Simplicial Decomposition with Disaggregated Representation for the Traac Assignment Problem

The class of simplicial decomposition (SD) schemes have shown to provide e cient tools for nonlinear network ows. When applied to the tra c assignment problem, shortest route subproblems are solved in order to generate extreme points of the polyhedron of feasible ows, and, alternately, master problems are solved over the convex hull of the generated extreme points. We review the development of simplicial decomposition and the closely related column generation methods for the tra c assignment problem; we then present a modi ed, disaggregated, representation of feasible solutions in SD algorithms for convex problems over Cartesian product sets, with application to the symmetric tra c assignment problem. The new algorithm, which is referred to as disaggregate simplicial decomposition (DSD), is given along with a specialized solution method for the disaggregate master problem. Numerical results for several well known test problems and a new one are presented. These experimentations indicate that only few shortest route searches are needed; this property is important for large-scale applications. The modi cation proposed maintains the advantages of SD, and the results show that the performance of the new algorithm is at least comparable to that of state-of-the-art codes for tra c assignment. Moreover, the reoptimization capabilities of the new scheme are signi cantly better; this is a main motive for considering it. The reoptimization facilities, especially with respect to changes in origin-destination ows and network topology, make the new approach highly pro table for more complex models, where tra c assignment problems arise as subproblems.