A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time

A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time

The cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have...

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Main Authors: Wen-Xiang Wu, Hai-Jun Huang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/271358
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spelling doaj-1143cc79a61f4c628a47a6cdedf152b32020-11-24T23:30:03ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/271358271358A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of TimeWen-Xiang Wu0Hai-Jun Huang1Beijing Key Lab of Urban Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, ChinaSchool of Economics and Management, Beihang University, Beijing 100191, ChinaThe cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. We develop a path-based gradient projection algorithm for solving the cost-based system optimum model, based on Goldstein-Levitin-Polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. The Sioux Falls network tested is used to verify the effectiveness of the algorithm.http://dx.doi.org/10.1155/2014/271358
collection DOAJ
language English
format Article
sources DOAJ
author Wen-Xiang Wu
Hai-Jun Huang
spellingShingle Wen-Xiang Wu
Hai-Jun Huang
A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time
Journal of Applied Mathematics
author_facet Wen-Xiang Wu
Hai-Jun Huang
author_sort Wen-Xiang Wu
title A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time
title_short A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time
title_full A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time
title_fullStr A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time
title_full_unstemmed A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time
title_sort path-based gradient projection algorithm for the cost-based system optimum problem in networks with continuously distributed value of time
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description The cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. We develop a path-based gradient projection algorithm for solving the cost-based system optimum model, based on Goldstein-Levitin-Polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. The Sioux Falls network tested is used to verify the effectiveness of the algorithm.
url http://dx.doi.org/10.1155/2014/271358
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AT haijunhuang apathbasedgradientprojectionalgorithmforthecostbasedsystemoptimumprobleminnetworkswithcontinuouslydistributedvalueoftime
AT wenxiangwu pathbasedgradientprojectionalgorithmforthecostbasedsystemoptimumprobleminnetworkswithcontinuouslydistributedvalueoftime
AT haijunhuang pathbasedgradientprojectionalgorithmforthecostbasedsystemoptimumprobleminnetworkswithcontinuouslydistributedvalueoftime
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