铁路专用线取送车问题的帕累托前沿分析

郑亚晶; 张德坤

doi:10.3969/j.issn.0258-2724.20240464

铁路专用线取送车问题的帕累托前沿分析

doi: 10.3969/j.issn.0258-2724.20240464

华南理工大学土木与交通学院，广东广州 510640

基金项目: 国家自然科学基金项目（52072128）

详细信息

作者简介:
郑亚晶（1982—），男，博士，讲师，研究方向为轨道交通运输组织优化. E-mail：ctyjzheng@scut.edu.cn

中图分类号: U292.2
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出版历程
- 收稿日期: 2024-09-13
- 修回日期: 2025-04-26
- 网络出版日期: 2026-11-09

Pareto Frontier Analysis of Placing-in and Taking-out Wagons on Railway Sidings

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China

Funds: Supported by the National Natural Science Foundation of China（52072128）

摘要

摘要:
为兼顾铁路专用线取车、送车和调移作业中的多目标优化需求，并为取送车作业方案选择提供决策依据，构建以混合型布置形式专用线为对象的两层级优化模型，第一层级最小化调机走行总时间，第二层级在保证第一层级最优的前提下，同时最小化专用线入线车小时消耗和走行车辆公里数. 为求解该模型，设计多目标模拟退火算法：首先，利用单目标模拟退火算法求解仅覆盖调移需求装卸站的最短路径；然后，依据混合型专用线分层特性构造插入算子，将剩余取送车需求装卸站插入最短路径，形成满足调机走行总时间最小的初始方案；最后，将道岔及货运站视为根节点、顺次经过的节点视为子树，提出交换同一根下子树访问顺序的邻域变换方法. 算例结果表明：算法获得的帕累托前沿由5个非劣解构成，各方案的调机走行总时间均为304 min，入线车小时消耗为6219～6317 min，走行车辆公里数为1443.1～1481.5 km；超体积（HV）值在降温约40次后达到最大，验证了算法具有良好的收敛性能，可有效获得铁路专用线取送车问题的帕累托前沿.
- 混合型专用线 /
- 取送车作业 /
- 多目标优化 /
- 模拟退火算法
Abstract:
A two-level optimization model for the placing-in and taking-out wagons problem on hybrid railway sidings was constructed. The primary objective was to minimize the total running time of shunting locomotives, while the secondary objective was to minimize both the total wagon-hours on sidings and the total wagon-kilometers traveled, with the precondition that the primary objective remained optimal. To solve this model, a multi-objective simulated annealing algorithm was designed. First, the shortest path covering only the loading stations with transfer demands was obtained using a single-objective simulated annealing algorithm. Then, an insertion operator was developed based on the hierarchical characteristics of hybrid sidings to incorporate the remaining loading stations with placing-in and taking-out demands into the shortest path, generating an initial scheme with the minimum shunting locomotive running time. Furthermore, turnouts and freight stations were treated as root nodes, while sequentially visited nodes within the same root were regarded as subtrees; a neighborhood transformation method was proposed by exchanging the visiting order of subtrees under the same root. A numerical case was conducted to validate the model and algorithm. Results indicate that the proposed algorithm yielded a Pareto front consisting of five non-dominated solutions, each with a shunting locomotive running time of 304 min, total wagon-hours ranging from 6219 to 6317 min, and total wagon-kilometers ranging from 1443.1 to 1481.5 km. The Hypervolume (HV) value reached its maximum after approximately 40 cooling iterations, demonstrating the favorable convergence performance of the algorithm.
- Hybrid sidings /
- Placing-in and taking-out wagons /
- Multi-objective optimization /
- Simulated annealing algorithm

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图 1 混合型专用线

Figure 1. Hybrid sidings

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图 2 初始取送车方案的编码解码示意

Figure 2. Diagram illustrating the encoding and decoding of the initial placing-in and taking-out wagons plan

