具有遗憾值约束的鲁棒性交通网络设计模型研究

Robust Transportation Network Design Modeling with Regret Value

由于交通网络设计决策的长期性,许多参数会随时间而变化,因此在鲁棒性交通网络设计问题中考虑不确定性因素至关重要.当OD需求不确定时,同时考虑期望行程时间和最大遗憾值,引入一种新的鲁棒性度量标准,将α-鲁棒解的概念应用到交通网络设计问题中,提出了一种具有遗憾值约束的鲁棒性交通网络设计模型.然后设计遗传算法求解模型,得出不同遗憾值下网络设计的最佳方案.最后,以Nguyen-Dupius网络作为算例证明了遗传算法求解鲁棒性问题的有效性.详细分析了期望行程时间与最大遗憾值之间的权衡关系,权衡曲线表明,最大遗憾值的降低并不一定导致期望行程时间的较大增加;并将鲁棒优化模型与随机优化模型作比较,结果表明,鲁棒优化模型比随机优化模型更能规避不确定性带来的风险.

Based on long-term transportation network design decisions and potential parameter variations, it is important that demand uncertainty is considered in transportation modeling. In this paper, we present a novel robustness measure that combines the two objectives by minimizing the expected travel time while bounding the relative regret in each scenario facing uncertain origin-destination demand （OD demand）. The concept of α-robust solution is introduced into the transportation network design problem. We propose a robust transportation network design model with regret value constraints, then design an algorithm based on the genetic algorithm to solve the problem and obtain the optimal solutions for different regret values. Finally, numerical results based on the Nguyen-Dupuis network validate the effectiveness of the algorithm. While detailed analysis on trade-offs, between the expected travel time and the maximum regret value, shows that large reductions in maximum regret do not necessarily result in a great increase in expected travel time. Meanwhile, we compared the robust model presented with the stochastic model and numerical examples demonstrate that the robust planning network is more reliable and less risky than the stochastic model if demand uncertainty is considered in modeling.