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

Abstract

<p style='text-indent:20px;'>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.</p>