, Volume 44, Issue 2, pp 289-313
Date: 04 Dec 2007

Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem

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Abstract

The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem can be formulated as a variational inequality, and several algorithms have been devised for its efficient solution. In this work we propose a new approach that combines two existing procedures: the master problem of a simplicial decomposition algorithm is solved through the analytic center cutting plane method. Four variants are considered for solving the master problem. The third and fourth ones, which heuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems—including a subset of the transportation networks of Madrid and Barcelona—show the effectiveness of the approach.

The authors are indebted to J. Barceló for his encouragement in the initial stages of this work; to M. Denault and J.-L. Goffin for providing us with a MATLAB prototype of their ACCPM algorithm for variational inequalities; to the referees for suggesting the fourth solution variant of the paper, the inclusion of difficult asymmetric problems and the comparison with the origin-based algorithm; and to H. Bar-Gera who provided and assisted us with an implementation of his origin-based algorithm.
D. Rosas supported by a grant from the Universidad Nacional Autónoma de México.
J. Castro supported by Spanish MEC grant MTM2006-05550.
L. Montero supported by Spanish CICYT grant BFM2002-04548-C03-01.