Traffic assignment problem (TAP) in static equilibrium conditions is based on the Wardrop´s
first principle. The mathematical solution of this problem involves significant computation
times for the analysis of large transportation networks, especially in the context of design.
Thus, the development of efficient computational methodologies is of the greatest concern.
In this article, a reduced order model for TAP, based on a Finite Element Approach (FEA),
is proposed. Such methodology involves four main ideas: a) the TAP formulation including
as variables the travel times from any node of the network to the corresponding destination
points, b) the solution of the governing algebraic equation system by means of an efficient
iterative approach, known as “Physarum”, that takes the travel times as the main unknowns,
c) the interpolation of travel times in certain urban subdomains, denominated “finite
elements”, in terms of the values corresponding to some main nodes previously selected
(reduced unknowns), d) the use of the Galerkin’s method to express the TAP in terms of the
reduced unknowns. The model formulation is presented and a numerical example is given
to show its efficiency.