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图 3 编码示意

Figure 3. Encoding diagram

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图 4 $ {f}_{1} $解码及计算示意

Figure 4. Diagram illustrating the decoding and computation of $ {f}_{1} $

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图 5 $ {f}_{21} $解码及计算示意

Figure 5. Diagram illustrating the decoding and computation of $ {f}_{21} $

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图 6 $ {f}_{22} $解码及计算示意

Figure 6. Diagram illustrating the decoding and computation of $ {f}_{22} $

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图 7 $ {f}_{31} $解码及计算示意

Figure 7. Diagram illustrating the decoding and computation of $ {f}_{31} $

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图 8 $ {f}_{32} $解码及计算示意

Figure 8. Diagram illustrating the decoding and computation of $ {f}_{32} $

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图 9 $ {f}_{33} $解码及计算示意

Figure 9. Diagram illustrating the decoding and computation of $ {f}_{33} $

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图 10 邻域变换示意

Figure 10. Neighborhood transformation illustration

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图 11 算法流程

Figure 11. Algorithm flow chart

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图 13 帕累托前沿

Figure 13. Pareto front

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图 14 算法进化过程

Figure 14. Algorithm evolution process diagram

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表 1 道岔分层结果

Table 1. Hierarchical result

放射枝	装卸站
放射枝1	1		2、3
放射枝1			2				3
放射枝2	4
放射枝3	5				6
放射枝4	11	7、8、9、10
		7		8、9、10
				8		9、10
						9		10

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表 2 调机在各段上的走行时间及走行距离

Table 2. Running time and running distance on each section for shunting locomotive

专用线	走行时间/min	距离/km	专用线	走行时间/min	距离/km	专用线	走行时间/min	距离/km
O-A	7	3.0	O-C	10	4.2	E-F	12	5.0
A-1	11	4.6	C-5	15	6.3	E-7	6	2.5
A-B	5	2.1	C-6	6	2.5	F-G	4	1.7
B-2	4	1.7	O-D	3	1.3	F-8	14	5.8
B-3	8	3.3	D-11	7	2.9	G-9	7	2.9
O-4	16	6.7	D-E	9	3.8	G-10	8	3.3

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表 3 各装卸站待送车辆数与待取车辆数

Table 3. Number of vehicles waiting to be delivered and picked up at each loading station 辆

装卸站	待送车辆数	待取车辆数
1	1	1
2	3	4
3	4	3
4	2	5
5	5	2
6	3	4
7	2	1
8	1	3
9	4	2
10	3	5
11	2	2

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表 4 调移需求

Table 4. Transfer demand

调移起始站	调移目标站	调移车辆数/辆	是否位于同一枝
1	2	2	是
1	8	3	否
2	4	1	否
4	7	3	否
7	10	3	是

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表 5 算例结果

Table 5. Example result

取送车方案	$ {f}_{1} $/min	$ {f}_{2} $/min	$ {f}_{3} $/km
0→1→2→3→0→4→0→7→10→9→8→11→0→6→5→0	304	6219	1481.5
0→1→2→3→0→4→0→7→9→10→8→11→0→6→5→0	304	6239	1474.1
0→1→2→3→0→4→0→7→10→9→8→11→0→5→6→0	304	6249	1453.9
0→1→2→3→0→4→0→7→9→10→8→11→0→5→6→0	304	6269	1446.5
0→1→3→2→0→4→0→7→9→10→8→11→0→5→6→0	304	6317	1443.1

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铁路专用线取送车问题的帕累托前沿分析

doi: 10.3969/j.issn.0258-2724.20240464

作者简介: 郑亚晶（1982—），男，博士，讲师，研究方向为轨道交通运输组织优化. E-mail：ctyjzheng@scut.edu.cn

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Pareto Frontier Analysis of Placing-in and Taking-out Wagons on Railway Sidings

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作者简介:
郑亚晶（1982—），男，博士，讲师，研究方向为轨道交通运输组织优化. E-mail：ctyjzheng@scut.edu.cn