目的 基于飞机货舱装载布局问题,提出一种满足实际装载约束前提下,提升业载量,并保障负载平衡的优化方案。方法 首先,构建一个综合考量业载限制、重心偏移、体积利用率、转动惯量等多重指标的优化模型。其次,提出一种融合灰狼优化与遗传算法的混合求解策略。该算法将灰狼算法的社会层级搜索机制与遗传算法的进化操作深度结合,通过两阶段初始化策略生成高质量初始种群;采用锦标赛选择与α狼精英直接继承相结合的方式保留优秀个体,并执行单点交叉和基于重心距离的变异操作,以提升种群多样性和解的可行性,同时动态调整收敛因子和变异概率,以平衡算法的探索和开发能力。结果 实验以波音777F货机为载体,设计20组算例进行测试,在复杂约束条件下,所提算法能够使转动惯量平均降低约28%,横向不平衡度平均下降约42%,计算时间平均减少约91%,同时保持了较高装载率。结论 该算法能够有效解决航空货运三维装载问题,优化布局呈现“核-壳型”稳定结构,有利于载荷集中和飞行稳定,研究成果验证了该算法在航空货运三维装载优化中的有效性和工程实用价值。
Abstract
The work aims to propose an optimized solution that maximizes payload while ensuring load balance under practical loading constraints to deal with the cargo hold loading layout problem in aircraft. First, an optimization model that comprehensively considered multiple indicators, including payload capacity, center of gravity deviation, volume utilization, and moment of inertia, was constructed. Then, a hybrid solution strategy combining the Grey Wolf Optimizer and Genetic Algorithm was proposed. This algorithm deeply integrated the hierarchical search mechanism of Grey Wolf Optimizer with the evolutionary operations of Genetic Algorithm. A two-stage initialization strategy was employed to generate a high-quality initial population. The algorithm retained superior individuals through a combination of tournament selection and elite inheritance of the alpha wolf, and enhanced population diversity and solution feasibility via single-point crossover and a mutation operation based on the center-of-gravity distance. Meanwhile, convergence factors and mutation probabilities were dynamically adjusted to balance exploration and exploitation capabilities. Experiments were conducted using 20 test instances designed for the Boeing 777F freighter under complex constraints. Results showed that the proposed algorithm achieved an average reduction of approximately 28% in moment of inertia, a 42% average decrease in lateral imbalance, and a 91% reduction in computation time, while maintaining a high loading rate. The algorithm effectively addresses the three-dimensional loading problem in air cargo. The optimized layout demonstrates a stable "core-shell" structure, which promotes load centralization and flight stability. The research results validate the effectiveness and engineering applicability of the proposed method in the field of three-dimensional air cargo loading optimization.
关键词
航空货运 /
三维装载 /
灰狼优化算法 /
遗传算法 /
组合优化
Key words
air cargo /
3D loading /
grey wolf optimization algorithm /
genetic algorithm /
combined optimization
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] DUAN S L, JIANG S L, DAI H, et al.The Applications of Hybrid Approach Combining Exact Method and Evolutionary Algorithm in Combinatorial Optimization[J]. Journal of Computational Design and Engineering, 2023, 10(3): 934-946.
[2] KUO R J, HO P C, ZULVIA F E.Application of Metaheuristics Algorithm on a Multi-Objective Container Loading Problem Considering Container’s Utilization and Vehicle's Balance[J]. Applied Soft Computing, 2023, 143: 110417.
[3] 文淦, 袁雷峰, 王旭东, 等. 基于改进NSGA-Ⅱ算法的不规则集装器装载优化[J]. 北京航空航天大学学报, 2025, 51(3): 992-1004.
WEN G, YUAN L F, WANG X D, et al.Loading Optimization of Irregular Unit Load Device Based on Improved NSGA-Ⅱ Algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2025, 51(3): 992-1004.
[4] 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.
[5] 张长勇, 王彤. 基于混合遗传算法的飞机腹舱装载优化[J]. 包装工程, 2024, 45(21): 200-207.
ZHANG C Y, WANG T.Optimization of Aircraft Cargo Hold Loading Based on a Hybrid Genetic Algorithm[J]. Packaging Engineering, 2024, 45(21): 200-207.
[6] 张长勇, 张春婷. 基于混合智能算法的航空集装箱多目标装载优化[J]. 包装工程, 2024, 45(15): 215-225.
ZHANG C Y, ZHANG C T.Multi-Objective Optimization of Air Container Loading Based on Hybrid Intelligent Algorithm[J]. Packaging Engineering, 2024, 45(15): 215-225.
[7] 彭佩云. 滚装海运物流的船队调度与货物配载优化研究[D]. 大连: 大连海事大学, 2024: 28-57.
PENG P Y.Research on Fleet Scheduling and Cargo Stowage Optimization of Ro-Ro Marine Logistics[D]. Dalian: Dalian Maritime University, 2024: 28-57.
[8] LIMBOURG S, SCHYNS M, LAPORTE G.Automatic Aircraft Cargo Load Planning[J]. Journal of the Operational Research Society, 2012, 63(9): 1271-1283.
[9] 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: 13-31.
ZHAO Y F.Research on the Optimization of Air Cargo Aircraft Loading of Express Delivery Enterprises in China[D]. Changchun: Jilin University, 2016: 13-31.
[10] 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 R P, JIA X Y, ZHAO X L, et al.Research on Loading, Optimization and Accurate Modeling and Simulation of Civil Aviation Cargo Aircraft[J]. Computer Simulation, 2019, 36(3): 20-26.
[11] FENG B, LI Y Z, SHEN Z M.Air Cargo Operations: Literature Review and Comparison with Practices[J]. Transportation Research Part C: Emerging Technologies, 2015, 56: 263-280.
[12] BUNAHRI R R, SUPARDAM D, PRAYITNO H, et al.Determination of Air Cargo Performance: Analysis of Revenue Management, Terminal Operations, and Aircraft Loading (Air Cargo Management Literature Review)[J]. Dinasti International Journal of Management Science (DIJMS), 2023, 4(5): 166-179.
[13] 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 X L, LI Y F, WANG Z Y, 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.
[14] 赵向领, 左蕾. 货运飞机装箱与配载组合优化[J]. 航空动力学报, 2024, 39(11): 482-492.
ZHAO X L, ZUO L.Optimization of Cargo Aircraft Packing and Stowage Combination[J]. Journal of Aerospace Power, 2024, 39(11): 482-492.
[15] MIRJALILI S, MIRJALILI S M, LEWIS A.Grey Wolf Optimizer[J]. Advances in Engineering Software, 2014, 69: 46-61.
[16] HOLLAND J H.Genetic Algorithms[J]. Scientific American, 1992, 267(1): 66-72.
基金
中央高校基本科研业务费-高水平成果培育项目（3122025TD08）;中国交通教育研究会教育科学研究重点课题（JT2024ZD066）
PDF(2560 KB)
渝公网安备 50010702501716号 渝ICP备15012534号-2
