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.