Train Speed Trajectory Optimization using Dynamic Programming with speed modes decomposition

Wang, Pu; Peng, Yi Qiang; Gao, Xuejin; Gao, Huihui

doi:10.1088/1757-899x/569/4/042019

IOP Conf. Ser.: Mater. Sci. Eng.

2019

DOI: 10.1088/1757-899x/569/4/042019

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Train Speed Trajectory Optimization using Dynamic Programming with speed modes decomposition

Pu Wang

Yi Qiang Peng²,

Xuejin Gao

et al.

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Cited by 2 publications

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“…Haahr et al ( 11 ) used dynamic programming to solve a time–space graph formulation and generate improved train speed profiles with reduced energy consumption. To avoid the dimension disaster caused by dynamic programming algorithms, Wang et al ( 12 ) proposed a train operation model based on conditions to find the final value of train traction energy consumption. Lu et al ( 13 ) transformed the control operation sequence optimization problem of train operation in the interval into solving the train speed at different preset positions, and solved the energy-saving optimization curve of a single train at different times with comparing the solving effects of ant colony algorithm, genetic algorithm, and dynamic programming.…”

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Train Operation Curve Optimization for an Urban Rail Interval With Multi-Parameter Adjustment

Deng

Zhong

et al. 2022

Transportation Research Record: Journal of the Transportation R

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This paper proposes an energy consumption optimization method of train operation by controlling multiple parameters for an urban rail interval. The parameters include the maximum operation speed, the ratio of the minimum coasting speed to the maximum speed, the maximum traction, and the braking force. Based on the mass belt model, an optimization model of train operation is built with these parameters as decision variables. The objective function is to minimize the energy consumption and the penalty on the running time delays for the observed rail interval. A simulated annealing algorithm is designed to solve the model, which adopts synergic adjustment of multiple parameters based on the influence of the running time with variation of each parameter. A numerical example of Guangzhou Metro Line 8 is adopted to test the method. The results show that the maximum operation speed has a decisive influence on the optimal train operation strategy, interval running time, and energy consumption; the train traction has a direct effect on energy consumption; the train braking force has multiple optimal solutions; moreover, the energy-saving strategy has a significant effect on energy saving in a longer running time.

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mentioning

confidence: 99%

Train Operation Curve Optimization for an Urban Rail Interval With Multi-Parameter Adjustment

Deng

Zhong

et al. 2022

Transportation Research Record: Journal of the Transportation R

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Dynamic programming in applied tasks which are allowing to reduce the options selection

Karpov

Struchenkov

2020

Rossijskij tehnologičeskij žurnal

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The article discusses the dynamic programming algorithm developed by R. Bellman, based on the search for the optimal trajectory connecting the nodes of a predefined regular grid of states. Possibilities are analyzed for a sharp increase in the effectiveness of using dynamic programming in solving applied problems with specific features, which allows us to refuse to split a regular grid of states and implement an algorithm for finding the optimal trajectory when rejecting not only unpromising options for paths leading to each of the states, and all of them continuations, as in R. Bellmanʼs algorithm, but also actually hopeless states and all variants of paths emanating from them. The conditions are formulated and justified under which the rejection of hopeless states is possible. It has been established that many applied problems satisfy these conditions. To solve such problems, a new dynamic programming algorithm described in the article is proposed and implemented. Concrete examples of such applied problems are given: the optimal distribution of a homogeneous resource between several consumers, the optimal loading of vehicles, the optimal distribution of finances when choosing investment projects. To solve these problems, dynamic programming algorithms with rejecting unpromising paths, but without rejecting states, were previously proposed. The number of hopeless states that appear at various stages of dynamic programming and, accordingly, the effectiveness of the new algorithm depends on the specific numerical values of the source data. For the two-parameter problem of optimal loading of vehicles with weight and volume constraints, the results of comparative calculations by the R. Bellman algorithm and the new dynamic programming algorithm are presented. As a source of data for a series of calculations, pseudorandom numbers were used. As a result of the analysis, it was shown that the comparative efficiency of the algorithm with rejection of states increases with increasing dimension of the problem. So, in the problem of the optimal choice of items for loading a vehicle of a given carrying capacity with a number of items of 150, the number of memorized states and the counting time are reduced by 50 and 57 times, respectively, when using the new algorithm compared to the classical algorithm of R. Bellman. And for 15 items, the corresponding numbers are 13 and 4.

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Train Speed Trajectory Optimization using Dynamic Programming with speed modes decomposition

Cited by 2 publications

References 7 publications

Train Operation Curve Optimization for an Urban Rail Interval With Multi-Parameter Adjustment

Train Operation Curve Optimization for an Urban Rail Interval With Multi-Parameter Adjustment

Dynamic programming in applied tasks which are allowing to reduce the options selection

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