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doi: 10.3934/dcdss.2020200

An adaptive genetic algorithm for solving the optimization model of car flow organizat

1. 

School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China

2. 

School of Railway Tracks and Transportation, Wuyi University, Jiangmen 529020, China

* Corresponding author: Wenxian Wang

Received  March 2019 Revised  May 2019 Published  December 2019

Organizing the direct train flow of the loading area can reduce the load of the technical station along the way, accelerate the turnover of wagons and the delivery of goods, and facilitate the better integration of cargo flow and train flow. By analyzing three typical car organization forms in loading area and the hourly consumption index of the train flow in the loading area, a 0-1 nonlinear optimization model for direct routes distribution of trains in railway loading areas is constructed, with the goal of minimizing the total vehicle hour consumption of the train flow, and is bound by the uniqueness of the car flow organization and the number of trains compiled by each loading area and technical station. According to the complex characteristics of the model and the characteristics of the constraints, an improved genetic algorithm that limit spatial search strategy can be designed. This algorithm ensures the spatial feasibility of the solution during the execution through the adaptive adjustment of the crossover operator and the mutation operator. Finally, the effectiveness of the algorithm and model is verified by the example study and the case study of Huangdao loading area.

Citation: Ji Zhang, Hongxia Lv, Boer Deng, Wenxian Wang. An adaptive genetic algorithm for solving the optimization model of car flow organizat. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020200
References:
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A. Arjand, Analysis of Rail Classification Policies, Informs, 21 (1983), 293-314.   Google Scholar

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X. CaoB. Lin and H. Yan, Optimization of direct freight train service in the loading place, Journal of China Railway Society, 28 (2006), 6-11.   Google Scholar

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W. Gao and W. Wang, A tight neighborhood union condition on fractional (G, F, N ', M)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298.  doi: 10.4064/cm6959-8-2016.  Google Scholar

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L. JiB. Lin and Z. Wang, Study on the optimization of car flow organization for loading area based on logistics cost, Journal of the China Railway Society, 31 (2009), 1-6.   Google Scholar

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B. LinS. ZhuD. Shi and et al., The optimal model of the direct train formation plan for loading area, China Railway Science, 16 (1995), 108-114.   Google Scholar

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B. LinS. Zhu and Q. Zhao, A step function model of the train formation plan and its equivalent transformation, Journal of Southwest Jiaotong University, 29 (1994), 91-96.   Google Scholar

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Y. MasoudF. Amir and N. Behnam, Solving railroad blocking problem using ant colony optimization algorithm, Applied Mathematical Modelling, 35 (2011), 5579-5591.  doi: 10.1016/j.apm.2011.05.018.  Google Scholar

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H. N. NewtonC. Barnhart and P. H. Vance, Constructing railroad blocking plans to minimize handling costs, Transportation Science, 32 (1998), 330-345.  doi: 10.1287/trsc.32.4.330.  Google Scholar

[11]

L. Qiang, Model and algorithm optimized organization scheme for through train from loading points based on endpoint-for-weight, Journal of the China Railway Society, 31 (2009), 91-96.   Google Scholar

[12]

A. RavindraJ. Krishna and L. Jian, Solving real-life railroad blocking problems, Interfaces, 37 (2007), 404-419.   Google Scholar

[13]

D. YuH. Liu and C. Bresser, Peak load management based on hybrid power generation and demand response, Energy, 163 (2018), 969-985.  doi: 10.1016/j.energy.2018.08.177.  Google Scholar

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B. Zhao and H. Wu, Pharmacological characteristics analysis of two molecular structures, Applied Mathematics and Nonlinear Sciences, 2 (2017), 93-110.  doi: 10.21042/AMNS.2017.1.00008.  Google Scholar

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P. ZhaoJ. Zhang and B. Tang, Study on the optimization model of car flow organization in the loading area of heavy haul railway based on the combined trains, China Railway Science, 31 (2010), 116-121.   Google Scholar

show all references

References:
[1]

A. Arjand, Analysis of Rail Classification Policies, Informs, 21 (1983), 293-314.   Google Scholar

[2]

X. CaoB. Lin and H. Yan, Optimization of direct freight train service in the loading place, Journal of China Railway Society, 28 (2006), 6-11.   Google Scholar

[3]

W. Gao and W. Wang, A tight neighborhood union condition on fractional (G, F, N ', M)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298.  doi: 10.4064/cm6959-8-2016.  Google Scholar

[4]

M. HuangX. Xue and W. Liu, Optimization of the organization scheme for though trains initiating from car loading locations, China Railway Science, 11 (1990), 99-106.   Google Scholar

[5]

L. JiB. Lin and Z. Wang, Study on the optimization of car flow organization for loading area based on logistics cost, Journal of the China Railway Society, 31 (2009), 1-6.   Google Scholar

[6]

B. LawrenceG. BruceS. Allan and et al., A model for blocking of trains, Transportation Research Part B, 14 (1980), 115-120.  doi: 10.1016/0191-2615(80)90037-5.  Google Scholar

[7]

B. LinS. ZhuD. Shi and et al., The optimal model of the direct train formation plan for loading area, China Railway Science, 16 (1995), 108-114.   Google Scholar

[8]

B. LinS. Zhu and Q. Zhao, A step function model of the train formation plan and its equivalent transformation, Journal of Southwest Jiaotong University, 29 (1994), 91-96.   Google Scholar

