A computational study of path-based methods for optimal traffic assignment with both inelastic and elastic demand

In this work we consider traffic assignment problems with both inelastic and elastic demand. As well-known, the elastic demand problem can be reformulated as a fixed demand problem by a suitable modification of the network representation. Then, the general network equilibrium problem we consider is a constrained convex minimization problem whose variables are the path flows. We define a framework where different path-based methods can be embedded. The framework is a Gauss–Seidel decomposition method, where the subproblems are inexactly solved by a line search along a feasible and descent direction. The key features of the framework are the definition of an initial stepsize based on second-order information and the use of an adaptive column generation strategy recently proposed in the literature. The extensive computational experiments, performed even on huge networks, show that path-based methods, suitably designed and implemented, may be an efficient tool for network equilibrium problems. In particular, in the solution of problems with elastic demand, a presented path equilibration algorithm obtained (in all the networks) levels of accuracy never reached (to our knowledge), say a relative gap of the order of 10^-14. Therefore, this latter algorithm may represent the state-of-art for traffic assignment problems with elastic demand.