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枢纽航线网络在设计的过程中，容易受到需求和成本数据发生变化带来的影响。往往造成构建出来的最优网络，在需求发生变化的条件下，与实际对应的最优解存在较大的最低成本优化偏差。为了降低这种网络优化中的不确定性带来的风险，得到在多种可能的需求和成本条件下均可获得较好效果的鲁棒最优解，文中采用了一个多目标优化的遗传算法进行研究。首先将各种不同的需求和成本条件作为需要同时优化的多个目标函数，然后采用一个遗传算法来表示所有可能的枢纽航线网路结构，并搜索多目标优化的鲁棒最优网络解。最后本文对该搜索算法的收敛性进行了证明，数值实验结果表明了算法的有效性。

Robust Optimization of Hub-and-Spoke Airline Network Design Based on Multi-Objective Genetic Algorithm

In the process of designing hub network, the selection of hub airports is influenced by the change of the demand and cost. Under the condition of changing in demand, this may lead to large minimum cost deviation between the designed optimal network and real optimal network, respectively. To reduce the risk caused by the uncertainty in network optimization and get the optimal robust solution of hub network under the multi-possible conditions of demand and cost, a method based on multi-objective optimization genetic algorithm is proposed in this paper. The convergence of the algorithm has been proved, and the experimental results demonstrate the availability of the algorithm. First, multiple objective functions needing to be optimized simultaneously are formulated from different conditions of needs and cost, then a genetic algorithm is used to provide all possible routes of the network hub structure, and robust optimal network solution for multi-objective optimization is searched. The convergence of the search algorithms is proved to be effective by the numerical results.