[9]

Y. MasoudF. Amir and N. Behnam, Solving railroad blocking problem using ant colony optimization algorithm, Applied Mathematical Modelling, 35 (2011), 5579-5591.  doi: 10.1016/j.apm.2011.05.018.  Google Scholar

[10]

H. N. NewtonC. Barnhart and P. H. Vance, Constructing railroad blocking plans to minimize handling costs, Transportation Science, 32 (1998), 330-345.  doi: 10.1287/trsc.32.4.330.  Google Scholar

[11]

L. Qiang, Model and algorithm optimized organization scheme for through train from loading points based on endpoint-for-weight, Journal of the China Railway Society, 31 (2009), 91-96.   Google Scholar

[12]

A. RavindraJ. Krishna and L. Jian, Solving real-life railroad blocking problems, Interfaces, 37 (2007), 404-419.   Google Scholar

[13]

D. YuH. Liu and C. Bresser, Peak load management based on hybrid power generation and demand response, Energy, 163 (2018), 969-985.  doi: 10.1016/j.energy.2018.08.177.  Google Scholar

[14]

B. Zhao and H. Wu, Pharmacological characteristics analysis of two molecular structures, Applied Mathematics and Nonlinear Sciences, 2 (2017), 93-110.  doi: 10.21042/AMNS.2017.1.00008.  Google Scholar

[15]

P. ZhaoJ. Zhang and B. Tang, Study on the optimization model of car flow organization in the loading area of heavy haul railway based on the combined trains, China Railway Science, 31 (2010), 116-121.   Google Scholar

Figure 1.  Range of loading and unloading area
Figure 2.  Schematic diagram of the car flow organization in the loading area
Figure 3.  Topological schematic diagram of the railway line
Figure 4.  Schematic diagram of the car flow organization code in the chromosome
Figure 5.  Car flow organization coding mode diagram
Figure 6.  Schematic diagram of an unreasonable traffic organization code
Figure 7.  Schematic diagram of the traditional single point crossover of the car flow organization
Figure 8.  Schematic diagram of traditional single point variation of car flow organization
Figure 9.  Schematic diagram of the genetic algorithm process
Figure 10.  Schematic diagram of simplified road network structure and car flow
Figure 11.  Genetic algorithm convergence curve
Figure 12.  Railway network structure related to Huang-Dao Station
Figure 13.  Genetic algorithm convergence curve
Table 1.  Technical parameters of car flow and car flow organization 1
Car flow rate $ \overline{m}_{st} $ $ \omega_{ff} $ $ \omega_{zf} $ $ \omega_{zz} $
$ N_{7} $ 22 30 10 15 18
$ N_{8} $ 30 40 10 15 18
$ N_{9} $ 16 40 10 15 18
$ N_{10} $ 50 40 10 15 18
$ N_{11} $ 32 40 10 15 18
Car flow rate $ \overline{m}_{st} $ $ \omega_{ff} $ $ \omega_{zf} $ $ \omega_{zz} $
$ N_{7} $ 22 30 10 15 18
$ N_{8} $ 30 40 10 15 18
$ N_{9} $ 16 40 10 15 18
$ N_{10} $ 50 40 10 15 18
$ N_{11} $ 32 40 10 15 18
Table 2.  Technical parameters of main marshalling station of railroad network
Marshalling station 1 2 3 4 5 6
$ t_{k}(Hour) $ 5 5 6 5 5 6
$ \overline{m}_{sk} $(Car) - 30 30 30 30 30
Marshalling station 1 2 3 4 5 6
$ t_{k}(Hour) $ 5 5 6 5 5 6
$ \overline{m}_{sk} $(Car) - 30 30 30 30 30
Table 3.  Technical parameters of car flow and car flow organization of Huang-Dao Station
Car flow rate $ \overline{m}_{st} $ $ \omega_{ff} $ $ \omega_{zf} $ $ \omega_{zz} $
$ N_{11} $ 6 40 12 15 17
$ N_{12} $ 26 50 12 15 17
$ N_{13} $ 75 50 12 15 17
$ N_{14} $ 18 50 12 15 17
$ N_{15} $ 16 50 12 15 17
$ N_{16} $ 19 50 12 15 17
$ N_{17} $ 37 50 12 15 17
$ N_{18} $ 70 50 12 15 17
$ N_{19} $ 90 50 12 15 17
Car flow rate $ \overline{m}_{st} $ $ \omega_{ff} $ $ \omega_{zf} $ $ \omega_{zz} $
$ N_{11} $ 6 40 12 15 17
$ N_{12} $ 26 50 12 15 17
$ N_{13} $ 75 50 12 15 17
$ N_{14} $ 18 50 12 15 17
$ N_{15} $ 16 50 12 15 17
$ N_{16} $ 19 50 12 15 17
$ N_{17} $ 37 50 12 15 17
$ N_{18} $ 70 50 12 15 17
$ N_{19} $ 90 50 12 15 17
Table 4.  Technical parameters of main marshalling station of railroad network
Marshalling station 1 2 3 4 5 6
$ t_{k}(Hour) $ 3 3 4 3 3 4
$ \overline{m}_{sk} $(Car) 40 40 40 40 40 40
Marshalling station 1 2 3 4 5 6
$ t_{k}(Hour) $ 3 3 4 3 3 4
$ \overline{m}_{sk} $(Car) 40 40 40 40 40 40
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