A general MPCC model and its solution algorithm for continuous network design problem

Authors:
Jeff X. Ban;Henry X. Liu;Michael C. Ferris;Bin Ran
Affiliations:
California Center for Innovative Transportation (CCIT), University of California, 2105 Bancroft Way, Suite 300, Berkeley, CA94720-3830, United States;Department of Civil Engineering, University of Minnesota, Minneapolis, United States;Computer Sciences Department, University of Wisconsin, Madison, United States;Department of Civil and Environmental Engineering, University of Wisconsin, Madison, United States
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

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Abstract

This paper formulates the continuous network design problem as a mathematical program with complementarity constraints (MPCC), with the upper level a nonlinear programming problem and the lower level a nonlinear complementarity problem. Unlike in most previous studies, the proposed framework is more general, in which both symmetric and asymmetric user equilibria can be captured. By applying the complementarity slackness condition of the lower-level problem, the original bilevel formulation can be converted into a single-level and smooth nonlinear programming problem. In order to solve the problem, a relaxation scheme is applied by progressively restricting the complementarity condition, which has been proven to be a rigorous approach under certain conditions. The model and solution algorithm are tested for well-known network design problems and promising results are shown.