基于无容量限制的p-枢纽中位问题的随机优化

在枢纽网络设计时, 未来的成本和需求等参数具有不确定性. 为了使设计的网络能在各种情景下具有最优的期望成本, 提出了无容量限制的多分配严格p-枢纽中位随机优化模型. 考虑到模型本身的结构特点和复杂程度, 采用了PH分解算法结合增广拉格朗日松弛算法, 将原问题转化为若干个独立子问题来求解. 使用了基于经典算例的随机数据集合对模型和算法进行了测试, 算例结果表明尤其在情景数量较大的情况下, 算法体现出较高的效率. 同时, 通过随机解价值分析了使用随机优化模型对于该算例的意义.

Stochastic optimization for uncapacitated p-hub median problems

The parameters of hub-and-spoke network design are usually uncertain. In order to get the minimal expectation cost of the network for all scenarios, this paper presents a stochastic uncapacitated strict p-hub median model under the uncertainties of parameters. Based on the model with its high complexity, the progressive hedging method combined with the augmented Lagrangian relaxation is introduced to solve the model. This algorithm can divide the primal problem into several subproblems effectively. Finally, a case study based on the classical data sets shows the effect of using the combined method, and the importance of adopting stochastic optimization method by the comparison over the values of stochastic solution.