranged by the administrators usually result in an imbalanced usage percentage between showgrounds and a low total usage percentage for all showgrounds. In this paper, we developed a decision support system that considers the characteristics of exposition timetabling. The proposed system applies ant colony optimization for determining the near-optimal timetable of expositions. The ants are grouped into teams representing multi-layer ant paths for priority ranking. This improvement allows us to classify candidate expositions with different time preferences. The showground timetabling of an exposition center is used to validate the proposed system. The timetable proposed by the decision support system ensures a higher efficiency and a higher total usage percentage of the showgrounds than the timetable proposed by a human expert.

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Takamatsu, Mizuyo, and Azuma Taguchi. "Bus Timetable Design to Ensure Smooth Transfers in Areas with Low-Frequency Public Transportation Services." Transportation Science 54, no. 5 (September 2020): 1238–50. http://dx.doi.org/10.1287/trsc.2019.0918.

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This study investigates the timetable design problem in areas with low-frequency public transportation services. In Japan, rural areas face sparse populations and rapid growth in the percentage of elderly people. In these areas, many bus lines offer fewer than 10 services per day. In addition to low-frequency services, it is also inconvenient to transfer to another bus or train service. Thus, there is a strong need to design a timetable that ensures smooth transfers among buses and trains. We tackle this problem by adopting existing bus lines and train timetables as much as possible to avoid drastic changes such as an increase in the number of services. Based on this approach, we present a mathematical optimization model to generate a revised bus timetable that shortens waiting time for transfers compared with the current timetable. We apply our model to a part of the Tohoku District in Japan and demonstrate its usefulness in the real world.

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Yang, Guang, Junjie Wang, Feng Zhang, Shiwen Zhang, and Cheng Gong. "A Real-Time Timetable Rescheduling Method for Metro System Energy Optimization under Dwell-Time Disturbances." Journal of Advanced Transportation 2019 (December 2, 2019): 1–11. http://dx.doi.org/10.1155/2019/5174961.

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Automatic Train Systems (ATSs) have attracted much attention in recent years. A reliable ATS can reschedule timetables adaptively and rapidly whenever a possible disturbance breaks the original timetable. Most research focuses the timetable rescheduling problem on minimizing the overall delay for trains or passengers. Few have been focusing on how to minimize the energy consumption when disturbances happen. In this paper, a real-time timetable rescheduling method (RTTRM) for energy optimization of metro systems has been proposed. The proposed method takes little time to recalculate a new schedule and gives proper solutions for all trains in the network immediately after a random disturbance happens, which avoids possible chain reactions that would attenuate the reuse of regenerative energy. The real-time feature and self-adaptability of the method are attributed to the combinational use of Genetic Algorithm (GA) and Deep Neural Network (DNN). The decision system for proposing solutions, which contains multiple DNN cells with same structures, is trained by GA results. RTTRM is upon the foundation of three models for metro networks: a control model, a timetable model and an energy model. Several numerical examples tested on Shanghai Metro Line 1 (SML1) validate the energy saving effects and real-time features of the proposed method.

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Chen, Angyang, Xingchen Zhang, Junhua Chen, and Zhimei Wang. "Joint optimization of high-speed train timetables, speed levels and stop plans for increasing capacity based on a compressed multilayer space-time network." PLOS ONE 17, no. 3 (March 3, 2022): e0264835. http://dx.doi.org/10.1371/journal.pone.0264835.

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With the steady increase in passenger volume of high-speed railways in China, some high-speed railway sections have faced a difficult situation. To provide more transport services, it is necessary to add as many trains as possible in a section to increase capacity. To solve this problem, a compressed multilayer space-time network model is constructed with the maximum number of trains that can be scheduled in the train timetable as the objective. The combination of the train stop plan and speed level is represented by the layer of network where the train is located, and constraints such as train selection, train safety, train overtake and cross-line trains are considered. A method based on timing-cycle iterative optimization is designed to decompose the original problem into multiple subproblems, and the solving order of the subproblems is determined by a heuristic greedy rule. Taking the Beijing-Jinan section of the Beijing-Shanghai high-speed railway as an example, the maximum number of trains was increased by 12.5% compared with the timetable before optimization. The saturated timetables provide detailed schedules, which helps decision-makers better adjust the timetable to run more trains.

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Guo, Haiyang, Yun Bai, Qianyun Hu, Huangrui Zhuang, and Xujie Feng. "Optimization on metro timetable considering train capacity and passenger demand from intercity railways." Smart and Resilient Transport 3, no. 1 (February 1, 2021): 66–77. http://dx.doi.org/10.1108/srt-06-2020-0004.

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Purpose To evacuate passengers arriving at intercity railway stations efficiently, metros and intercity railways usually share the same station or have stations close to each other. When intercity trains arrive intensively, a great number of passengers will burst into the metro station connecting with the intercity railway station within a short period, while the number of passengers will decrease substantially when intercity trains arrive sparsely. The metro timetables with regular headway currently adopted in real-world operations cannot handle the injected passenger demand properly. Timetable optimization of metro lines connecting with intercity railway stations is essential to improve service quality. Design/methodology/approach Based on arrival times of intercity trains and the entire process for passengers transferring from railway to metro, this paper develops a mathematical model to characterize the time-varying demand of passengers arriving at the platform of a metro station connecting with an intercity railway station. Provided the time-varying passenger demand and capacity of metro trains, a timetable model to optimize train departure time of a bi-direction metro line where an intermediate station connects with an intercity railway station is proposed. The objective is to minimize waiting time of passengers at the connecting station. The proposed timetable model is solved by an adaptive large neighborhood search algorithm. Findings Real-world case studies show that the prediction accuracy of the proposed model on passenger demand at the connecting station is higher than 90%, and the timetable model can reduce waiting time of passengers at the connecting station by 28.47% which is increased by 5% approximately than the calculation results of the generic algorithm. Originality/value This paper puts forward a model to predict the number of passengers arriving at the platform of connection stations via analyzing the entire process for passengers transferring from intercity trains to metros. Also, a timetable optimization model aiming at minimizing passenger waiting time of a metro line where an intermediate station is connected to an intercity railway station is proposed.

