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This paper proposes an optimization algorithm, the dimension-down iterative algorithm DDIA, for solving a mixed transportation network design problem MNDP, which is generally expressed as a mathematical programming with equilibrium constraint MPEC. The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium UE problem. The idea of the proposed solution algorithm DDIA is to reduce the dimensions of the problem. A group of variables discrete-continuous is fixed to optimize another group of variables continuous-discrete alternately; then, the problem is transformed into solving a series of CNDPs continuous network design problems and DNDPs discrete network design problems repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions i.e., different local optimal solutions. Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.

Autor: Xinyu Liu, Qun Chen



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