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1. 重庆交通大学 山地城市交通系统与安全重庆市重点实验室, 重庆 400074;
2. 重庆交通大学 交通运输学院, 重庆 400074;
3. 中国中铁二院工程集团有限责任公司, 四川 成都 610031

Collaborative optimization model for oversaturated multiple intersections based on the rough set theory
CHEN Jian1,2, CHEN Jian3, SHAO Yiming1,2 , DENG Tianmin1,2
1. Chongqing Key Lab of Traffic System & Safety in Mountain Cities, Chongqing Jiaotong University, Chongqing 400074, China;
2. School of Traffic and Transportation, Chongqing Jiaotong University, Chongqing 400074, China;
3. China Railway Eryuan Engineering Group Co., Ltd, Chengdu 610031, China
Abstract: To solve the defect that the existing fuzzy intelligent control method is only suitable for a single intersection under unsaturated state, and to meet the need of coordination control of regional traffic for oversaturated multiple intersections, an optimization control strategy for main channel at peak time was proposed. The fuzzy control model with multiple decision attributes was established on the basis of knowledge reasoning in rough sets theory. It took multiple intersections state information as condition attributes, and the elongation mode, phase, and green light timing, as decision attributes. The methods of attribute reduction of the discernibility matrix and the frequency of attribute were used in the model, then some decision rules were extracted. The results show that the efficiency of regional traffic was improved via 3-8 more seconds of green light signal at the main channel. In addition, the extension time is not only related to the maximum queue length of vehicles under oversaturated vehicle conditions, but also the extension mode and phase of green light, which is consistent with the experience of traffic police.
Key words: traffic engineering     traffic control     multiple intersections     oversaturated     rough set theory     decision rule

1 粗糙集的基本理论

1.1 知识与等价类

1.2 上近似集与下近似集

 图 1 上近似集与下近似集关系图Fig. 1 Relation of upper approximation set and lower approximation set
1.3 属性约简

2 协同优化模型 2.1 通道划分

2.2 属性选择

2.3 属性值模糊化

2.4 决策表构建与属性约简 2.4.1 决策表构建

2.4.2 基于可辨识矩阵与属性频度的属性约简

1)如果决策表中的条件属性值与决策属性值存在连续变量，则进行离散化处理。属性约简集合B=∅，Core=∅。

2)根据决策表与式(8)生成可辨识矩阵M。

3)找出可辨识矩阵的核集合Core(属性组合数为1)，并更新约简集合B=Core

4)删除可辨识矩阵中与B交集不为空的元素，M=M-QQ={CijCij∩B=∅}；并且从条件属性集合C中删除B中元素，C=C-B

5)计算条件属性集合C中剩余的所有元素在可辨识矩阵 M中出现的次数p(c)，将最大次数所对应的元素添加入约简属性集合B中，B=B+cqp(cq)=max{p(c)}。

6)如果M=∅，则输出约简集合B；否则，返回3)。

2.4.3 规则提取

2.5 评价指标计算

3 实例分析

 图 2 重庆市江北区新南路4个交叉口地理分布Fig. 2 Geographical distribution of four intersections in Xinnan road, Jiangbei district, Chongqing
 图 3 新南路交叉口仿真建模Fig. 3 Simulation modeling of Xinnan road intersections

 条件属性 决策属性
 N qz1 qc1 qz2 qc2 qz3 qc3 qz4 qc4 W E G
 1 4 3 2 3 3 4 3 5 4 0 0 3 2 4 4 3 5 5 4 2 6 5 1 1 7 3 4 3 4 4 3 5 5 6 6 1 0 5 4 4 3 3 4 4 3 4 4 5 0 0 4 5 4 2 2 3 2 3 3 5 5 0 0 3 6 4 5 5 5 4 4 3 5 6 1 1 5 7 4 3 3 3 4 4 3 5 5 0 0 4 8 4 4 3 4 4 5 4 4 5 0 1 3 9 4 2 2 3 2 4 3 5 5 0 0 3 10 4 4 3 4 4 5 4 4 5 1 0 4

W为决策属性，根据决策表约简算法，得到约简集合为{qz2qz3qz4}。将相同决策规则合并，并通过式(9)~(11)计算各决策规则评价指标值如表 2所示。

 qz2 qz3 qz4 W Support Accuracy Coverage 3 3 5 0 1 1 0.17 3 4 5 0 3 1 0.50 4 3 4 0 1 1 0.17 4 5 6 1 1 1 0.25 5 4 5 1 1 1 0.25 5 4 6 1 1 1 0.25

 qz1 qz4 E Support Accuracy Coverage 2 5 0 2 1 0.29 3 4 0 1 1 0.14 3 5 0 2 1 0.29 3 6 0 1 1 0.14 4 6 1 1 1 0.33 5 5 1 1 1 0.33

G为决策属性，得到约简集合为{qc1qz3qz4}。将相同决策规则合并，最终约简结果如表 4所示。

 qc1 qz3 qz4 G Support Accuracy Coverage 2 3 5 3 1 1 0.25 2 4 5 3 2 1 0.50 3 3 4 4 1 1 0.33 3 4 5 4 1 1 0.33 4 5 6 5 1 1 0.50 5 4 5 5 1 1 0.50 3 4 6 7 1 1 1.00

 条件属性 决策属性 q z1 q c1 q z2 q z3 q z4 W E G RS RS M M L 0 0 3 M RS M RL L 0 0 3 M M RL M RL 0 0 4 L M L RL L 1 1 4 M RL RL L VL 1 1 5 / L / RL L / / 5 RL M L RL VL 1 1 7

4 结束语

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DOI: 10.11992/tis.201406045

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#### 文章信息

CHEN Jian, CHEN Jian, SHAO Yiming, DENG Tianmin

Collaborative optimization model for oversaturated multiple intersections based on the rough set theory

CAAI Transactions on Intelligent Systems, 2015, 10(05): 783-789.
DOI: 10.11992/tis.201406045