An Algorithm for the Mixed Transportation Network Design Problem.
An Algorithm for the Mixed Transportation Network Design Problem.
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DOI：
10.1371/journal.pone.0162618
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发表时间：
2016
期刊：
影响因子：
3.7
通讯作者：
Chen Q
中科院分区：
文献类型：
--
作者：
Liu X;Chen Q
本文提出了一种求解混合交通网络设计问题的优化算法——降维迭代算法（DDIA），该问题一般表示为具有平衡约束的数学规划（MPEC）。MNDP的上层旨在通过扩展现有链路和增加新的候选链路来优化网络性能，而下层则是传统的Wardrop用户平衡（UE）问题。提出的求解算法（DDIA）的思想是降低问题的维数。固定一组变量（离散/连续），交替优化另一组变量（连续/离散）；然后，将问题转化为一系列连续网络设计问题（cndp）和离散网络设计问题（DNDPs）的反复求解，直到问题收敛到最优解。该算法的优点是求解过程简单，易于应用。数值算例表明，对于没有预算约束的MNDP，使用DDIA可以在几次迭代内找到最优解。然而，对于有预算约束的MNDP，其结果取决于初始值的选择，从而导致不同的最优解（即不同的局部最优解）。对如何获得有意义的初始值给出了一些想法，例如分别考虑新建和改建项目的预算。
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.
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DOI：
10.1016/0191-2615(79)90004-3
发表时间：
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影响因子：
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