| A Skew Gradient-Based Newton Method for Traffic Assignment with Side Constraints |
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| 作者姓名： | 程琳 王炜 朱志坚 于春青 |
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| 作者单位： | Transportation College Southeast University Nanjing 210018 China，Transportation College Southeast University Nanjing 210018 China，Transportation College Southeast University Nanjing 210018 China，Transportation College Southeast University Nanjing 210018 China |
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| 基金项目： | 国家自然科学基金;国家重点基础研究发展计划(973计划) |
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| 摘 要： | In this paper we describe how the capacitated user equilibrium can be approximated by sequential uncapacitated models by the use of a penalty function. The efficiency of the method is governed by the algo-rithmic performance of the uncapacitated model. A skew gradient-based Newton method is used to solve the capacitated user equilibrium within the feasible region of path flows. In the path-flow region, the straight gradient is defined as the derivative of the objective function with respect to the flow of the corresponding path, while the skew gradient is defined for each particular origin destination pair and is characterized by the average cost of all the paths for that pair. Instead of movement of flow toward the shortest path, in the equilibration procedure path flows below the average decrease and path flows above the average increase. The characteristics of the Newton method with the column generation procedure are combined to achieve the efficient determination of the equilibrium point. Numerical experiments demonstrate the excellent performance of the proposed method and highlight its potential applications.
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| 关 键 词： | 交通分配 边约束 牛顿法 倾斜梯度 交通流类型 用户平衡 |
| 收稿时间： | 8 October 2006. |
| 修稿时间： | 2006-10-08 |
A Skew Gradient-Based Newton Method for Traffic Assignment with Side Constraints |
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| Lin Cheng, « &#x;, Wei Wang, , Zhijian Zhu, &#x;ý
,Chunqing Yu, î&#x;&#x;.A Skew Gradient-Based Newton Method for Traffic Assignment with Side Constraints[J].Tsinghua Science and Technology,2007,12(2):184-191. |
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| Authors: | Lin Cheng « &#x; Wei Wang Zhijian Zhu &#x;ý
Chunqing Yu î&#x;&#x; |
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| Institution: | Transportation College, Southeast University, Nanjing 210018, China |
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| Abstract: | In this paper we describe how the capacitated user equilibrium can be approximated by sequential uncapacitated models by the use of a penalty function. The efficiency of the method is governed by the algo-rithmic performance of the uncapacitated model. A skew gradient-based Newton method is used to solve the capacitated user equilibrium within the feasible region of path flows. In the path-flow region, the straight gradient is defined as the derivative of the objective function with respect to the flow of the corresponding path, while the skew gradient is defined for each particular origin destination pair and is characterized by the average cost of all the paths for that pair. Instead of movement of flow toward the shortest path, in the equilibration procedure path flows below the average decrease and path flows above the average increase. The characteristics of the Newton method with the column generation procedure are combined to achieve the efficient determination of the equilibrium point. Numerical experiments demonstrate the excellent performance of the proposed method and highlight its potential applications. |
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| Keywords: | traffic assignment side constraint Newton method skew gradient |
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