A New Look at Projected Gradient Method for Equilibrium Assignment

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Abstract
A new adaptation of Rosen's projected gradient algorithm for solving fixed-demand equilibrium traffic assignments is developed. It is based on a Gauss-Seidel decomposition scheme in which origin-destination pairs are considered sequentially. The method operates in the space of path flows and shares this approach with earlier work on adapting the gradient projection method, the restricted simplicial decomposition, and the projected gradient adapted for solving equilibrium traffic assignments with explicit capacity constraints. The details of the algorithm are nevertheless quite different and are intended to solve large-scale problem instances. The development of the method is provided, and then computational experiments are performed with an implementation done with the Emme software package. Performance comparisons are carried out against the linear approximation method and the origin base algorithm code of Bar-Gera. The algorithm compares well with these methods and achieves relative gaps of the order of 10-6 or 10-7 in reasonable computing times. It also has the advantage of reaching more modest relative gaps of the order of 10-4 in much shorter computing times than the linear approximation method.

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