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

*(English)*Zbl 1180.90028Summary: 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.

##### MSC:

90B10 | Deterministic network models in operations research |

##### Keywords:

mathematical programs with equilibrium constraints; mathematical program with complementarity constraints; traffic assignment; user equilibrium##### Software:

MacMPEC
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\textit{J. X. Ban} et al., Math. Comput. Modelling 43, No. 5--6, 493--505 (2006; Zbl 1180.90028)

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##### References:

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