﻿ 基于不同目标下的城际铁路列车开行频率优化
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (4): 472-477.  DOI: 10.11908/j.issn.0253-374x.2018.04.008 0

### 引用本文

YE Yuling, ZHOU Yunfei, YANG Luqi. Optimization Research on the Operation Frequency of Intercity Trains under Different Targets[J]. Journal of Tongji University (Natural Science), 2018, 46(4): 472-477. DOI: 10.11908/j.issn.0253-374x.2018.04.008

### 文章历史

1. 同济大学 道路与交通工程教育部重点实验室，上海 201804;
2. 成都市双流区交通运输局，四川 成都 610200

Optimization Research on the Operation Frequency of Intercity Trains under Different Targets
YE Yuling 1, ZHOU Yunfei 1, YANG Luqi 2
1. Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China;
2. Transportation Bureau of Shuangliu District, Chengdu 610200, China
Abstract: A bi-level programming model was established, of which the upper-level pursues the maximum railway enterprise's benefits and the minimum social cost respectively, and the lower-level was modeled based on users equilibrium theory, to figure out sharing rate of different transport modes, passenger flow of different-ranks intercity trains and operating frequency of trains with different dwell plans and objectives. The bi-level model was solved by simulated annealing (SA) algorithm. In the end, this paper contrasted and analyzed the operating frequency of intercity trains under the two different objectives respectively by a sample to provide theoretic support for optimal management of railway in intercity passenger corridor.
Key words: intercity passenger corridor    operation frequency    enterprise benefits    total social cost    bi-level programming model

1 城际运输通道内的客流分配 1.1 城际客运通道虚拟网络

G=(N, A)为运输通道网络，其符号和变量定义如下：N为网络中节点的集合, 包括车站节点、列车发车节点、列车停车节点；A为网络中弧段的集合，包括上车弧段，下车弧段、乘车弧段、停车弧段；a为网络中的某一弧段，aAW为网络中所有OD(起终点)对的集合；w为网络的某一个OD对w, wWkw为OD对w之间的所有交通方式，k∈{g, r, b, c}，g表示城际列车，r表示普通铁路，b表示大巴，c表示小汽车；dw为OD对w之间的客运需求量；qwk为OD对w之间的某种方式的客运需求量；cwk为OD对w之间某种方式的广义出行费用；qmG为OD对w之间的城际铁路的客运需求量；Ta为弧段上a的阻抗函数；Qwl为OD对w之间的第l条路径的客流量.

1.2 基于用户均衡的交通流分配

 ${c_{wk}} = f\left( {{q_{wk}}} \right) = g\left( {{q_{wk}}} \right) - {V_{wk}}$ (1)
 ${V_{wk}} = {\theta _1}{P_{wk}} + {\theta _2}{Y_{wk}} + {\theta _3}{E_{wk}} + {\theta _4}{R_{wk}} + {\theta _5}{S_{wk}}$ (2)

 $\min \left( {{q_{wk}}} \right) = \sum\limits_{w \in W} {\sum\limits_{k \in K} {\int_0^{{q_{wk}}} {{C_{wk}}{\rm{d}}x} } }$ (3)

 $\sum\limits_k {{q_{wk}}} = {d_w},w \in W$ (4)
 ${q_{wk}} \ge 0,\;\;\;k \in K,w \in W$ (5)

 ${p_{wk}} = \frac{{{q_{wk}}}}{{{d_w}}}$ (6)

 $\min \left( {{q_{wk}}} \right) = \sum\limits_a {\int_0^{{q_a}} {{C_a}\left( q \right){\rm{d}}q} }$ (7)

 $\sum\limits_l {{q_{wl}}} = {q_{wG}},w \in W$ (8)
 ${q_{wl}} \ge 0,l \in {l_w},w \in W$ (9)
 ${q_a} = \sum\limits_w {\sum\limits_l {{q_{wl}}{\delta _{wal}}} } ,l \in {l_w},w \in W$ (10)

1.3 弧段阻抗函数 1.3.1 上车弧段的阻抗函数

 ${T_{a1}} = \alpha \left( {{t_{a{\rm{in}}}} + {w_t}} \right)$ (11)

 $w{t_a} = 0.5/\left( {{f_1} + {f_2} + {f_3}} \right)$ (12)

1.3.2 乘车弧段的阻抗函数

 ${T_{a2}} = {D_a}{P_{a1}} + \omega {t_{a{\rm{run}}}}{\left( {{q_a}/{U_a}} \right)^\theta } + \alpha \left( {{t_{a{\rm{run}}}} + {t_{a{\rm{stop}}}}} \right)$ (13)

1.3.3 下车弧段的阻抗函数
 ${T_{a2}} = \alpha {t_{a{\rm{out}}}}$ (14)

