航线网络区间鲁棒优化设计

为解决航空公司航线网络中枢纽机场具体位置及OD流路径设计问题, 根据航线网络设计参数OD 流量和单位流成本的不确定性, 定义了区间型情景集, 建立了区间型绝对鲁棒优化模型, 设计了将修正最短路算法与人工智能算法相结合进行求解的有效算法,并利用航线网络设计经典数据及中国航空网络OD数据对模型进行了验证. 研究结果表明:该模型的最优鲁棒解具有全局最优性,确定型优化模型为本文模型在悲观准则下,当OD 流量和单位流成本确定时的特例;在不同情景的悲观准则和乐观准则下的模型目标值之间的相关系数达到0.99以上;在悲观准则下,用本文模型计算出标准算例的归一化后的最优目标值为784.47,比确定型模型最优目标值减少了16.65%,比相对鲁棒优化模型最优目标值减少了29.07%. 

Interval Robust Optimization of Airline Network Designing

In order to determine the specific locations of hubs and optimize the path design of origin-destination (OD) flows of airline network, an interval scenario set was defined and a new absolute interval robust optimization model was established, taking into account the uncertainty of design parameters OD flows and unit flow cost of the hub-and-spoke network.The model was solved by combination of the modified shortest path algorithm with artificial intelligence algorithms, and then verified in two numerical cases using the classic data for airline network design and the OD data of Chinese airline network, respectively. The results show that the optimal solutions obtained from the absolute interval robust optimization model have global optimality, and the deterministic robust optimization model is a special case of the proposed model under pessimistic rules when the values of the OD flows and cost of unit flow are determined; the correlation coefficient of the two groups of objective values obtained from pessimistic and optimistic rules is more than 0.99 in different scenarios. In the standard example under the pessimistic rule, the optimal objective value calculated from the proposed model, after normalized, is 784.47, which is 16.65% less than the optimal objective value of the deterministic optimization model and 29.07% less than the optimal objective value of the relative interval robust optimization model.