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Liu, Jiang, Tian-tian Li, Bai-gen Cai, and Jiao Zhang. "Boundary Identification for Traction Energy Conservation Capability of Urban Rail Timetables: A Case Study of the Beijing Batong Line." Energies 13, no. 8 (April 24, 2020): 2111. http://dx.doi.org/10.3390/en13082111.

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Energy conservation is attracting more attention to achieve a reduced lifecycle system cost level while enabling environmentally friendly characteristics. Conventional research mainly concentrates on energy-saving speed profiles, where the energy level evaluation of the timetable is usually considered separately. This paper integrates the train driving control optimization and the timetable characteristics by analyzing the achievable tractive energy conservation performance and the corresponding boundaries. A calculation method for energy efficient driving control solution is proposed based on the Bacterial Foraging Optimization (BFO) strategy, which is utilized to carry out batch processing with timetable. A boundary identification solution is proposed to detect the range of energy conservation capability by considering the relationships with average interstation speed and the passenger volume condition. A case study is presented using practical data of Beijing Metro Batong Line and two timetable schemes. The results illustrate that the proposed optimized energy efficient driving control approach is capable of saving tractive energy in comparison with the conventional traction calculation-based train operation solution. With the proposed boundary identification method, the capability space of the energy conservation profiles with respect to the energy reduction and energy saving rate is revealed. Moreover, analyses and discussions on effects from different passenger load conditions are given to both the weekday and weekend timetables. Results of this paper may assist the decision making of rail operators and engineers by enhancing the cost effectiveness and energy efficiency.

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Li, Jian, Lu Zhang, Bu Liu, Ningning Shi, Liang Li, and Haodong Yin. "Travel-Energy-Based Timetable Optimization in Urban Subway Systems." Sustainability 15, no. 3 (January 19, 2023): 1930. http://dx.doi.org/10.3390/su15031930.

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Timetable optimization for urban subways is aimed at improving the transportation service. In congested subway systems, the effects of crowding at stations and inside the vehicles have not been properly addressed in timetabling. Moreover, it is difficult to show the time of values in different riding conditions. In this paper, we consider the passenger-travel process as a physical activity expending energy and formulate a travel energy expenditure function for a heavily congested urban subway corridor. A timetable optimization model is proposed to minimize the total energy expenditure, including waiting on the platform and travelling in the vehicle. We develop a heuristic generic algorithm to solve the optimization problem through a special binary coding method. The model is applied to the Yi-zhuang line in the Beijing subway system to obtain a passenger-oriented energy-minimizing timetable. Compared with using the existing timetable, we find a 20% reduction in average energy expenditure per passenger and a RMB 47,500 increase in social profits as the result of the timetable optimization.

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Alghamdi, H., T. Alsubait, H. Alhakami, and A. Baz. "A Review of Optimization Algorithms for University Timetable Scheduling." Engineering, Technology & Applied Science Research 10, no. 6 (December 20, 2020): 6410–17. http://dx.doi.org/10.48084/etasr.3832.

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The university course timetabling problem looks for the best schedule, to satisfy given criteria as a set of given resources, which may contain lecturers, groups of students, classrooms, or laboratories. Developing a timetable is a fundamental requirement for the healthy functioning of all educational and administrative parts of an academic institution. However, factors such as the availability of hours, the number of subjects, and the allocation of teachers make the timetable problem very complex. This study intends to review several optimization algorithms that could be applied as possible solutions for the university student course timetable problem. The reviewed algorithms take into account the demands of institutional constraints for course timetable management.

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Kosolap, A. I., and T. M. Dubovik. "OPTIMIZATION OF TIMETABLE AT THE UNIVERSITY." Radio Electronics, Computer Science, Control, no. 3 (October 9, 2021): 175–83. http://dx.doi.org/10.15588/1607-3274-2021-3-15.

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Context. In this paper, we consider a well-known university scheduling problem. Such tasks are solved several times a year in every educational institution. The problem of constructing an optimal schedule remains open despite numerous studies in this area. This is due to the complexity of the corresponding optimization problem, in particular, its significant dimension. This complicates its numerical solution with existing optimization methods. Scheduling models also need improvement. Thus, schedule optimization is a complex computational problem and requires the development of new methods for solving it. Objective. Improvement of optimization models for timetabling at the university and the use of new effective methods to solve them. Method. We use the exact quadratic regularization method to solve timetabling optimization problems. Exact quadratic regularization allows transforming complex optimization models with Boolean variables into the problem of maximizing the vector norm on a convex set. We use the efficient direct dual interior point method and dichotomy method to solve this problem. This method has shown significantly better results in solving many complex multimodal problems. This is confirmed by many comparative computational experiments. The exact quadratic regularization method is even more effective in solving timetabling problems. This optimization method is used for the first time for this class of problems, so it required the development of adequate algorithmic support. Results. We propose a new, simpler timetabling optimization model that can be easily implemented software in Excel with the OpenSolver, RoskSolver, and others. We give a small example of building a schedule and describe step-by-step instructions for obtaining the optimal solution. Conclusions. An efficient new technology developed for university timetable, which is simple to implement and does not require the development of special software. The efficiency of the technology is ensured by the use of a new method of exact quadratic regularization.

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Shen, Yi, Gang Ren, and Yang Liu. "Timetable Design for Minimizing Passenger Travel Time and Congestion for a Single Metro Line." PROMET - Traffic&Transportation 30, no. 1 (February 26, 2018): 21–33. http://dx.doi.org/10.7307/ptt.v30i1.2281.

