首页 关于本刊 编 委 会 期刊动态 作者中心 审者中心 读者中心 下载中心 联系我们 English
 自动化学报  2017, Vol. 43 Issue (7): 1220-1233 PDF

1. 城市道路交通智能控制技术北京市重点实验室 北京 100144;
2. 北方工业大学电气与控制工程学院 北京 100144;
3. 北京城市系统工程研究中心 北京 100035;
4. 中国科学院自动化研究所 北京 100190

Urban Area Oversaturated Traffic Signal Optimization Control Based on MFD
LIU Xiao-Ming1,2, TANG Shao-Hu1,2,3, ZHU Feng-Hua4, CHEN Zhao-Meng1,2
1. Beijing Key Laboratory of Urban Road Traffic Intelligent Technology, Beijing 100144;
2. College of Electrical and Control Engineering, North China University of Technology, Beijing 100144;
3. Beijing Research Center of Urban System Engineering, Beijing 100035;
4. Institute of Automation, Chinese Academy of Sciences, Beijing 100190
Manuscript received : March 4, 2016, accepted: August 31, 2016.
Foundation Item: Supported by National Natural Science Foundation of China (61374191), National Science and Technology Support Program (2014BAG03B01), and the Great Wall Scholars Program (CIT & TCD20150301)
Corresponding author. TANG Shao-Hu Research associate at Beijing Research Center of Urban System Engineering. He received his Ph. D. degree from North China University of Technology in 2017. His research interest covers urban resilience, traffic control, and intelligent algorithm. Corresponding author of this paper.E-mail:tshaohu@163.com
Recommended by Associate Editor DONG Hai-Rong
Abstract: In order to solve traffic efficiency reduction of road network, which is caused by overlarge traffic demand of urban regions at peak hours, and resource waste of roads due to the heterogeneity of traffic distribution, this paper proposes an optimization model of control for oversaturated area based on inherent attributes macroscopic fundamental diagram (MFD) of regional road network, and builds up the bi-level programming optimization of objective function for boundary and internal signal control. Furthermore, an adaptive dynamic programming (ADP) model based on back propagation (BP) neural network is employed to solve the regional signal control of bi-level programming. Simulation results verify the validity of this method. The investigation of this paper has certain guidance for urban traffic management such as control and management of traffic demand, formulation of congestion policy, etc.
Key words: Regional traffic signal optimization     macroscopic fundamental diagram (MFD)     bi-level programming     adaptive dynamic programming (ADP)     back propagation (BP) neural network

1 过饱和区域MFD控制优化模型 1.1 基本思路

 图 1 过饱和区域边界及内部交叉口示意图 Figure 1 Boundary of oversaturated area and internal intersection diagram

 图 2 过饱和区域信号控制优化模型框架 Figure 2 Frame of oversaturated area traffic signal optimization control model
1.2 边界需求控制

 图 3 路网两种MFD关系模型 Figure 3 Two MFD relational models of network

 \begin{align}\frac{{\rm d}n(t) }{\mathrm{d} t}= q_{\rm in}(t)-q_{\rm out}(t)+v(t)\end{align} (1)

 \begin{align}q_{\rm in}(t)= \sum\limits_{i=1}^{I}q_{i\_{\rm in}}(t)=\sum\limits_{i=1}^{I}\sum\limits_{j=1}^{P}\pi _{ij}k_{ij}g_{ij\_{\rm in}}C_{\rm cap}\end{align} (2)

 $\left\{ {\begin{array}{*{20}{l}} {\mathop {\lim }\limits_{t \to T} ({Q_{{\rm{out}}}}) = \bar n}\\ {\mathop {\lim }\limits_{t \to T} (n(t) - n(t - 1)) = \psi } \end{array}} \right.$ (3)

 \begin{align}q_{\rm in}(t)-\bar{n}+{d} (t)=0\end{align} (4)

 $\left\{ {\begin{array}{*{20}{l}} {{{\bar g}_{i\_{\rm{in}}}} = {\alpha _i} \times \frac{{\bar n - d(t)}}{{\sum\limits_{i = 1}^I {\sum\limits_{j = 1}^P {{k_{ij}} \times {C_{{\rm{cap}}}}} } }}}\\ {{{\bar g}_{ij{\rm{\_in}}}} = {\beta _j} \times {{\bar g}_{i\_{\rm{in}}}}} \end{array}} \right.$ (5)

 ${\alpha _i} = \frac{{{{\bar q}_{i\_{\rm{in}}}}}}{{\sum\limits_{i = 1}^I {{{\bar q}_{i\_{\rm{in}}}}} }}$ (6)
 ${\beta _j} = \frac{{{{\bar q}_{ij{\rm{\_in}}}}}}{{\sum\limits_{j = 1}^P {{{\bar q}_{ij{\rm{\_in}}}}} }}$ (7)

1.3 内部均衡控制

 ${N_j}(t + 1) = {N_j}(t) + {Q_{j\_{\rm{in}}}}(t) - {Q_{j\_{\rm{out}}}}(t)$ (12)
 ${Q_{j\_{\rm{in}}}}(t) = \sum\limits_{{i_q} \in V_j^I} {{\alpha _{{i_q}j}}{\eta _{{i_q}}}(t){N_{{i_q}}}(t)}$ (13)
 ${Q_{j\_{\rm{out}}}}(t) = \sum\limits_{{k_q} \in V_j^D} {{\alpha _{j{k_q}}}{\eta _j}(t){N_j}(t)}$ (14)

