An efficient approach to solving the road network equilibrium traffic assignment problem

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

“…The third variant also represents the feasible set by (23) and the optimality conditions of its analytic center are (24)(25)(26)(27). However, unlike the second variant, the starting point is heuristically obtained as…”

“…Equations (29) are approximately the optimality conditions (24)(25)(26)(27), but for the primal feasibility. Indeed, it can be easily proved that (29)-setting ǫ = 0-are the optimality conditions of the perturbed analytic center problem max λ,s…”

“…Many specialized strategies have been developed since [24], where an adaptation of the Frank-Wolfe method [12] was applied to its optimization formulation. Projection algorithms in the space of arc flows [7] and path flows [5] have also been applied.…”

User-equilibrium Route Set Analysis of a Large Road Network

“…The effectiveness of her algorithm for large networks was studied by several researchers; see Boyce and Bar-Gera (2004) for a recent review. Other young researchers at that same time proposed and tested algorithms for solving the user-equilibrium problem with fixed OD flows (LeBlanc et al, 1975;Nguyen, 1974;Florian and Nguyen, 1976), building upon the pioneering theoretical research of Jorgensen (1963), Dafermos (1968) and Brynooghe et al (1969). More recently, Patriksson (1994) thoroughly synthesized the accumulated literature from this 40-year research effort, and proposed his own userequilibrium algorithms for fixed and variable flow problems (Larsson and Patriksson, 1992;Lundgren and Patriksson, 1998).…”

Transportation networks equilibration with discrete choice models

“…The first ones dealt (rigorously) with the route choice and netowrk equilibrium only [e.g., Nguyen (1974) and LeBlanc (1975)] by casting the problem as a mathematical program. Ruiter and Ben-Akiva (1977) developed a complete equilibrium forecasting system incorporating an integrated set of production oriented disaggregate models, and a conceptually similar model system was used by Jacobson (1977); both methods, however, are not guaranteed to produce the desired results (in terms of convergence to a defined equilibrium).…”