Algorithms for the Pareto solution of the multicriteria traffic equilibrium problem with capacity constraints of arcs

Zhi Lin; Zaiyun Peng

doi:10.3934/jimo.2022104

Article Contents

2023, Volume 19, Issue 5: 3694-3705. Doi: 10.3934/jimo.2022104

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Algorithms for the Pareto solution of the multicriteria traffic equilibrium problem with capacity constraints of arcs

Zhi Lin^, and
Zaiyun Peng

College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

^*Corresponding author: Zhi Lin
^*Corresponding author: Zhi Lin

Received: October 2021

Revised: March 2022

Early access: June 2022

Published: May 2023

The first author is supported by Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016) and Group Building Scientific Innovation Project for universities in Chongqing (CXQT21021)

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Abstract

We focus on the multicriteria traffic equilibrium problem with capacity constraints of arcs. First, we generalize Beckmann's formula to deal with multicriteria traffic equilibrium problems with capacity constraints of arcs and prove that the solution of the mathematical programming problem is a Pareto traffic equilibrium flow with capacity constraints of arcs. Furthermore, we present a restricted algorithm for computing the Pareto traffic equilibrium flow with capacity constraints of arcs. Using the restricted algorithm, one does not need to know the set of available paths joining origin-destination pairs. This proves very helpful for complex traffic networks. Finally, for the algorithms of the Pareto traffic equilibrium flow, we give two examples to exemplify calculation processes.

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Mathematics Subject Classification: Primary: 49J40, 49J53; Secondary: 90B20.

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Figure 1. The traffic network $ \aleph $

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Figure 2. The weighted network $ \hat{\aleph}^{1} $

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Figure 3. The weighted network $ \hat{\aleph}^{2} $

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Figure 4. The weighted network $ \hat{\aleph}^{3} $

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