, Volume 4, Issue 2, pp 225256
First online:
A simplicial decomposition algorithm for solving the variational inequality formulation of the general traffic assignment problem for large scale networks
 L. MonteroAffiliated withStatistics and Operations Research Dept. Facultat d'Informàtica, Universitat Politècnica de Catalunya
 , J. BarcelóAffiliated withStatistics and Operations Research Dept. Facultat d'Informàtica, Universitat Politècnica de Catalunya
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The class of simplicial decomposition methods has been shown to constitute efficient tools for the solution of the variational inequality formulation of the general traffic assignment problem. This paper presents a particular implementation of such an algorithm, with emphasis on its ability to solve large scale problems efficiently.
The convergence of the algorithm is monitored by the primal gap function, which arises naturally in simplicial decomposition schemes. The gap function also serves as an instrument for maintaining a reasonable subproblem size, through its use in column dropping criteria. The small dimension and special structure of the subproblems also allows for the use of very efficient algorithms; several algorithms in the class of linearization methods are presented.
When restricting the number of retained extremal flows in a simplicial decomposition scheme, the number of major iterations tends to increase. For large networks the shortest path calculations, leading to new extremal flow generation, require a large amount of the total computation time. A special study is therefore made in order to choose the most efficient extremal flow generation technique.
Computational results on symmetric problems are presented for networks of some large cities, and on asymmetric problems for some of the networks used in the literature. Computational results for bimodal models of some large cities leading to asymmetric problems are also discussed.
Keywords
Traffic Equilibria Variational Inequalities Simplicial Decomposition Methods Projection Methods Quadratic Programming Title
 A simplicial decomposition algorithm for solving the variational inequality formulation of the general traffic assignment problem for large scale networks
 Journal

Top
Volume 4, Issue 2 , pp 225256
 Cover Date
 199612
 DOI
 10.1007/BF02568510
 Print ISSN
 11345764
 Online ISSN
 18638279
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Traffic Equilibria
 Variational Inequalities
 Simplicial Decomposition Methods
 Projection Methods
 Quadratic Programming
 Industry Sectors
 Authors

 L. Montero ^{(1)}
 J. Barceló ^{(1)}
 Author Affiliations

 1. Statistics and Operations Research Dept. Facultat d'Informàtica, Universitat Politècnica de Catalunya, c. Pau Gargallo 5, 08028, Barcelona, Spain