| Citation: | ZHAO Xiangling, ZUO Lei. Optimization of cargo aircraft packing and stowage combination[J]. Journal of Aerospace Power, 2024, 39(11):20220844 doi: 10.13224/j.cnki.jasp.20220844 |
To guide the packing operation, raise aircraft payload, and boost transportation effectiveness, models of the combination of air cargo palletization (ACP) and aircraft weight and balance (AWB) were developed. The bi-level optimization model (BOM), the combinatorial optimization model (COM), and the improved combinatorial optimization model (IOM) were proposed, and the objectives of the models were the maximum payload and the minimum center of gravity (CG) deviation from a defined target CG. The models also took into account a wide range of restrictions in real packing and stowing operations, such as limitations on capacity, weight, loading position, aircraft balance, and other factors in aircraft and unit loading devices. Four scenarios with various conditional data for three models were tested and analyzed using the commercial solver Gurobi, by taking the B777F as an example. Tests showed that while the BOM had the greatest CG deviation and the smallest mean payload (97 412.37 kg), it also had the fastest solution speed. For cases solved within the time limit, the mean computational time was 87.77 s, but the mean CG deviation was 1.35%. And there were some unacceptable cases where the maximum approached 3.66%. The COM test required the longest time for completion; 48% of the cases cannot be solved in the given time limit, and the mean took 880.25 s for completion, making it a challenge to accept in real-life scenarios. The IOM had an acceptable solution time, with a mean of 424.79 s, the best target optimization effect, and the greatest payload, with a mean of 97 679.77 kg; all CG deviations were controlled within 1.16%, with a mean of 0.79%.
| [1] |
BRANDT F,NICKEL S. The air cargo load planning problem-a consolidated problem definition and literature review on related problems[J]. European Journal of Operational Research,2019,275(2): 399-410. doi: 10.1016/j.ejor.2018.07.013
|
| [2] |
TECHANITISAWAD A,TANGWIWATWONG P. A GA-based heuristic for the interrelated container selection loading problems[J]. Industrial Engineering and Management Systems,2004,3: 22-37.
|
| [3] |
CESCHIA S,SCHAERF A. Local search for a multi-drop multi-container loading problem[J]. Journal of Heuristics,2013,19(2): 275-294. doi: 10.1007/s10732-011-9162-6
|
| [4] |
LIU D S,TAN K C,HUANG S Y,et al. On solving multiobjective Bin packing problems using evolutionary particle swarm optimization[J]. European Journal of Operational Research,2008,190(2): 357-382. doi: 10.1016/j.ejor.2007.06.032
|
| [5] |
BAYRAKTAR T,ERSÖZ F,KUBAT C. Effects of memory and genetic operators on Artificial Bee Colony algorithm for Single Container Loading problem[J]. Applied Soft Computing,2021,108: 107462. doi: 10.1016/j.asoc.2021.107462
|
| [6] |
GIMENEZ-PALACIOS I,ALONSO M T,ALVAREZ-VALDES R,et al. Logistic constraints in container loading problems: the impact of complete shipment conditions[J]. TOP,2021,29(1): 177-203. doi: 10.1007/s11750-020-00577-8
|
| [7] |
LI Yanzhi,TAO Yi,WANG Fan. A compromised large-scale neighborhood search heuristic for capacitated air cargo loading planning[J]. European Journal of Operational Research,2009,199(2): 553-560. doi: 10.1016/j.ejor.2008.11.033
|
| [8] |
TANG C H. A scenario decomposition-genetic algorithm method for solving stochastic air cargo container loading problems[J]. Transportation Research Part E: Logistics and Transportation Review,2011,47(4): 520-531. doi: 10.1016/j.tre.2010.11.013
|
| [9] |
KALUZNY B L,SHAW R H A D. Optimal aircraft load balancing[J]. International Transactions in Operational Research,2009,16(6): 767-787. doi: 10.1111/j.1475-3995.2009.00723.x
|
| [10] |
VERSTICHEL J,VANCROONENBURG W,SOUFFRIAU W,et al. A mixed integer programming approach to the aircraft weight and balance problem[J]. Procedia- Social and Behavioral Sciences,2011,20: 1051-1059. doi: 10.1016/j.sbspro.2011.08.114
|
| [11] |
HUANG Kuancheng,CHI Wenhou. A Lagrangian relaxation based heuristic for the consolidation problem of airfreight forwarders[J]. Transportation Research Part C: Emerging Technologies,2007,15(4): 235-245. doi: 10.1016/j.trc.2006.08.006
|
| [12] |
BOOKBINDER J H,ELHEDHLI S,LI Zichao. The air-cargo consolidation problem with pivot weight: models and solution methods[J]. Computers & Operations Research,2015,59: 22-32.