1.4 双层规划优化

 $\left\{ {\begin{array}{*{20}{l}} {\mathop {\lim }\limits_{t \to T} ({Q_{{\rm{out}}}}) = Q_{{\rm{out}}}^{\max }}\\ {\mathop {\lim }\limits_{t \to T} (n(t) - n(t - 1)) = \psi } \end{array}} \right.$ (23)

 ${J_u}(t) = \frac{1}{{Q_{{\rm{out}}}^{\max }}} = \frac{1}{{\max \left[ {\sum\limits_{i = 1}^I {\sum\limits_{j = 1}^P {{k_{ij}}{g_{i{j\_{{\rm{out}}}}}}{C_{{\rm{cap}}}}} } } \right]}}$ (24)

 $\left\{ {\begin{array}{*{20}{l}} {{g_{{\rm{out}}\_\min }} ＜ {g_{i\_{\rm{out}}}} ＜ {g_{{\rm{out}}\_\max }}}\\ {{g_{{\rm{in}}\_\min }} ＜ {g_{i\_{\rm{in}}}} ＜ {g_{{\rm{in}}\_\max }}}\\ {\sum {{g_{i\_{\rm{out}}}}} + \sum {{g_{i\_{\rm{in}}}}} + {L_{{\rm{lost}}}} = {C_i}}\\ {\sum\limits_{i = 1}^4 {{N_i} ＜ {N_{{i\_{\max }}}}} }\\ {\mathop {\lim }\limits_{t \to T} (\left| {n(t) - n(t - 1)} \right|) = \varepsilon }\\ {\mathop {\lim }\limits_{t \to T} (\left| {n(t) - \bar n} \right|) = \delta } \end{array}} \right.$ (25)

 $\begin{array}{l} {J_d}(t) = \min \left[ {\sum\limits_{i = 1}^n {{x_i}} + \frac{1}{2}\sum\limits_{i = 1}^n {{{\left| {{x_j} - {x_i}} \right|}^2}} } \right],{\rm{ }}\\ \qquad \qquad \qquad \qquad \qquad i = 1, \cdots ,n,\;i \ne j \end{array}$ (26)

 $\left\{ {\begin{array}{*{20}{l}} {{x_i} = \frac{{{N_i}}}{{{N_{i\_\max }}}}}\\ {{N_i} = {N_{{\rm{left}}}} + {Q_{i\_{\rm{in}}}} - {Q_{i\_{\rm{out}}}}}\\ {{Q_{i\_{\rm{in}}}} = \left( {g_l^uk_l^u + g_s^uk_l^u + g_r^uk_l^u} \right)s}\\ {{Q_{{i\_{{\rm{out}}}}}} = \left( {g_l^dk_l^d + g_s^dk_l^d + g_r^dk_l^d} \right)s}\\ {{N_i} ＜ {N_{{i\_{\max }}}}}\\ {\left( {g_l^uk_l^u + g_s^uk_l^u + g_r^uk_l^u} \right)s + {N_{{\rm{left}}}} ＜ {N_{i\_\max }}}\\ {g_l^u + g_s^u + g_r^u ＜ {G^u}}\\ {g_l^d + g_s^d + g_r^d ＜ {G^d}} \end{array}} \right.$ (27)

1.5 模型分析

 $n(t) = \sum\limits_{j \in V_j^I} {{N_j}(t)}$ (28)

 $\left\{ {\begin{array}{*{20}{l}} {{O_{j,j + 1}}(t) = \frac{{{L_j} - \frac{{{N_j}(t){L_j}}}{{{N_{j,\max }}}}}}{{{v_j}}} - \frac{{{L_j}{N_j}(t)}}{{\lambda {N_{j,\max }}}}}\\ {0 ＜ \max {x_j} ＜ A,\;j ＞ 0} \end{array}} \right.$ (29)

 ${s_i}{k_i}{g_i}(t + 1) + {N_j}(t) \le {N_{j\_\max }},\;\;\forall i \in V_j^I$ (30)

 图 5 评价网络结构图 Figure 5 Valuation network diagram

 图 6 执行网络结构图 Figure 6 Executive network diagram
2.2 求解步骤

 $\left\{ {\begin{array}{*{20}{l}} {{{\left[ {1 - \frac{{{C_i}(t - 1)}}{{{C_i}(t)}}} \right]}^2} + {{\left[ {1 - \frac{{{r_i}(t - 1)}}{{{r_i}(t)}}} \right]}^2} \le {p_i},}\\ {\quad \quad \quad \quad \forall x_i^r(t - 1) ＜ 1,\;r = 1,2,3,4}\\ {\frac{{\sum {{n_i}} }}{N} \le e} \end{array}} \right.$ (34)

 图 8 ADP模型训练值与标准值对比及误差 Figure 8 Comparison and deviation between training value and standard value of ADP model

3.2 结果分析

 图 9 路网车辆平均延误对比 Figure 9 Comparison of network vehicle average delay
 图 10 路网车辆数对比 Figure 10 Comparison of network vehicle number
 图 11 路网车辆占有率对比 Figure 11 Comparison of network vehicle occupancy
 图 12 路网车辆平均停车次数对比 Figure 12 Comparison of network vehicle average stops

 图 13 路径1和路径2平均延误对比 Figure 13 Comparison of average delay between Route 1 and Route 2
 图 14 路径3和路径4平均延误对比 Figure 14 Comparison of average delay between Route 3 and Route 4
 图 15 路径1和路径2平均停车次数对比 Figure 15 Comparison of average stops between Route 1 and Route 2
 图 16 中路径3和路径4平均停车次数对比文标题 Figure 16 Comparison of average stops between Route 3 and Route 4
4 结论