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摘要:
为解决航空运输成本高，运输资源闲置、浪费多的问题，对航线联营下基于转运的飞机航线路径优化问题进行研究。基于货物转运问题，考虑联盟对运营的影响，引入航空联盟选择概率，确定转运前后航段运输的承运及托运问题，并考虑托运运输的衔接问题。由于航空网络中双机场容量限制，运行中全货机飞行时段及空域容量的限制，以总成本最小化为目标，建立了航线联营下基于转运的航线路径优化模型（T-AAAFRP）。设计了改进的遗传算法求解模型。通过实例分析，研究选址和路径优化问题。研究结果表明：设计的算法具有较高的收敛性；转运点数量变化的过程中，双机场城市总被选择作为转运点；需求量、飞机固定成本的变化对优化决策有较大影响；飞机载重量、联盟承运与托运的分摊系数、决策者风险偏好的变化对优化决策有较小影响；总体上转运点数量越多，所承担的总成本越小，使用的飞机数量越少。
Abstract:In order to solve the problems of the high cost of air transportation and waste of idle transportation resources, this paper puts forward the research on route optimization of aircraft based on transshipment under route alliance. Firstly, based on the problem of cargo transfer, considering the impact of the alliance on the operation, the selection probability of aviation alliance is introduced to determine the self operation and outsourcing of segment transportation before and after the transfer, and the connection of outsourcing transportation is also considered. The aircraft route optimization model based on transshipment, known as the T-AAAFRP model, is then built in the alliance environment while taking into account the capacity limitation of double airports in the aviation network, the capacity limitation of all cargo aircraft in flight time and airspace in operation, and taking the total cost minimization as the goal Secondly, an adaptive genetic algorithm is used to solve the model. Finally, through a case study, the location and path optimization problems are studied. The results show that the algorithm designed in this paper has high convergence. In the process of changing the number of transfer points, double airport cities are always selected as transfer points. The change of demand and aircraft fixed cost has great influence on optimization decision. The decision to optimize is greatly influenced by changes in demand and aircraft fixed costs. The weight of aircraft, the sharing coefficient of alliance self operation and outsourcing, and the change of decision-maker’s risk preference have little influence on the optimization decision. But on the whole, the larger the number of transfer points, the smaller the total cost and the smaller the number of aircraft used. However, generally speaking, the more transfer sites there are, the lower the overall cost and the fewer aircraft are needed.
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图 8 基于基因工程的染色体交叉过程
Figure 8. Chromosome crossover process based on genetic engineering
图 14 不同飞机固定成本下的计算结果
Figure 14. Calculation results under different aircraft fixed costs
图 15 不同成本与收益的系数下的计算结果
Figure 15. Calculation results under different coefficients of cost and benefit
图 16 不同航空联盟成本分摊系数下的计算结果
Figure 16. Calculation results under different cost sharing coefficients of aviation alliance
图 17 不同决策者对损失的敏感度下的计算结果
Figure 17. Calculation results under different sensitivity of decision maker to loss
