Container Loading Optimization for Bulk Cargo under Variable Packaging Box Dimensions

XU Mengchen; YANG Yihua; XIANG Qiaoling; YANG Jianglong; WANG Xiuli

doi:10.19554/j.cnki.1001-3563.2026.17.032

PDF(5374 KB)

Packaging Engineering ›› 2026, Vol. 47 ›› Issue (17) : 317-326. DOI: 10.19554/j.cnki.1001-3563.2026.17.032

Green Packaging and Circular Economy

Container Loading Optimization for Bulk Cargo under Variable Packaging Box Dimensions

XU Mengchen^a, YANG Yihua^b, XIANG Qiaoling^a, YANG Jianglong^a,*, WANG Xiuli^a

Author information +

History +

Abstract

To address the issues of fixed packaging box dimensions, poor space adaptability and the difficulty of jointly improving loading weight and space utilization in homogeneous bulk cargo container loading, the work aims to construct a joint optimization model for packaging box dimensions and loading schemes to enhance the transport benefits of bulk cargo containers. Centered on dynamic packaging box dimension optimization, a Dual-Layer Grid Search Heuristic (DLGSH) was proposed. The three-dimensional bin packing problem was reduced to a two-dimensional layout problem via a spatial quartering strategy, and optimal packaging box dimensions were globally searched at a millimeter step size while the two-dimensional layout was jointly optimized. Under constraints such as bulk density, dimension ratios, and packaging thickness, the collaborative solution of dimensional optimization and loading layout was achieved and the effectiveness of the algorithm was verified from both theoretical and simulation aspects. Experiments based on four product specifications at a rice-processing enterprise showed that loading weight increased by 14.67%-31.72% and space utilization by 1.62-12.79%. Across 10 differentiated test cases, DLGSH achieved average loading-weight advantages of 2.16% and 2.40% over a hybrid genetic algorithm and a three-stage computational intelligence framework, respectively. DLGSH demonstrates stable solution quality and strong global search capability, providing support for bulk cargo container loading optimization and logistics packaging design.

Key words

container loading optimization / variable dimension items / dual-layer grid search heuristic algorithm / spatial quartering strategy

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

XU Mengchen, YANG Yihua, XIANG Qiaoling, YANG Jianglong, WANG Xiuli. Container Loading Optimization for Bulk Cargo under Variable Packaging Box Dimensions[J]. Packaging Engineering. 2026, 47(17): 317-326 https://doi.org/10.19554/j.cnki.1001-3563.2026.17.032

References

[1] 赵浩方, 荆波, 王秀丽, 等. 城市供应粮食物资集装箱装载优化问题研究[J].包装工程, 2025, 46(17): 296-303.
ZHAO H F, JING B, WANG X L, et al.Research on Container Loading Optimization of Urban Grain and Material Supply[J]. Packaging Engineering, 2025, 46(17): 296-303.
[2] 柳虎威, 周丽, 杨江龙, 等. 健康营养食品包装协同创新的产业博弈机制与治理优化研究[J]. 包装工程, 2025, 46(23): 1-12.
LIU H W, ZHOU L, YANG J L, et al.Research on Industrial Game Mechanism and Governance Optimization of Collaborative Innovation in Healthy and Nutritious Food Packaging[J]. Packaging Engineering, 2025, 46(23): 1-12.
[3] 王秀丽, 赵浩方, 荆波, 等. 基于绿色循环包装的政企社三方演化博弈研究[J]. 包装工程, 2025, 46(15): 24-36.
WANG X L, ZHAO H F, JING B, et al.Research on Tripartite Evolutionary Game of Government- Enterprise-Society Based on Green Circular Packaging[J]. Packaging Engineering, 2025, 46(15): 24-36.
[4] 柳虎威, 周丽, 杨江龙, 等. 基于生命周期评估的生物基包装材料可持续性评价与应用优化研究[J]. 包装工程, 2025, 46(19): 291-297.
LIU H W, ZHOU L, YANG J L, et al.Sustainability Evaluation and Application Optimization of Bio-based Packaging Materials Based on Life Cycle Assessment[J]. Packaging Engineering, 2025, 46(19): 291-297.
[5] 徐江, 王航, 周艳杰, 等. 基于混合遗传算法的可变尺寸货物装箱问题研究[J]. 包装工程, 2024, 45(13): 259-267.
XU J, WANG H, ZHOU Y J, et al.Research on Variable-Size Cargo Packing Problem Based on Hybrid Genetic Algorithm[J]. Packaging Engineering, 2024, 45(13): 259-267.
[6] MARTELLO S, PISINGER D, VIGO D.The Three- Dimensional Bin Packing Problem[J]. Operations Research, 2000, 48(2): 256-267.
[7] BISCHOFF E E, MARRIOTT M D.A Comparative Evaluation of Heuristics for Container Loading[J]. European Journal of Operational Research, 1990, 44(2): 267-276.
[8] 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 Accurate Modeling and Simulation of Loading Optimization for Civil Aviation Cargo Aircraft[J]. Computer Simulation, 2019, 36(3): 20-26.
[9] 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): 475-485.
ZHAO X L, ZUO L.Combined Optimization of Packing and Stowage for Cargo Aircraft[J]. Journal of Aerospace Power, 2024, 39(11): 475-485.
[10] FAROE O, PISINGER D, ZACHARIASEN M.Guided Local Search for the Three-Dimensional Bin-Packing Problem[J]. INFORMS Journal on Computing, 2003, 15(3): 267-283.
[11] 曹先彬, 刘克胜, 王煦法. 基于免疫遗传算法的装箱问题求解[J]. 小型微型计算机系统, 2000, 21(4): 361-363.
CAO X B, LIU K S, WANG X F.Solution to Packing Problem Based on Immune Genetic Algorithm[J]. Mini-Micro Systems, 2000, 21(4): 361-363.
[12] SUN B, LI G, WANG S, et al.Two-dimensional Bin-Packing Problem with Conflicts and Load Balancing: A Hybrid Chaotic and Evolutionary Particle Swarm Optimization Algorithm[J]. Computers & Industrial Engineering, 2025(200): 110851.
[13] 亓明凯, 王迪, 张立晔. 基于分层强化学习的在线三维装箱模型[J]. 计算机工程, 2025, 51(6): 731-739.
QI M K, WANG D, ZHANG L Y.Online Three-Dimensional Packing Model Based on Hierarchical Reinforcement Learning[J]. Computer Engineering, 2025, 51(6): 731-739.
[14] HAOUARI M, MHIRI M.Lower and Upper Bounding Procedures for the Bin Packing Problem with Concave Loading Cost[J]. European Journal of Operational Research, 2024(312): 56-69.
[15] ZHOU Y, WANG X, WANG H, et al.A Computational Intelligence Method to Solve the Problem of Packing Variable-Length Fresh Products into Fixed-Size Bins[J]. Computers & Industrial Engineering, 2025(209): 111450.
[16] ANILY S, BRAMEL J, SIMCHI-LEVI D.Worst-case Analysis of Heuristics for the Bin Packing Problem with General Cost Structures[J]. Operations Research, 1994, 42(2): 287-298.
[17] ZHU W, CHEN S, DAI M, et al.Solving a 3D Bin Packing Problem with Stacking Constraints[J]. Computers & Industrial Engineering, 2024(188): 109814.
[18] CRAINIC T G, PERBOLI G, TADEI R.Extreme Point-Based Heuristics for Three-Dimensional Bin Packing[J]. INFORMS Journal on Computing, 2008, 20(3): 368-384.