Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem

Chung Cheng Lu, Hani S. Mahmassani, Xuesong Zhou

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

A variety of analytical and simulation-based models and algorithms have been developed for the dynamic user equilibrium (DUE) traffic assignment problem. This paper aims to develop a theoretically sound simulation-based DUE model and its solution algorithm, with particular emphasis on obtaining solutions that satisfy the DUE conditions. The DUE problem is reformulated, via a gap function, as a nonlinear minimization problem (NMP). The NMP is then solved by a column generation-based optimization procedure which embeds (i) a simulation-based dynamic network loading model to capture traffic dynamics and determine experienced path travel costs for a given path flow pattern and (ii) a path-swapping descent direction method to solve the restricted NMP defined by a subset of feasible paths. The descent direction method circumvents the need to compute the gradient of the objective function in finding search directions, or to determine suitable step sizes, which is especially valuable for large-scale simulation-based DUE applications. Computational results for both small and large real road networks confirm that the proposed formulation and solution algorithm are effective in obtaining near-optimal solutions to the DUE problem.

Original languageEnglish (US)
Pages (from-to)345-364
Number of pages20
JournalTransportation Research Part B: Methodological
Volume43
Issue number3
DOIs
StatePublished - Mar 2009
Externally publishedYes

Fingerprint

simulation
traffic
equilibrium model
road network
Equilibrium problem
Set theory
travel
Flow patterns
Acoustic waves
costs
Simulation
Costs
Optimal solution
Assignment problem
Travel cost
Column generation
Gradient
Network dynamics
Objective function
Road network

Keywords

  • Column generation algorithm
  • Dynamic traffic assignment
  • Dynamic user equilibrium
  • Gap function
  • Traffic simulation

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Transportation

Cite this

Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem. / Lu, Chung Cheng; Mahmassani, Hani S.; Zhou, Xuesong.

In: Transportation Research Part B: Methodological, Vol. 43, No. 3, 03.2009, p. 345-364.

Research output: Contribution to journalArticle

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