图 18 不同风险损失时权重的大小下的计算结果
Figure 18. Calculation results under the weight of different risk losses
表 1 修正后禁忌表主要参数设置
Table 1. Revised taboo list Main parameter setting
参数 数值 $ \delta $ 2.5 $ \alpha $ 0.6 $\beta $ 1.6 $\tau $ 0.9 $ \vartheta $ 2.5 ${P_x}$ 服从 U (0.4, 1) ${D_{{1_{ij}}}}$ 服从 U (0, 30000) $ {\varsigma _1} $/(元·h−1) 2000 $ {\varsigma _2} $/元 30000 ${\lambda _2}$ 0.8 
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表 2 不同转运点数量的优化选择结果
Table 2. Optimal selection results of different number of transfer points
转运点个数 转运点位置 飞机数量 总成本/元 最优选择 2 [7郑州，8武汉] 30 1422415 − [6沈阳，7郑州] 23 1191386 √1 [1北京，6沈阳，8武汉] 20 1109964 − [2广州，6沈阳，9成都] 18 1054360 √2 4 [1北京，7郑州，8武汉，9成都] 25 1237837 − [1北京，2广州，6沈阳，9成都] 11 901209 √3 [1北京，6沈阳，7郑州，8武汉，9成都] 16 1010882 − [1北京，2广州，6沈阳，8武汉，9成都] 9 834697 √4 6 [1北京，2广州，6沈阳，7郑州，8武汉，9成都] 8 807710 5 注：“−”表示不是最优选择；“√1、√2、√3、√4、√5”表示最优选择1、最优选择2、最优选择3、最优选择4、最优选择5。
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表 3 5种方案的最优飞机机队路线
Table 3. Optimal aircraft fleet route of five schemes
转运点位置 飞机线路 [6沈阳，7郑州] 5-(7)-11-(7)-32-(6)-2-5 4-2-(6)-5-(7)-25-4 5-31-(6)-2-(6)-26-17-9-5 4-37-10-(7)-5-(7)-37-4 5-37-(6)-22-(6)-37-5-32-5 5-(7)-2-(6)-5-(6)-36-5 4-21-37-(7)-25-(6)-2-4 5-22-2-(6)-35-(6)-2-5 4-36-(6)-2-(6)-26-9-4 4-(7)-15-(6)-2-(6)-37-4 5-9-11-(7)-5-(7)-25-(7)-18-5 5-2-(6)-36-(7)-5-(7)-2-(7)-5 5-26-11-37-26-11-5 4-37-(7)-5-(7)-18-(7)-2-4 5-(7)-20-(7)-2-(6)-5 5-11-37-(6)-9-(6)-2-37-5 5-21-5-(7)-25-26-(6)-2-5 5-2-(6)-12-37-(6)-30-5 5-37-11-(7)-5-(7)-21-2-5 5-37-(6)-2-(6)-15-2-5 5-(6)-22-(6)-5-17-25-5 4-18-2-(6)-37-4 5-17-37-20-(7)-5-(7)-31-5 [2广州，6沈阳，9成都] 4-3-9-(6)-7-(6)-5-11-12-4 5-37-(6)-20-(2)-5-(2)-5 5-(9)-11-(9)-32-(9)-11-(2)-3-5 4-(6)-22-(6)-5-(9)-25-(2)-10-4 5-31-5-32-5-(6)-21-5 4-37-(2)-3-(9)-5-(2)-22-25-4 4-37-(2)-22-(2)-25-37-(6)-26-4 5-37-(9)-5-(2)-22-(2)-5 4-10-(6)-36-(9)-5-(9)-11-(2)-3-4 4-18-17-(2)-25-(2)-17-37-4 4-17-(2)-3-(2)-5-(6)-21-4 4-11-(9)-5-(9)-31-7-(6)-37-4 4-(9)-25-(2)-18-(2)-26-11-4 5-7-(6)-36-(9)-5-(9)-15-37-5 4-37-(2)-25-26-11-(9)-11-4 4-(2)-21-(6)-37-(9)-5-(9)-3-4 5-(9)-3-(2)-25-3-5 5-37-(9)-5-(9)-37-(9)-36-5 [1北京，2广州，6沈阳，9成都] 5-(2)-31-5-32-5 5-(9)-37-(7)-7-5 4-11-(2)-32-(2)-11-(7)-21-(7)-37-4 5-25-(9)-17-37-11-5 5-22-(9)-37-(2)-25-26-(9)-5 4-(6)-22-(9)-37-(2)-25-26-(9)-10-37-4 4-37-(9)-5-25-(9)-10-4 5-26-5-(2)-25-(2)-5-(6)-20-5 4-36-(9)-5-(9)-17-(7)-5-(7)-21-4 4-37-(6)-20-(6)-36-37-4 4-11-26-11-(7)-25-4 4-22-(6)-5-(2)-25-(2)-18-4 [1北京，2广州，6沈阳，8武汉，9成都] 4-38-(3)-5-11-4 4-32-11-22-(9)-38-(2)-26-4 5-12-(2)-35-(2)-12-26-5 4-27-12-37-5-38-(3)-25-(6)-4 4-11-(9)-38-5-11-22-4 5-21-11-(2)-26-(2)-11-27-5 5-(9)-18-(3)-26-(3)-18-(9)-38-5 4-38-27-37-38-4 4-12-11-(6)-25-(3)-38-11-4 [1北京，2广州，6沈阳，7郑州，8武汉，9成都] 5-32-5-11-5-(8)-21-5 4-25-(2)-17-(7)-36-5-11-26-(8)-37-4 4-11-(1)-32-(1)-11-(8)-25-4 5-(7)-18-(1)-25-(1)-18-(7)-37-5 5-26-5 4-26-5-(1)-25-4 4-11-(8)-21-(7)-37-(2)-22-(2)-37-4 5-37-(8)-5-5
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