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This paper brings a proposal for a timetable optimization model for minimizing the passenger travel time and congestion for a single metro line under time-dependent demand. The model is an integer-programming model that systemically considers the passenger travel time, the capacity of trains, and the capacity of platforms. A multi-objective function and a recursive optimization method are presented to solve the optimization problem. Using the model we can obtain an efficient timetable with minimal passenger travel time and minimal number of congestion events on platforms. Moreover, by increasing the number of dispatches, the critical point from congestion state to free-flow state and the optimal timetable with minimal cost for avoiding congestion on platforms can be obtained. The effectiveness of the model is evaluated by a real example. A half-regular timetable with fixed headways in each operation period and an irregular timetable with unfixed headway are investigated for comparison.

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Meng, Xuelei, Bingmou Cui, Limin Jia, Yong Qin, and Jie Xu. "Networked Timetable Stability Improvement Based on a Bilevel Optimization Programming Model." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/290937.

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Train timetable stability is the possibility to recover the status of the trains to serve as arranged according to the original timetable when the trains are disturbed. To improve the train timetable stability from the network perspective, the bilevel programming model is constructed, in which the upper level programming is to optimize the timetable stability on the network level and the lower is to improve the timetable stability on the dispatching railway segments. Timetable stability on the network level is defined with the variances of the utilization coefficients of the section capacity and station capacity. Weights of stations and sections are decided by the capacity index number and the degrees. The lower level programming focuses on the buffer time distribution plan of the trains operating on the sections and stations, taking the operating rules of the trains as constraints. A novel particle swarm algorithm is proposed and designed for the bilevel programming model. The computing case proves the feasibility of the model and the efficiency of the algorithm. The method outlined in this paper can be embedded in the networked train operation dispatching system.

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Gao, Bowen, Decun Dong, Yusen Wu, and Dongxiu Ou. "Macroscopic Real-Time Timetable Rescheduling Approach for High-Speed Railway under Complete Blockages Using a Three-Stage Algorithm." Transportation Research Record: Journal of the Transportation Research Board 2676, no. 3 (November 2, 2021): 535–50. http://dx.doi.org/10.1177/03611981211052960.

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The rescheduling of train timetables under a complete blockage is a challenging process, which is more difficult when timetables contain lots of trains. In this paper, a mixed integer linear programming (MILP) model is formulated to solve the problem, following the rescheduling strategy that blocked trains wait inside the stations during the disruption. When the exact end time of the disruption is known, trains at stations downstream of the blocked station can depart early. The model aims at minimizing the total delay time and the total number of delayed trains under the constraints of station capacities, activity time, overtaking rules, and rescheduling strategies. Because there are too many variables and constraints of the MILP model to be solved, a three-stage algorithm is designed to speed up the solution. Experiments are carried out on the Beijing–Guangzhou high-speed railway line from Chibibei to Guangzhounan. The original timetable contains 162 trains, including 29 cross-line trains and 133 local trains. The simulation results show that our model can handle the optimization task of the timetable rescheduling problem very well. Compared with the one-stage algorithm, the three-stage algorithm is proved to greatly improve the solving speed of the model. All instances can get a better optimized disposition timetable within 450 to 600 s, which is acceptable for practical use.

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El-Shourbagy, Mahmoud. "Timetable Optimization in Urban Areas.(Dept.C)." MEJ. Mansoura Engineering Journal 19, no. 1 (March 1, 1994): 1–12. http://dx.doi.org/10.21608/bfemu.2021.162654.

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Borndörfer, Ralf, Heide Hoppmann, and Marika Karbstein. "Passenger routing for periodic timetable optimization." Public Transport 9, no. 1-2 (August 2, 2016): 115–35. http://dx.doi.org/10.1007/s12469-016-0132-0.

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Gorbachev, A. M. "Mathematical model of aperiodic timetables of urban electric transport." Automation on Transport 6, no. 4 (December 2020): 499–517. http://dx.doi.org/10.20295/2412-9186-2020-6-4-499-517.

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The analysis of scientifi c publications and timetable models is given. Existing works have been used as a basis of a classification of timetables by the frequency of time values. The urban transport network is presented in the form of a multigraph. The transition from a multigraph of the urban transport network to a network of events characterizing the traffi c process is considered. Constraints on time values have been formalized to solve the main problem of the scheduling theory. The proposed formalization factors in the specifi cs of traffic management planning in Russia and other post-Soviet countries. A mathematical model of aperiodic timetables for the ground urban electric transport traffic based on the theory of linear programming is presented. The optimization criterion for solving the main problem of the scheduling theory has been substantiated. The uniformity of traffi c intervals is used as an optimization criterion for solving the main problem of the scheduling theory. The article provides tabular timetables used in urban transport to describe the traffi c process in the absence of significant events on the line. The implementation of the model presented in this article is exemplified by the automated tram and trolleybus timetable design software being part of the automated urban electric transport control system currently used in Saint Petersburg to form tram and trolleybus timetables. The examples of calculating the vehicle departure interval diagrams have been used to demonstrate the function of aligning the traffi c intervals. In conclusion, the advantages and development paths of the proposed model of aperiodic timetables for the ground urban electric transport traffic are listed

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Zhao, Ning, Zhongbei Tian, Stuart Hillmansen, Lei Chen, Clive Roberts, and Shigen Gao. "Timetable Optimization and Trial Test for Regenerative Braking Energy Utilization in Rapid Transit Systems." Energies 15, no. 13 (July 2, 2022): 4879. http://dx.doi.org/10.3390/en15134879.

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Rapid transit systems play a significant role in supporting rapid social and economic development in large cities all over the world. However, the systems consume a large amount of energy, which brings increasing environmental concerns. A number of energy-saving technologies have been studied on railways. However, few of the outcomes have been tested and evaluated in practice. This paper presents the development of a timetable optimization and trial test on a metro line to reach the full potential of the train regenerative braking system. To achieve this purpose, a timetable optimization algorithm has been developed, and a trial test of the optimal timetable has been arranged on a metro line for a whole day. In the test, all the trains running in the network were organized to operate in accordance with the optimal timetable. The trial test results indicate that by applying the optimal timetable, the regenerative braking energy utilization can be improved, thereby reducing the overall network energy usage.

