基于容量损失的鲁棒性网络设计问题

Robust Network Design Problem Based on Loss of Capacity

由于网络设计决策的长期性,许多参数会随时间而变化,因此在交通运输网络设计问题中考虑不确定性因素至关重要。研究了在交通运输网络中边的容量有随机损失时的鲁棒性网络设计问题。边的容量损失是指实际运行时的可用容量小于初始设立的容量。假设容量损失是1个随机变量,首先建立了带有机会约束的鲁棒性交通运输网络设计模型,然后利用Hoeffding's不等式对机会约束进行了安全近似,将问题转化为一般的混合整数规划问题。鲁棒性模型使得当容量有波动时,网络仍以一定的概率正常运行。最后通过数值算例比较了单源和多源2种网络结构下网络设计的最优成本,并分析了成本与鲁棒性之间的关系,同时对容量的不确定性水平做了敏感性分析。

Based on long-term network design decisions and potential parameter variations, it is important to consider the uncertainty in transportation network design. The robust transportation network design problem with stochastic loss of edge capacity is researched. Edge capacity loss means the capacity of the edge is less than the total capacity established in actual operation. Assuming that the loss of edge capacity is a random variable, a robust transportation network design model with chance constraints is established, and the chance constraints are approximated safely by using Hoeffding＇s inequality and the problem is transformed to a general mixed integer programming. The robust model guarantees the network operates properly with a certain probability when the capacity fluctuates. Finally, the design costs between single-source network and multi- source network are compared through a nmnerical example. Meanwhile, the trade-offs between the system cost and the robustness is analyzed, the sensitivity analysis on the uncertain level of the capacity is also investigated.