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摘要:
为解决因突发事件产生的航空公司航班中断问题，对中断的离港航班进行恢复，构建最小化航空公司总延误成本和最小化乘客总延误时间的双目标优化模型，设计基于支配强度的自适应非支配排序遗传算法(ANSGA2-DS)。提出3种改进操作：快速支配排序方法、新的拥挤距离和自适应精英保留策略。通过福州长乐国际机场某航空公司的运行数据对所提算法进行验证，实验结果表明：与传统的先规划先服务方法相比，所提算法得到的解有大幅优化；与
ε 约束法相比，所提算法的求解时间总体上低于ε 约束法，且求解结果接近ε 约束法所得最优结果；与NSGA2、MOEAD等多目标优化算法相比，所提算法表现出更优的性能，能够有效且高效地解决问题,为航空公司达成优化的解决方案提供基础。Abstract:To solve the problem of airline flight disruption caused by emergencies, this paper recovers the disrupted departure flight. A bi-objective optimization model for minimizing airline delay cost and passenger delay time is constructed. An adaptive non-dominated sorting genetic algorithm-Ⅱ based on dominant strengths (ANSGA2-DS) is designed. The novel crowding distance, the adaptive elitist retention technique, and the quick dominant sorting approach are the three enhanced operations that are given. The proposed algorithm is verified by the operation data of an airline in Fuzhou Changle International Airport. The experimental results reveal that, compared with the traditional first scheduling first serve method, the algorithm proposed in this paper can reduce the costs greatly. In contrast to the
ε -constraint approach, theε -constrained approach requires a longer solution time, and the resulting solution results are similar to those of theε -constrained approach. Compared with the NSAG2 algorithm and the MOEAD algorithm, the algorithm proposed in this paper shows better performance. The proposed algorithm can solve the problem effectively and efficiently, and provide a basis for airlines to reach an optimized solution. -
图 3 ANSGA2-DS、NSGA2和MOEAD在3种场景中解的分布
Figure 3. Distribution of solutions of ANSGA2-DS, NSGA2 and MOEAD in three scenarios
图 4 不同算法中每个航班延误成本的比较
Figure 4. Comparison of each flight delay cost in different algorithms
图 5 不同算法中每个航班延误时间的比较
Figure 5. Comparison of each flight delay time in different algorithms
表 1 3种场景的信息
Table 1. Information of three scenarios
场景 航班数 中断持续时间/min 可分配的时隙数量 A 8 193 8 B 14 215 14 C 25 289 25 
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表 2 场景A的信息
Table 2. Information of scenario A
航班号 原始离港时间 分配的时隙时间 乘客人数 1 11:10 11:45 134 2 11:25 12:20 330 3 11:47 12:16 182 4 11:59 12:55 149 5 12:05 13:55 222 6 12:28 13:58 379 7 12:55 14:00 112 8 12:59 14:23 310
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表 3 场景B的信息
Table 3. Information of scenario B
航班号 原始离港时间 分配的时隙时间 乘客人数 1 13:30 14:06 248 2 13:40 14:17 330 3 13:45 14:49 332 4 13:55 14:53 207 5 13:59 14:58 225 6 14:20 14:59 218 7 14:29 15:08 150 8 14:29 15:20 137 9 14:40 15:32 167 10 14:48 15:36 129 11 14:50 15:47 83 12 14:51 15:57 283 13 14:54 16:05 180 14 15:37 17:05 332
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表 4 场景C的信息
Table 4. Information of scenario C
航班号 原始离港时间 分配的时隙时间 乘客人数 1 16:20 16:50 134 2 16:25 16:58 109 3 16:34 17:37 317 4 16:40 17:55 339 5 17:48 18:32 129 6 17:55 19:58 285 7 18:23 20:05 300 8 18:40 20:11 225 9 18:49 20:15 134 10 19:15 20:22 78 11 19:45 20:25 109 12 19:48 20:30 285 13 19:59 20:32 167 14 19:59 20:46 225 15 20:13 20:51 233 16 20:27 21:55 86 17 20:30 22:00 137 18 20:38 22:04 135 19 20:40 22:32 285 20 20:56 22:41 112 21 21:00 22:50 317 22 21:09 22:59 285 23 21:15 23:00 202 24 21:25 23:05 134 25 22:30 23:09 129
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表 5 不同参数组合结果
Table 5. Results of different parameter combination values
实验编号 组合参数 求解时间/s 解的数量 Z1/美元 Z2/min 平均间距/% Np ${p_{\text{m}}}$ ${p_{\text{c}}}$ 1 40 0.1 0.8 92.73 6 252519.67 265044 4.85 2 40 0.2 0.3 64.71 5 253105.21 270816 7.36 3 40 0.3 0.5 76.58 4 252137.38 265281 4.80 4 80 0.1 0.3 158.69 8 253409.55 275075 6.52 5 80 0.2 0.5 182.62 7 253223.97 264024 4.73 6 80 0.3 0.8 220.19 7 252830.51 262543 3.99 7 120 0.1 0.5 248.54 6 253572.43 267058 5.49 8 120 0.2 0.8 328.45 8 252246.05 263460 4.12 9 120 0.3 0.3 236.78 8 252798.59 280937 8.47
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表 6 FSFS、ECA和ANSGA2-DS的计算结果
Table 6. Computational results of FSFS, ECA and ANSGA2-DS
场景 Z1/美元 Z2/min 求解时间/s Pareto 解个数 最大
公平
价格/%ANSGA2-DS
与 ECA的
平均间距/%FSFS ECA ANSGA2-DS FSFS ECA ANSGA2-DS FSFS ECA ANSGA2-DS FSFS ECA ANSGA2-DS A 282825.07 134789.56 135268.1 212552 149608 149832 14.57 23.42 7 14.23 4.88 B 389964.38 251490.85 253142.78 301887 243765 259467 345.91 40.73 6 5.61 4.71 C 739695.86 524925.70 531868.435 638448 416997 436982 9316.28 149.95 4 4.36 6.26
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表 7 ANSGA2-DS、NSGA2和MOEAD的最优值、最大公平价格与反向世代距离的比较
Table 7. Comparison of the optimal value, the maximum price of fairness and IGD among ANSGA2-DS, NSGA2 and MOEAD
场景 Z1/美元 Z2/min 最大公平价格/% 反向世代距离/105 ANSGA2-DS NSGA2 MOEAD ANSGA2-DS NSGA2 MOEAD ANSGA2-DS NSGA2 MOEAD ANSGA2-DS NSGA2 MOEAD A 135268.1 136414.04 138989.7 149832 154586 157940 14.23 19.38 23.71 1.18 1.36 1.58 B 253142.78 254551.42 255670.78 259467 262036 265789 5.61 7.05 8.33 2.83 2.91 2.98 C 531868.44 536551.42 540642.78 436982 442036 457467 4.36 5.82 7.12 6.48 6.70 7.42
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