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The lower level problem is ridesharing user equilibrium (RUE).
The lower level problem is the user equilibrium traffic assignment problem.
The lower level problem is formulated as a certain traffic assignment model.
In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level problem.
As a bilevel problem with an NP-hard lower level problem, there is no algorithm for solving the model exactly.
The lower level problem is the user equilibrium assignment model, which is solved by the Gradient projection algorithm.
At the lower level problem, the user equilibrium flow is determined by Wardrop's first principle and can be formulated as an equivalent minimization problem.
For the system-optimized flows, a user equilibrium traffic assignment problem with marginal costs can be solved at the lower level problem.
Second, a link-based bi-level program is proposed in which the lower level problem describes the user equilibrium traffic condition characterized by the locations of refueling stations.
While under the network investment decisions of the upper level problem, the lower level problem is to maximize the consumer surplus of every demand scenario with consideration of the collaborations of transportation modes, traffic load balancing and capacity constraints.
The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users.
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CEO of Professional Science Editing for Scientists @ prosciediting.com