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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.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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