Carrier aircraft landing scheduling problem based on improved gray wolf optimization
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摘要:
针对第一类着舰模式下的舰载机着舰调度问题进行了研究，建立着舰调度模型，以最小化加权着舰延误时间和、着舰完成时间为优化目标，考虑舰载机战损程度、剩余燃油量的影响。为减轻人工调度的负担，提出一种改进灰狼优化(IGWO)算法对调度模型进行优化求解，在灰狼优化(GWO)算法的基础上，改进算法选择历史最优解灰狼个体为$\alpha $狼，引入混沌算子，设置算法参数更新控制变量，以应对GWO算法后期收敛速度慢、可能陷入局部最优解的缺点。通过不同规模着舰调度案例仿真和算法对比，验证了IGWO算法的有效性，所提算法在30、60、90机规模着舰调度案例中的优化效果均优于对比算法，证明其具备一定工程应用价值。
Abstract:The carrier aircraft landing scheduling problem under class one landing mode is studied, and a landing scheduling model is established with the optimization objectives of minimizing the weighted sum of landing delay time, and landing completion time. The model takes into account the impact of the battle damage level and fuel remaining in carrier aircraft. To reduce the burden of manual scheduling, an improved gray wolf optimization (IGWO) algorithm is proposed to optimally solve the scheduling model. In order to address the drawbacks of slow convergence in the late stages of optimization and potential falls into local optimal solutions, the improved algorithm, which is based on the gray wolf optimization (GWO) algorithm, selects the historical optimal solution gray wolf individual as wolf, introduces the chaos operator, and sets the control variable to control the updating of the algorithm parameter. The effectiveness of the IGWO algorithm is verified through the simulation and comparison with different optimization algorithms. The algorithm outperforms the comparison algorithms in the landing scheduling cases with 30, 60, and 90 aircraft, indicating that it has some engineering application value.
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图 2 第1类着舰模式下舰载机等待航线
Figure 2. Awaiting route of carrier aircraft under class one landing mode
图 3 第1类着舰模式下舰载机进近着舰航线
Figure 3. Approach and landing route of carrier aircraft under class one landing mode
图 5 GWO算法改进前后$\omega $的位置更新
Figure 5. Position updating of $\omega $ before and after GWO algorithm improvement
图 6 参数$ e $控制下参数$ a $的更新过程
Figure 6. Updating process of $ a $ under control of parameter $ e $
图 9 算法最优解收敛曲线对比
Figure 9. Comparison of optimal solution of algorithms convergence curves
表 1 案例中使用的舰载机参数
Table 1. Parameters of carrier aircraft used in cases
i I O/L W w E/s 1 1 1 200 90 0.304 6 0 2 1 1 500 100 0.060 7 0 3 1 1 600 90 0.256 1 0 4 2 1 000 100 0.121 4 80 5 2 1 500 90 0.268 2 80 6 2 1 400 100 0.072 9 80 
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表 2 参数值组合
Table 2. Parameter values combinations
参数值水平 Ps e rb Nf 1 30 0.8 0.2 200 2 50 1.0 0.4 500 3 80 2.0 0.6 800
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表 3 正交实验及其参数对应的$ A_{{\mathrm{RV}}}$
Table 3. Orthogonal experiments and its corresponding ${ A_{{\mathrm{RV}}}}$
实验次数 Ps e rb Nf ARV 1 30 0.8 0.2 200 0.3717 2 30 1.0 0.4 500 0.2993 3 30 2.0 0.6 800 0.4032 4 50 0.8 0.4 800 0.3401 5 50 1.0 0.6 200 0.3343 6 50 2.0 0.2 500 0.3144 7 80 0.8 0.6 500 0.3120 8 80 1.0 0.2 800 0.3665 9 80 2.0 0.4 200 0.4798
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表 4 正交实验参数水平$\overline A_{{\mathrm{RV}}}$
Table 4. $\overline A_{{\mathrm{RV}}}$ of orthogonal experiments parameter level
参数值水平 取Ps对应值 取e对应值 取rb对应值 取Nf对应值 1 0.3581 0.3413 0.3509 0.3953 2 0.3296 0.3333 0.3731 0.3086 3 0.3861 0.3991 0.3498 0.3699
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表 5 仿真实验结果
Table 5. Simulation experiment results
min 规模 最优值 IGWO FPDGWO[29] GWO[9] VWMPIO[30] TLBO[31] DLGA[32] 30 64.2 64.7 64.3 64.6 64.7 64.6 60 286.5 294.9 295.2 311.1 309.8 306.3 90 496.5 513 505.6 536.3 510.9 551.2 规模 平均值 IGWO FPDGWO[29] GWO[9] VWMPIO[30] TLBO[31] DLGA[32] 30 64.7 66.1 65.4 66.4 65.9 65.3 60 297 305.2 309.7 326.8 321.1 316.2 90 512 553.1 543.7 572.5 552.2 567.1 规模 最劣值 IGWO FPDGWO[29] GWO[9] VWMPIO[30] TLBO[31] DLGA[32] 30 65.7 67.5 66.5 67.9 67.3 66.1 60 303 313.2 343.3 343.6 330.8 322.5 90 545.1 584.8 596.1 588.5 573.9 581.1
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