航路时空资源分配的多目标优化方法

为了提高航空公司与空管方之间的协同决策程度, 降低航班延误水平, 以航路飞行的航班为研究对象, 研究了航路时空资源的多目标分配; 考虑实际运行条件下航班的唯一性约束、时间顺序约束和可行性约束的影响, 以航班在流量受限区所分配的飞行航迹和进入时隙为决策变量, 以航班总延误成本最小和航空公司延误公平损失偏差系数最小为目标函数, 构建了多目标非线性0-1整数规划模型; 基于模型特点引用了非支配排序遗传算法(NSGA-Ⅱ), 并利用排列编码法设计了一种整数基因编码方式, 以最大限度保证基因产生可行解集; 为了验证模型与算法的有效性, 基于南中国海地区航班运行实例, 对算法搜寻最优解的性能进行了研究, 并将此算法与传统按时刻表分配(RBS)方法进行了对比。研究结果表明: 改进编码方式的NSGA-Ⅱ算法使解集种群在约50代后世代距离从600收敛至30并稳定, 具有良好的收敛性; 针对实例中的多目标优化模型共生成有6组解的帕累托解集, 结果有66.7%的概率完全支配RBS方法, 且优化结果中航班平均延误成本比RBS方法降低了8.5%, 平均公平损失偏差系数降低了70.6%。可见提出的航路时空资源多目标优化方法的执行效果显著, 可在降低总延误成本的基础上兼顾各航空公司的公平性, 是解决航路飞行航班航迹与时隙资源分配问题的一种有效方法。 

Multi-objective optimization method of air route space-time resources allocation

To improve the degree of collaborative decision-making between airlines and air traffic controllers, as well as reduce the level of flight delays, air route flights were used as a research object and the multi-objective allocation of route space-time resources was studied. The effects of uniqueness, time sequence, and feasibility constraints of flights under actual operating conditions were considered and the flight trajectory and entry time slot assigned by the flight in the restricted area were viewed as decision variables. The lowest total flight delay cost and the lowest airline delay fair loss deviation coefficient were regarded as objective functions. A multi-objective nonlinear 0-1 integer programming model was constructed. Based on the characteristics of the model reference, the non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ) was used and an integer gene encoding scheme was designed by the permutation encoding method. A feasible solution set was generated to maximize genes. To verify the validities of the model and algorithm, based on the South China sea area flight operation example, the performance of searching for the optimal solution was studied and the algorithm was compared with the traditional ration-by-schedule(RBS) method. Research result shows that the improved encoding style of the NSGA-Ⅱ algorithm makes the generation distance of the solution set population converge from 600 to 30 and becomes stable after approximately 50 generations, with suitable convergence. The Pareto solution set with six solutions is generated for the multi-objective optimization model, with a 66.7% probability that the RBS method is completely dominated by the results. The average flight delay cost in the optimization results is 8.5% lower than that of the RBS method, and the average fair loss deviation coefficient is 70.6% lower. The implementation effect of the multi-objective optimization method for the space-time resources of the air route is remarkable. The fairness of each airline can be considered on the basis of reducing the total delay cost, making this an effective method for solving the problem of flight trajectory and slot resource allocation.