
5.
BILEVEL PROGRAMMING MODEL AND SOLUTION METHOD FOR MIXED TRANSPORTATION NETWORK DESIGN PROBLEM
Haozhi ZHANG;Ziyou GAO
Journal of Systems Science and Complexity
2009, 22 (3):
446459.
By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixedinteger, nonlinear bilevel programming problem, in which the lowerlevel problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimalvalue function, the lowerlevel assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent singlelevel optimization problem. By exploring the inherent nature of the MNDP, the optimalvalue function for the lowerlevel equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an allornothing assignment. Finally, a smallscale transportation network and a largescale network are presented to verify the proposed model and algorithm.
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