Similarly to origin-based methods, the problem is partitioned by destinations in the LUCE procedure. The main idea is to seek at each node a user equilibrium for the local route choice of drivers directed toward the destination among the arcs of its forward star.. The travel alternatives that make up the local choice sets are the arcs that belong to the current bush. A bush is an acyclic sub-graph that connects each origin to the destination at hand. The cost functions associated to these alternatives express the average impendence to reach the destination linearized at the current flow pattern.
The unique solutions to such local linear equilibria in terms of destination flows, recursively applied for each node of the bush in topological order, provide a descent direction with respect to the classical sum-integral objective function. The network loading is then performed through such splitting rates, thus avoiding explicit path enumeration. In this assignment procedure, proportionality is considered by default (Proportionality in route distribution).
