Assignment is the choice of paths in a network. Dynamic assignment adds the choice of departure time and takes into account the dynamics of flow propagation in the network. Dynamic assignment constitutes an essential element of the formation of the equilibrium between supply and demand in urban transportation networks. Thus dynamic assignment impacts the short term dynamics of transportation networks and the long-term equilibrium leading to land-use features.

The standard approach to assignment is based on Wardrop-like approaches, with the following hypotheses:

• Users are rational: they evaluate routes based on objective attributes,
• They chose the route(s) with maximum utility.

Such approaches are limited in scope. Equilibrium occurs within homogeneous classes of users (same origin, destination, mode, activity), conditioned by the impact of equilibrium of other classes. Equilibriums are usually not unique and can be calculated numerically based on fixed point or variational inequality techniques.

If the demand model is more realistic, i.e. if activity chains are taken into account, the formation of the equilibrium becomes correspondingly more complex and beyond reach of numerical tractability.

The paper proposes a multiagent based approach to this problem, both for the description of the networks dynamics and for the calculation of the transportation system equilibrium. For the latter, a cross-entropy approach close to the Jin field method is proposed.

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