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Bärmann, Andreas, Alexander Martin, and Oskar Schneider. "Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling." Transportation Science 55, no. 3 (May 2021): 747–67. http://dx.doi.org/10.1287/trsc.2020.1021.

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Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to use slight shifts in the departure times from the stations to avoid too many simultaneous departures. This limits peak consumption and can help to improve the stability of the power supply. To this end, we derive efficient formulations for the problem of an optimal timetable adjustment based on a given timetable draft, two of which even allow for totally unimodular polyhedral descriptions. The proper choice of the objective function allows the incorporation of the priorities of either the train operating companies or the infrastructure manager. These include the avoidance of large peaks in average or instantaneous consumption and the improved use of recuperated braking energy. To solve the arising optimization models efficiently, we develop specially tailored exact Benders decomposition schemes that allow for the computation of high-quality solutions within a very short time. In an extensive case study for German railway passenger traffic, we show that our methods are capable of solving the problem on a nationwide scale. We see that the optimal adjustment of timetables entails a tremendous potential for reducing energy consumption.

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Zheng, Han, Junhua Chen, Zhaocha Huang, and Jianhao Zhu. "Joint Optimization of Multi-Cycle Timetable Considering Supply-to-Demand Relationship and Energy Consumption for Rail Express." Mathematics 10, no. 21 (November 7, 2022): 4164. http://dx.doi.org/10.3390/math10214164.

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Rail expresses play a vital role in intracity and intercity transportations. For accommodating multi-source passenger traffic with different travel demand, while optimizing the energy consumption, we propose a multi-cycle train timetable optimization model and a decomposition algorithm. A periodized spatial-temporal network that can support the integrated optimization of passenger service satisfaction and energy consumption considering multi-cycles is studied as the basis of the modeling. Based on this, an integrated optimization model taking the planning of the train spatial-temporal path, cycle length and active lines as variables is proposed. Then, for solving the issues caused by the complex relationships among the cycle length, line and train spatial-temporal path in large-scale cases, a hybrid heuristic Lagrangian decomposition method is investigated. Numerical experiments under different passenger flow demand scenarios are performed. The results show that the more fluctuating the passenger flow is, the more obvious the advantage of a multi-cycle timetable is. For the scenario with two passenger flow peaks, compared to a single-cycle timetable, the demand satisfaction ratio of the multi-cycle timetable is 4.44% higher and the train vacancy rate is 11.49% lower. A multi-cycle timetable also saves 3.24 h running time and 15,553.6 kwh energy consumption compared to a single-cycle timetable. Large-scale real cases show that this advantage still exists in practice.

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Guo, Jun En, and Hong Xia Zhang. "The Research of Special Laboratory Timetable Algorithm and Solving Conflicting Method." Applied Mechanics and Materials 220-223 (November 2012): 3064–67. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.3064.

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The laboratory timetable problem is an NP combinatorial optimization problem, and it is difficult to get the optimal solution. Under the traditional timetable algorithm, classes are arranged by week, and it is fixed and regular that when and where classes are arranged. Whereas under special laboratory timetable algorithm, teachers need book in advance, classes are arranged by term, and it is very flexible and random. So the traditional timetable algorithm cannot solve the problem of the laboratory timetable. In order to solve this problem, a special laboratory timetable algorithm and a solving conflicting method are presented in this paper. It has been proven that it is a better solution to the laboratory timetable problem, saves a lot of time for the laboratory personnel and is worth further promote the application.

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Liu, Hongjie, Tao Tang, Jidong Lv, and Ming Chai. "A Dual-Objective Substation Energy Consumption Optimization Problem in Subway Systems." Energies 12, no. 10 (May 17, 2019): 1876. http://dx.doi.org/10.3390/en12101876.

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Maximizing regenerative energy utilization is an important way to reduce substation energy consumption in subway systems. Timetable optimization and energy storage systems are two main ways to improve improve regenerative energy utilization, but they were studied separately in the past. To further improve energy conservation while maintaining a low cost, this paper presents a strategy to improve regenerative energy utilization by an integration of them, which determines the capacity of each Wayside Energy Storage System (WESS) and correspondingly optimizes the timetable at the same time. We first propose a dual-objective optimization problem to simultaneously minimize substation energy consumption and the total cost of WESS. Then, a mathematical model is formulated with the decision variables as the configuration of WESS and timetable. Afterwards, we design an ϵ -constraint method to transform the dual-objective optimization problem into several single-objective optimization problems, and accordingly design an improved artificial bee colony algorithm to solve them sequentially. Finally, numerical examples based on the actual data from a subway system in China are conducted to show the effectiveness of the proposed method. Experimental results indicate that substation energy consumption is effectively reduced by using WESS together with a correspondingly optimized timetable. Note that substation energy consumption becomes lower when the total size of WESS is larger, and timetable optimization further reduces it. A set of Pareto optimal solutions is obtained for the experimental subway line—based on which, decision makers can make a sensible trade-off between energy conservation and WESS investment accordingly to their preferences.

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Schlechte, Thomas, Ralf Borndörfer, Jonas Denißen, Simon Heller, Torsten Klug, Michael Küpper, Niels Lindner, Markus Reuther, Andreas Söhlke, and William Steadman. "Timetable optimization for a moving block system." Journal of Rail Transport Planning & Management 22 (June 2022): 100315. http://dx.doi.org/10.1016/j.jrtpm.2022.100315.

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Ojha, Deeptimanta, Rajesh Kumar, and Satyabrata Das. "Automated Timetable Generation using Bee Colony Optimization." International Journal of Applied Information Systems 10, no. 9 (May 5, 2016): 38–43. http://dx.doi.org/10.5120/ijais2016451553.