2 开行频率的双层规划模型 2.1 双层模型建立

2.1.1 铁路企业效益最大化

 $\max {Y_1} = \sum\limits_\beta {\sum\limits_l {\sum\limits_{{e_i}} {q_\beta ^{{e_i}}{P_\beta }{D_{{e_i}}}} } } - \sum\limits_\beta {\sum\limits_l {f_l^\beta s_l^\beta b_l^\beta {C_{\rm{G}}}} }$ (15)

 $\sum\limits_l {\sum\limits_\beta {{f_{\beta l}}} } \le {N_{{h_i}}},i \in n$ (16)
 $\sum\limits_l {\sum\limits_\beta {{f_{\beta l}}} } \le {N_{{e_i}}},i \in n$ (17)
 ${q_{{e_i}}} = \sum\limits_{{e_i} \in w} {{q_{wG}}} ,i \in m$ (18)
 ${q_{{e_i}}} \le \sum\limits_\beta {\sum\limits_{l \in L} {{f_{\beta l}}{A_{\beta l}}} } ,i \in m$ (19)
 ${q_{{e_i}{\beta _l}}} \le {f_{\beta l}}{A_{\beta l}},i \in m$ (20)
 ${f_{\beta l}} \ge 0$ (21)

2.1.2 社会总成本最小化

 ${R_{\rm{r}}} = \sum\limits_\beta {\sum\limits_l {{f_{\beta l}}{s_{\beta l}}{b_{\beta l}}{C_{rh}}} } + {f_{\rm{r}}}{s_{\rm{r}}}{b_{\rm{r}}}{C_{\rm{r}}}$ (22)

 ${R_{\rm{b}}} = \sum\limits_w {{C_{\rm{b}}}{s_{w{\rm{b}}}}{q_{w{\rm{b}}}}/{\delta _{\rm{b}}}}$ (23)

 ${R_{\rm{c}}} = \sum\limits_w {{q_{w{\rm{c}}}}{C_{\rm{c}}}{s_w}/{\delta _{\rm{c}}}}$ (24)

 ${R_{\rm{e}}} = \sum\limits_w {{E_{\rm{c}}}{q_{w{\rm{c}}}}{s_w}/{\delta _{\rm{c}}}}$ (25)

 $\begin{array}{l} \min Y = {R_{\rm{r}}} + {R_{\rm{b}}} + {R_{\rm{c}}} + {R_{\rm{e}}} = \sum\limits_\beta {\sum\limits_l {{f_{\beta l}}{s_{\beta l}}{b_{\beta l}}{C_{rh}}} } + \\ \;\;\;\;\;\;\;\;\;\;\;\;\sum\limits_w {{C_{\rm{b}}}{s_{w{\rm{b}}}}{q_{w{\rm{b}}}}/{\delta _{\rm{b}}}} + \sum\limits_w {{q_{w{\rm{c}}}}{C_{\rm{c}}}{s_w}/{\delta _{\rm{c}}}} + \\ \;\;\;\;\;\;\;\;\;\;\;\;\sum\limits_w {{E_{\rm{c}}}{q_{w{\rm{c}}}}{s_w}/{\delta _{\rm{c}}}} + {f_{\rm{r}}}{s_{\rm{r}}}{b_{\rm{r}}}{C_{\rm{r}}} \end{array}$ (26)

2.2 模型的模拟退火算法设计

3 算例研究 3.1 算例参数

 图 1 城市之间的距离 Fig.1 Distance between cities

3.2 结果分析

 图 2 不同目标下运输通道交通方式分担率的对比 Fig.2 Comparison among sharing rate of all transport modes in transport corridor under different objectives

(1) 以社会总成本最小为目标时，由于综合考虑了小汽车外部成本的内部化，小汽车广义出行费用增加，使得小汽车的使用者向其他交通方式转移，大部分转移至城际铁路，因而城际铁路的最优开行频率增加.同时开行频率的增加会降低其广义出行费用，引起采用其他交通方式出行的旅客向城际铁路转移，城际铁路分担率的上升、其他交通方式中小汽车客流分担率的下降尤其明显.

(2) 以铁路运营企业效益最大化为目标时，城际铁路的最优开行频率比以社会总成本最小化为目标时低，各等级列车的席位利用率增大，其中直达模式的利用率达到了90%以上.以社会成本最小化为目标时，城际列车的交通分担率提高，城际列车开行的数量增加，但此时各列车的席位利用率下降，铁路企业效益也会下降.一定程度上说明此时增加城际列车开行数量并没有吸引足够的客流来弥补企业运营成本的增加.

(3) 从上表可见需要在牺牲企业效益的前提下才能够达到社会总成本最小，因此政府部门为促进运输通道内社会总成本最小化时需要适当对铁路企业进行政策优惠或补贴，使得铁路企业的开行方案在企业效益目标和社会总成本目标中达到一致.

4 结语

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