An augmented Lagrangean scheme for capacitated traffic assignment problems

Abstract

The inclusion of explicit bounds on the link ows in tra c assignment models has been proposed as a means to obtain a more accurate description of the tra c behaviour than that given by the basic, uncapacitated, model. Although the capacitated problem has the advantage of being numerically more tractable than models involving travel cost functions which tend to in nity as ows approach the link capacities, it has received very limited attention in the past. The main reason for this is that the explicit capacities make the problem computationally more demanding, since they destroy the Cartesian product structure of the feasible set of the uncapacitated model, which enables the development of highly e cient solution procedures for that problem. The availability of e cient procedures for the basic model motivates the use of dualization approaches for handling the capacity constraints of the more complex model � we propose and evaluate an augmented Lagrangean method in which uncapacitated tra c assignment subproblems are solved with the disaggregate simplicial decomposition algorithm. This algorithm fully exploits the subproblems ' structure and also has very favourable reoptimization facilities. Both these properties are of greatest importance for achievin