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Grega, W. "Hierarchical Optimization Algorithm for Timetable Generation Problems." IFAC Proceedings Volumes 22, no. 10 (August 1989): 441–45. http://dx.doi.org/10.1016/s1474-6670(17)53214-0.

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Van Lieshout, Rolf N. "Integrated Periodic Timetabling and Vehicle Circulation Scheduling." Transportation Science 55, no. 3 (May 2021): 768–90. http://dx.doi.org/10.1287/trsc.2020.1024.

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Periodic timetabling is one of the most well-researched problems in the public transport optimization literature. However, the impact that timetabling has on the number of required vehicles, which directly translates to operator costs, is rarely considered. Therefore, in this paper, we consider the problem of jointly optimizing the timetable and the vehicle circulation schedule, which specifies the cyclic sequences of trips that vehicles perform. In order to obtain high-quality solutions to realistic instances, we improve an earlier proposed formulation by contraction techniques, three new valid inequalities, and symmetry-breaking constraints. Ultimately, this allows us to explore the trade-off between the number of vehicles and the attractiveness of the timetable from the passengers’ perspective. An extensive computational study demonstrates the effectiveness of the improved formulation. Moreover, using this approach, we are able to find timetables requiring substantially fewer vehicles at the cost of minimal increases of the average travel time of passengers.

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Gorbachev, Aleksey. "Review on optimization models and methods for shuttle urban and main transport timetables and traffic schedules." Transport automation research 8, no. 3 (September 13, 2022): 287–95. http://dx.doi.org/10.20295/2412-9186-2022-8-03-287-295.

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Review for used at the moment models and methods for the creation and optimization of shuttle timetables for urban and main transport is given in the article, major differences between post-Soviet and foreign experience in the technology of timetable and traffic schedule creation are considered. The article contains phased analysis of approaches to planning the work of urban transport. The issues of dividing the city transport network into routes, the problems of vehicle distribution between them are given, the mathematical models of shuttle transport timetables, the assignments of real vehicles of certain types to squads and drivers distribution between them for each date are presented, major reasons for using aperiodic urban transport traffic schedules on post-Soviet area are pointed. The history of the development of software automation systems for urban transport traffic schedules is narrated, there’re considered major approaches, implementing an automation for the creation of periodic, aperiodic and hybrid timetables and traffic schedules, for to develop modern informational systems for the being considered purposes.

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LI, XIANG, and XIN YANG. "A STOCHASTIC TIMETABLE OPTIMIZATION MODEL IN SUBWAY SYSTEMS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21, supp01 (July 2013): 1–15. http://dx.doi.org/10.1142/s0218488513400011.

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With fixed running times at sections, cooperative scheduling (CS) approach optimizes the dwell times and the headway time to coordinate the accelerating and braking processes for trains, such that the recovery energy generated from the braking trains can be used by the accelerating trains. In practice, trains always have stochastic departure delays at busy stations. For reducing the divergence from the given timetable, the operation company generally adjusts the running times at the following sections. Focusing on the randomness on delay times and running times, this paper proposes a stochastic cooperative scheduling (SCS) approach. Firstly, we estimate the conversion and transmission losses of recovery energy, and then formulate a stochastic expected value model to maximize the utilization of the recovery energy. Furthermore, we design a binary-coded genetic algorithm to solve the optimal timetable. Finally, we conduct experimental studies based on the operation data from Beijing Yizhuang subway line. The results show that the SCS approach can save energy by 15.13% compared with the current timetable, and 8.81% compared with the CS approach.

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Li, Wenxin, Qiyuan Peng, Qinlin Li, Chao Wen, Yongxiang Zhang, and Javad Lessan. "Joint Operating Revenue and Passenger Travel Cost Optimization in Urban Rail Transit." Journal of Advanced Transportation 2018 (December 16, 2018): 1–15. http://dx.doi.org/10.1155/2018/7805168.

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Urban rail transit (URT) scheduling requires designing efficient timetables that can meet passengers’ expectations about the lower travel cost while attaining revenue management objectives of the train operators. This paper presents a biobjective timetable optimization model that seeks maximizing the operating revenue of the railway company while lowering passengers’ average travel cost. We apply a fuzzy multiobjective optimization and a nondominated sorting genetic algorithm II to solve the optimization problem and characterize the trade-off between the conflicting objective functions under different types of distances. To illustrate the model and solution methodology, the proposed model and solution algorithms are validated against train operation record from a URT line of Chengdu metro in China. The results show that significant improvements can be achieved in terms of the travel cost and revenue return criteria when implementing the solutions obtained by the proposed model.

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Zhang, Qin, Xiaoning Zhu, Li Wang, and Shuai Wang. "Simultaneous Optimization of Train Timetabling and Platforming Problems for High-Speed Multiline Railway Network." Journal of Advanced Transportation 2021 (March 17, 2021): 1–16. http://dx.doi.org/10.1155/2021/6679008.

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The optimization problems of train timetabling and platforming are two crucial problems in high-speed railway operation; these problems are typically considered sequentially and independently. With the construction of high-speed railways, an increasing number of interactions between trains on multiple lines have led to resource assignment difficulties at hub stations. To coordinate station resources for multiline train timetables, this study fully considered the resources of track segments, station throat areas, and platforms to design a three-part space-time (TPST) framework from a mesoscopic perspective to generate a train timetable and station track assignment simultaneously. A 0-1 integer programming model is proposed, whose objective is to minimize the total weighted train running costs. The construction of a set of incompatible vertexes and links facilitates the expression of difficult constraints. Finally, example results verify the validity and practicability of our proposed method, which can generate conflict-free train timetables with a station track allocation plan for multiple railway lines at the same time.

