Article Contents
Article Contents

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

• *Corresponding author: Zhi Lin

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)

• 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.

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

 Citation:

• Figure 1.  The traffic network $\aleph$

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

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

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

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