|
| [13] |
张丽霞. 航空货运飞机装载问题研究[D]. 南京: 南京航空航天大学,2012. ZHANG Lixia. Research on air cargo loading problem[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2012. (in Chinese
ZHANG Lixia. Research on air cargo loading problem[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2012. (in Chinese)
|
| [14] |
赵雨霏. 我国快递企业航空货运飞机装载优化研究[D]. 长春: 吉林大学,2016. ZHAO Yufei. Research on optimization of air cargo loading express enterprises in China[D]. Changchun: Jilin University,2016. (in Chinese
ZHAO Yufei. Research on optimization of air cargo loading express enterprises in China[D]. Changchun: Jilin University, 2016. (in Chinese)
|
| [15] |
谷润平,贾旭颖,赵向领,等. 民航货机装载优化准确建模仿真研究[J]. 计算机仿真,2019,36(3): 20-26. GU Runping,JIA Xuying,ZHAO Xiangling,et al. Research on loading,optimization and accurate modeling and simulation of civil aviation cargo aircraft[J]. Computer Simulation,2019,36(3): 20-26. (in Chinese
GU Runping, JIA Xuying, ZHAO Xiangling, et al. Research on loading, optimization and accurate modeling and simulation of civil aviation cargo aircraft[J]. Computer Simulation, 2019, 36(3): 20-26. (in Chinese)
|
| [16] |
史永胜,王策. 货机主货舱多约束条件下集装器装载优化[J]. 科学技术与工程,2020,20(25): 10517-10522. SHI Yongsheng,WANG Ce. Container loading optimization under multiple constraints of cargo aircraft main cargo compartment[J]. Science Technology and Engineering,2020,20(25): 10517-10522. (in Chinese doi: 10.3969/j.issn.1671-1815.2020.25.058
SHI Yongsheng, WANG Ce. Container loading optimization under multiple constraints of cargo aircraft main cargo compartment[J]. Science Technology and Engineering, 2020, 20(25): 10517-10522. (in Chinese) doi: 10.3969/j.issn.1671-1815.2020.25.058
|
| [17] |
赵向领,杜有权. 基于遗传算法的民用航空器配载问题[J]. 中国科技论文,2021,16(8): 849-854. ZHAO Xiangling,DU Youquan. Civil aircraft stowage based on genetic algorithm[J]. China Sciencepaper,2021,16(8): 849-854. (in Chinese
ZHAO Xiangling, DU Youquan. Civil aircraft stowage based on genetic algorithm[J]. China Sciencepaper, 2021, 16(8): 849-854. (in Chinese)
|
| [18] |
姜昱君,韩锐. 民航客机货舱自动配平优化技术[J]. 计算机系统应用,2022,31(1): 159-167. JIANG Yujun,HAN Rui. Automatic load optimization technology for cargo hold of airliner[J]. Computer Systems & Applications,2022,31(1): 159-167. (in Chinese
JIANG Yujun, HAN Rui. Automatic load optimization technology for cargo hold of airliner[J]. Computer Systems & Applications, 2022, 31(1): 159-167. (in Chinese)
|
| [19] |
LIMBOURG S,SCHYNS M,LAPORTE G. Automatic aircraft cargo load planning[J]. Journal of the Operational Research Society,2012,63(9): 1271-1283. doi: 10.1057/jors.2011.134
|
| [20] |
VANCROONENBURG W,VERSTICHEL J,TAVERNIER K,et al. Automatic air cargo selection and weight balancing: a mixed integer programming approach[J]. Transportation Research Part E: Logistics and Transportation Review,2014,65: 70-83. doi: 10.1016/j.tre.2013.12.013
|
| [21] |
LURKIN V,SCHYNS M. The Airline Container Loading Problem with pickup and delivery[J]. European Journal of Operational Research,2015,244(3): 955-965. doi: 10.1016/j.ejor.2015.02.027
|
| [22] |
SON D H,KIM H J. An algorithm for the loading planning of air express cargoes[J]. Journal of Society of Korea Industrial and Systems Engineering,2016,39(3): 56-63. doi: 10.11627/jkise.2016.39.3.056
|
| [23] |
WONG E Y C,MO D Y,SO S. Closed-loop digital twin system for air cargo load planning operations[J]. International Journal of Computer Integrated Manufacturing,2021,34(7/8): 801-813.
|
| [24] |
赵向领,李云飞,王治宇,等. 基于装卸顺序的中型机多航段协同配载优化[J]. 北京航空航天大学学报,2024,50(4):1147-1161. ZHAO Xiangling,LI Yunfei,WANG Zhiyu,et al. Cooperating loading balance optimization for medium-sized aircraft with multiple flight legs based on loading and unloading sequence[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(4):1147-1161. (in Chinese
ZHAO Xiangling, LI Yunfei, WANG Zhiyu, et al. Cooperating loading balance optimization for medium-sized aircraft with multiple flight legs based on loading and unloading sequence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2024, 50(4): 1147-1161. (in Chinese)
|
| [25] |
KRICHEN S,DAHMANI N. Solving a load balancing problem with a multi-objective particle swarm optimisation approach: application to aircraft cargo transportation[J]. International Journal of Operational Research,2016,27(1/2): 62-84. doi: 10.1504/IJOR.2016.078455
|