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N, Buvaneswari, and Rekha S. "Timetable Scheduling using Bipartite Graph." International Journal for Research in Applied Science and Engineering Technology 10, no. 12 (December 31, 2022): 1854–56. http://dx.doi.org/10.22214/ijraset.2022.47641.

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Abstract: In any educational institution, the two most common academic scheduling problems are course timetabling and exam timetabling. A schedule is desirablewhich combines resources like teachers, subjects, students, classrooms in a way to avoid conflicts satisfying various essential and preferential constraints. The timetable scheduling problem is known to be NP Complete but the corresponding optimization problem is NP Hard. This problem is solved using bipartite graph. Hence a heuristic approach ispreferred to find a nearest optimal solution within reasonable running time

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Alomari, Khaled, Osama Almarashdi, Ala Marashdh, and Belal Zaqaibeh. "A New Optimization on Harmony Search Algorithm for Exam Timetabling System." Journal of Information & Knowledge Management 19, no. 01 (March 2020): 2040009. http://dx.doi.org/10.1142/s0219649220400092.

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Preparing an optimal exam timetable in universities is challenging for head of departments, especially for colleges with multiple number of departments, courses, and students. Harmony search algorithm is used by many researchers to solve this problem but none of them could get an optimal solution. In this paper, a new algorithm which is called optimised harmony search algorithm with distributed selections is proposed by optimising the harmony search algorithm and the genetic algorithm. The new algorithm could satisfy hard, soft, and general constraints and generate an optimal exam timetable for a huge number of courses and students. The proposed algorithm is implemented and applied on Jadara University, the algorithm uses an upper triangular matrix to reduce relationships and memory usage, a three-dimensional matrix to ease the exams timetable management a deterministic number generators to eliminate timeslots conflicts, and backtracking algorithm to enhance the population selections. Lecturers and students’ feedback showed a good satisfaction as well the system results.

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Li, Dewei, Shishun Ding, and Yizhen Wang. "Combinatorial Optimization of Service Order and Overtaking for Demand-Oriented Timetabling in a Single Railway Line." Journal of Advanced Transportation 2018 (September 12, 2018): 1–21. http://dx.doi.org/10.1155/2018/4613468.

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Train timetabling is crucial for passenger railway operation. Demand-oriented train timetable optimization by minimizing travel time plays an important role in both theory and practice. Most of the current researches of demand-oriented timetable models assume an idealized situation in which the service order is fixed and in which zero overtaking exists between trains. In order to extend the literature, this paper discusses the combinatorial effect of service order and overtaking by developing four mixed-integer quadratic programming timetabling models with different service order as well as overtaking conditions. With the objective of minimizing passengers’ waiting time and in-vehicle time, the models take five aspects as constraints, namely dwell time, running time, safety interval, overtaking, and capacity. All four models are solved by ILOG CPLEX; and the results, which are based on Shanghai-Hangzhou intercity high-speed rail data, show that either allowing overtaking or changing service order can effectively optimize the quality of timetable with respect to reducing the total passengers’ travel time. Although optimizing train overtaking and service order simultaneously can optimize the timetable more significantly, compared to overtaking, allowing the change of service order can help passengers save total travel time without extending the train travel time. Moreover, considering the computation effort, satisfying both of the conditions in the meantime, when optimizing timetable has not got a good cost benefit.

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Lan, Zekang, Shiwei He, Rui Song, and Sijia Hao. "Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach." Journal of Advanced Transportation 2019 (January 6, 2019): 1–13. http://dx.doi.org/10.1155/2019/2781590.

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In practice, vehicle scheduling is planned on a variable timetable so that the departure times of trips can be shifted in tolerable ranges, rather than on a fixed timetable, to decrease the required fleet size. This paper investigates the vehicle scheduling problem on a variable timetable with the constraint that each vehicle can perform limited trips. Since the connection-based model is difficult to solve by optimization software for a medium-scale or large-scale instance, a designed path-based model is developed. A Benders-and-Price algorithm by combining the Benders decomposition and column generation is proposed to solve the LP-relaxation of the path-based model, and a bespoke Branch-and-Price is used to obtain the integer solution. Numerical experiments indicate that a variable timetable approach can reduce the required fleet size with a tolerable timetable deviation in comparison with a fixed timetable approach. Moreover, the proposed algorithm is greatly superior to GUROBI in terms of computational efficiency and guarantees the quality of the solution.

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Wang, Anyu, Yan Cheng, Lei Nie, and Taku Fujiyama. "Railway Timetable Optimization for Air-Rail Intermodal Service." Journal of Physics: Conference Series 1972, no. 1 (July 1, 2021): 012070. http://dx.doi.org/10.1088/1742-6596/1972/1/012070.

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Chen, Qun. "Global Optimization for Bus Line Timetable Setting Problem." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/636937.

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This paper defines bus timetables setting problem during each time period divided in terms of passenger flow intensity; it is supposed that passengers evenly arrive and bus runs are set evenly; the problem is to determine bus runs assignment in each time period to minimize the total waiting time of passengers on platforms if the number of the total runs is known. For such a multistage decision problem, this paper designed a dynamic programming algorithm to solve it. Global optimization procedures using dynamic programming are developed. A numerical example about bus runs assignment optimization of a single line is given to demonstrate the efficiency of the proposed methodology, showing that optimizing buses’ departure time using dynamic programming can save computational time and find the global optimal solution.

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Guo, Xin, Huijun Sun, Jianjun Wu, Jiangang Jin, Jin Zhou, and Ziyou Gao. "Multiperiod-based timetable optimization for metro transit networks." Transportation Research Part B: Methodological 96 (February 2017): 46–67. http://dx.doi.org/10.1016/j.trb.2016.11.005.

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Zhou, Yuhe, Yun Bai, Jiajie Li, Baohua Mao, and Tang Li. "Integrated Optimization on Train Control and Timetable to Minimize Net Energy Consumption of Metro Lines." Journal of Advanced Transportation 2018 (2018): 1–19. http://dx.doi.org/10.1155/2018/7905820.

