【摘要】 针对多约束、大规模的三维装箱问题，研究建立相应的数学模型，提出了改进鲸鱼算法与模拟退火算法相结合的混合元启发式算法。该算法对鲸鱼算法进行离散化处理，包括个体编码方式及更新机制等，利用模拟退火解决局部最优陷阱，并设计启发式装载规则进行解码，优化装箱方案。利用Bischoff和Ratcliff教授在OR-Library所提供的三维装箱标准算例和实际企业货物订单数据作为仿真案例，涵盖了从弱异构到强异构的货物类型。本研究所提算法同时兼顾了全局搜索和局部搜索能力，在面对多种箱子类型时，具有较高的填充率，其中弱异构型货物平均容器填充率为92.24%,强异构型货物平均容器填充率为88.78%,总体平均容器填充率达91.29%,为三维装箱问题研究提供了一定的借鉴和参考价值。更多还原

【Abstract】 A mathematical model was established to address the multi-constraint, large-scale three-dimensional bin packing problem. A hybrid metaheuristic algorithm combining an improved whale algorithm with simulated annealing was proposed. The algorithm discretized the whale algorithm, including individual encoding and updating mechanisms, and utilized simulated annealing to overcome local optima traps. Moreover, a heuristic loading rule was designed for decoding and optimizing the packing solution. The algorithm was evaluated using standard packing instances from Bischoff and Ratcliff’s OR-Library, as well as real-world cargo order data, covering a range of cargo types from weakly heterogeneous to strongly heterogeneous. The proposed algorithm achieved a balance between global and local search capabilities, resulting in high packing efficiency for various types of containers. Specifically, the average container filling rate were 92.24% for weakly heterogeneous cargo, 88.78% for strongly heterogeneous cargo, and an overall average of 91.29%. This result provides valuable insights and references for the study of three-dimensional bin packing problems.更多还原