Solving a discrete multimodal transportation network design problem

Document Type

Journal Article

Publication Date


Subject Area

place - north america, operations - frequency, planning - route design, planning - network design, planning - integration, mode - bus


Multimodal network design, Road capacity expansion, Bus route layout, Active-set algorithm, Multimodal user equilibrium


This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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