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Energy-efficient metro operation has received increasing attention because of the energy cost and environmental concerns. This paper developed an integrated optimization model on train control and timetable to minimize the net energy consumption. The extents of train motoring and braking as well as timetable configurations such as train headway and interstation runtime are optimized to minimize the net energy consumption with consideration of utilizing regenerative energy. An improved model on train control is proposed to reduce traction energy by allowing coasting on downhill slopes as much as possible. Variations of train mass due to the change of onboard passengers are taken into account. The brute force algorithm is applied to attain energy-efficient speed profiles and an NS-GSA algorithm is designed to attain the optimal extents of motoring/braking and timetable configurations. Case studies on Beijing Metro Line 5 illustrate that the improved train control approach can save traction energy consumption by 20% in the sections with steep downhill slopes, in comparison with the commonly adopted train control sequence in timetable optimization. Moreover, the integrated model is able to significantly prolong the overlapping time between motoring and braking trains, and the net energy consumption is accordingly reduced by 4.97%.

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Schiewe, Philine, and Anita Schöbel. "Periodic Timetabling with Integrated Routing: Toward Applicable Approaches." Transportation Science 54, no. 6 (November 2020): 1714–31. http://dx.doi.org/10.1287/trsc.2019.0965.

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Periodic timetabling is an important, yet computationally challenging, problem in public transportation planning. The usual objective when designing a timetable is to minimize passenger travel time. However, in most approaches, it is ignored that the routes of the passengers depend on the timetable, so handling their routing separately leads to timetables that are suboptimal for the passengers. This has recently been recognized, but integrating the passenger routing in the optimization is computationally even harder than solving the classic periodic timetabling problem. In our paper, we develop an exact preprocessing method for reducing the problem size and a heuristic reduction approach in which only a subset of the passengers is considered. It provides upper and lower bounds on the objective value, such that it can be adjusted with respect to quality and computation time. Together, we receive an approach that is applicable for real-world problems. We experimentally evaluate the performance of the approach on a benchmark example and on three close-to-real-world instances. Furthermore, we prove that the ratio between the classic problem without routing and the problem with integrated routing is bounded under weak and realistic assumptions.

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Xu, Wen, Yuyan Tan, Bishal Sharma, and Ziyulong Wang. "Cyclic Timetable Scheduling Problem on High-speed Railway Line." Periodica Polytechnica Transportation Engineering 48, no. 1 (April 15, 2019): 31–38. http://dx.doi.org/10.3311/pptr.12312.

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Due to several obvious advantages both in transport marketing and train operation planning, the cyclic timetable has already applied in many high-speed railway (HSR) countries. In order to adopt the cyclic timetable in China's HSR system, a Mixed Integer Programmer (MIP) model is proposed in this paper involving many general constraints, such as running time, dwell time, headway, and connection constraints. In addition, the real-world overtaking rule that concerning a train with higher priority will not be overtaken by a slower one is incorporated into the cyclic timetable optimization model. An approach based on fixed departure is proposed to get a cyclic timetable with minimum total journey time within a reasonable time. From numerical investigations using data from Guangzhou-Zhuhai HSR line in China, the proposed model and associated approach are tested and shown to be effective.

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Zandavi, Seid Miad, Vera Chung, and Ali Anaissi. "Multi-user Remote Lab: Timetable Scheduling Using Simplex Nondominated Sorting Genetic Algorithm." ACM/IMS Transactions on Data Science 2, no. 2 (April 2, 2021): 1–13. http://dx.doi.org/10.1145/3437260.

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The scheduling of multi-user remote laboratories is modeled as a multimodal function for the proposed optimization algorithm. The hybrid optimization algorithm, hybridization of the Nelder-Mead Simplex algorithm, and Non-dominated Sorting Genetic Algorithm (NSGA), named Simplex Non-dominated Sorting Genetic Algorithm (SNSGA), is proposed to optimize the timetable problem for the remote laboratories to coordinate shared access. The proposed algorithm utilizes the Simplex algorithm in terms of exploration and NSGA for sorting local optimum points with consideration of potential areas. SNSGA is applied to difficult nonlinear continuous multimodal functions, and its performance is compared with hybrid Simplex Particle Swarm Optimization, Simplex Genetic Algorithm, and other heuristic algorithms. The results show that SNSGA has a competitive performance to address timetable problems.

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Wang, Li, Yong Qin, Jie Xu, and Limin Jia. "A Fuzzy Optimization Model for High-Speed Railway Timetable Rescheduling." Discrete Dynamics in Nature and Society 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/827073.

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A fuzzy optimization model based on improved symmetric tolerance approach is introduced, which allows for rescheduling high-speed railway timetable under unexpected interferences. The model nests different parameters of the soft constraints with uncertainty margin to describe their importance to the optimization purpose and treats the objective in the same manner. Thus a new optimal instrument is expected to achieve a new timetable subject to little slack of constraints. The section between Nanjing and Shanghai, which is the busiest, of Beijing-Shanghai high-speed rail line in China is used as the simulated measurement. The fuzzy optimization model provides an accurate approximation on train running time and headway time, and hence the results suggest that the number of seriously impacted trains and total delay time can be reduced significantly subject to little cost and risk.

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Li, Wenxin, Qiyuan Peng, Chao Wen, Shengdong Li, Xu Yan, and Xinyue Xu. "Integrated Optimization on Energy Saving and Quality of Service of Urban Rail Transit System." Journal of Advanced Transportation 2020 (January 3, 2020): 1–22. http://dx.doi.org/10.1155/2020/3474020.

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Optimizing to increase the utilization ratio of regenerative braking energy reduces energy consumption, and can be done without increasing the deviation of train running time in one circle. The latter entails that the train timetable is upheld, which guarantees that the demand for passenger transport services is met and the quality of services in the urban rail transit system is maintained. This study proposes a multi-objective optimization model for urban railways with timetable optimization to minimize the total energy consumption of trains while maximizing the quality of service. To this end, we apply the principles and ideas of calculus to reduce the power of the velocity in the train energy consumption model. This greatly simplifies the complexity of the optimization model. Then, considering the conflicting requirements of decision-makers, weight factors are added to the objective functions to reflect decision-makers’ preferences for energy-saving and the quality of service. We adopt the nondominated sorting genetic algorithm-II (NSGA-II) to solve the proposed model. A practical case study of the Yizhuang urban railway line in Beijing is conducted to verify the effectiveness of the proposed model and evaluate the advantages of the optimal energy saving timetable (OEST) in comparison to the optimal quality of service timetable (OQOST). The results showed that the OEST reduced total energy consumption by 8.72% but increased the deviation of trains running time in one circle by 728 s. The total energy consumption was reduced by 6.09%, but there was no increase in the deviation of train running time in one circle with the OQOST.

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Jin, Bo, Xiaoyun Feng, Qingyuan Wang, Pengfei Sun, and Qian Fang. "Train Scheduling Method to Reduce Substation Energy Consumption and Peak Power of Metro Transit Systems." Transportation Research Record: Journal of the Transportation Research Board 2675, no. 4 (January 5, 2021): 201–12. http://dx.doi.org/10.1177/0361198120974677.

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The rapid development of metro transit systems brings very significant energy consumption, and the high service frequency of metro trains increases the peak power requirement, which affects the operation of systems. Train scheduling optimization is an effective method to reduce energy consumption and substation peak power by adjusting timetable parameters. This paper proposes a train timetable optimization model to coordinate the operation of trains. The overlap time between accelerating and braking phases is maximized to improve the utilization of regenerative braking energy (RBE). Meanwhile, the overlap time between accelerating phases is minimized to reduce the substation peak power. In addition, the timetable optimization model is rebuilt into a mixed integer linear programming model by introducing logical and auxiliary variables, which can be solved by related solvers effectively. Case studies based on one of Guangzhou Metro Lines indicate that, for all-day operation, the utilization of RBE would likely be improved on the order of 23%, the substation energy consumption would likely be reduced on the order of 14%, and the duration of substation peak power would likely be reduced on the order of 66%.

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Chen, Yao, Baohua Mao, Yun Bai, Tin Kin Ho, and Zhujun Li. "Optimal Coordination of Last Trains for Maximum Transfer Accessibility with Heterogeneous Walking Time." Journal of Advanced Transportation 2019 (July 3, 2019): 1–13. http://dx.doi.org/10.1155/2019/9692024.

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Last train coordination aims to synchronize the arrival and departure times of the last feeder trains and the last connecting trains at transfer stations to improve the transfer accessibility of urban rail networks. This study focuses on the transfer accessibility between last trains with considering heterogeneous transfer walking time. Three mathematical models are developed on the last train timetable optimization. The first model fine-tunes the last train timetable under the given bound of the dwell time. The second one aims to allow the mutual transfers with the prolonged dwell time to maximize the transfer accessibility. A biobjective function is proposed to seek the trade-off between the maximal transfer accessibility and the minimal extension of dwell time. The third model considers the heterogeneity of transfer walking time that is represented as a random variable following a probability distribution. A discrete approximation method is proposed to reformulate the nonlinear model. The embedded Branch & Cut algorithm of CPLEX is applied to solve the models. A real case on the Shenzhen metro network is conducted to demonstrate the performance of the models. The three models all provide better last train timetable than the current timetable in practice. The sensitivity analysis manifests that the third model are always advantageous in the optimization of successful transfer passengers.

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Zheng, Yajing, Zihan Ma, Naiyu Liu, and Wenzhou Jin. "Study on Energy-Saving Optimization of Urban Rail Transit Train Timetable under Regenerative Braking." Mathematical Problems in Engineering 2022 (August 29, 2022): 1–10. http://dx.doi.org/10.1155/2022/5590736.

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Energy-saving driving and regenerative braking energy utilization are two main ways to realize energy-saving optimization of urban rail transit train timetables. On the basis of the more mature energy-saving driving achievements of the predecessors, the absorption utilization rate of regenerative braking energy is improved by adjusting the dwell time of trains in the station so that while a train is braking, other trains in the same electric section are just under traction. In this paper, the overlap time between the traction and braking processes of different trains is used as a measure of the proportion of regenerative braking energy that is absorbed. In order to maximize this overlap time, an energy-saving optimization model of urban rail transit train timetable based on regenerative braking technology was established. To facilitate the solution, the nonlinear constraints are converted to linear at the time of model construction in this paper. In the solution, the spatio-temporal local rolling algorithm and the commercial optimization software ILOG CPLEX are used for the solution. The solution results show that the method in this paper can effectively improve the absorption and utilization of regenerative braking energy.

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Zhou, Cheng Cheng, Lu Kai Zhang, and Liu Jiang Kang. "Modeling Timetable Coordination in Urban Mass Transit Networks." Advanced Materials Research 1030-1032 (September 2014): 2207–10. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.2207.

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Timetable coordination is very complex because of the number of alternative transfer directions involved in subway networks and lack of optimization principles. In this paper, transfer binary variable (TBV) that influence transferring are taken into considered in the model. By adjusting the dispatch time, dwell time at stations, the model can construct a high-quality timetable that improves the passenger transfer effectiveness. The numerical experiments show that our model improves TBV to 10 directions of 11 total transfer directions.

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Yang, Xin, Bin Ning, Xiang Li, and Tao Tang. "A Two-Objective Timetable Optimization Model in Subway Systems." IEEE Transactions on Intelligent Transportation Systems 15, no. 5 (October 2014): 1913–21. http://dx.doi.org/10.1109/tits.2014.2303146.

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Journal articles on the topic 'Timetable optimization'

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