Optimization of Cargo Location Allocation in Four-way Shuttle Warehousing System Based on Two-stage Hybrid Algorithm

doi:10.16182/j.issn1004731x.joss.24-0039

Abstract

Abstract:

To address issues such as the dense distribution of storage locations and the potential congestion of shuttle vehicles in the four-way shuttle dense storage system, a grid-based approach to the storage location distribution is developed. A location allocation model is then constructed with the goals of ensuring shelf stability, improving warehousing efficiency, and balancing equipment utilization. A two-stage hybrid algorithm is designed for the model. In the first stage, the local search strategy of non-dominant sequencing genetic algorithm(NSGA-II) is enhanced by incorporating the hill climbing algorithm to address a set of Pareto front sets. In the second stage, the Pareto front set is pruned using K-means. Simulation experiments are used to analyze the effectiveness of the model and algorithm. Results indicate significant optimizations in equipment usage balance (3.1%), shelf stability (4.5%), and warehousing efficiency (3.4%) compared to the target weighting scheme. The solution results and speed of the proposed two-stage hybrid optimization algorithm outperform those of the NSGA-II.

Key words: allocation of cargo locations, multi-objective optimization, non-dominant sequencing genetic algorithm, hill climbing algorithm, K-means

CLC Number:

TP391.9

Wu Zisong, Chang Daofang, Gai Yuchun. Optimization of Cargo Location Allocation in Four-way Shuttle Warehousing System Based on Two-stage Hybrid Algorithm[J]. Journal of System Simulation, 2025, 37(5): 1234-1245.

Figures/Tables 13

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References 22

1	占翔南,徐立云,凌旭峰等.多深度四向穿梭车仓储系统调度优化[J].计算机集成制造系统,2022,28(08):2496-2507.
	Zhan Xiangnan, Xu Liyun, Ling Xufeng, et al. Scheduling Optimization of Multi-depth Four-way Shuttle Storage System[J].Computer Integrated Manufacturing Systems,2022,28(08):2496-2507.
2	韩东亚, 陈然, 余玉刚, 等. 自动化立体仓库中出入库任务顺序与出库位置选择集成优化研究[J]. 中国管理科学, 2020, 28(10): 156-164.
	Han Dongya, Chen Ran, Yu Yugang, et al. Joint Optimization of Order Sequence and Pick Position in an AS/RS with Multiple In-the-aisle Pick Positions[J]. Chinese Journal of Management Science, 2020, 28(10): 156-164.
3	黄鹏, 姚锡凡, 胡晓阳, 等. 面向大规模立体仓库货位分配问题的两阶段混合优化算法[J]. 计算机集成制造系统, 2022, 28(8): 2481-2495.
	Huang Peng, Yao Xifan, Hu Xiaoyang, et al. Two-stage Hybrid Optimization Algorithm for Large-scale Automated Warehouse Storage Location Assignment Problem[J]. Computer Integrated Manufacturing Systems, 2022, 28(8): 2481-2495.
4	蔡安江, 叶康, 郭师虹, 等. 双向式自动化立体仓库货位分配优化[J]. 计算机集成制造系统, 2022, 28(12): 4046-4054.
	Cai Anjiang, Ye Kang, Guo Shihong, et al. Optimization of Storage Allocation in Two-way Automated Warehouse[J]. Computer Integrated Manufacturing Systems, 2022, 28(12): 4046-4054.
5	Wang Yanyan, Man Rongjun, Zhao Wanmeng, et al. Storage Assignment Optimization for Fishbone Robotic Mobile Fulfillment Systems[J]. Complex & Intelligent Systems, 2022, 8(6): 4587-4602.
6	Jiang Wei, Liu Jiyin, Dong Yun, et al. Assignment of Duplicate Storage Locations in Distribution Centres to Minimise Walking Distance in Order Picking[J]. International Journal of Production Research, 2021, 59(15): 4457-4471.
7	Guerriero F, Pisacane O, Rende F. Comparing Heuristics for the Product Allocation Problem in Multi-level Warehouses Under Compatibility Constraints[J]. Applied Mathematical Modelling, 2015, 39(23/24): 7375-7389.
8	李佳, 何非, 谢刚伟, 等. 四向穿梭车式密集仓储入库货位分配方法研究[J]. 计算机工程与应用, 2023, 59(24): 328-335.
	Li Jia, He Fei, Xie Gangwei, et al. Research on Location Allocation of Four-way Shuttle Storage and Retrieval System[J]. Computer Engineering and Applications, 2023, 59(24): 328-335.
9	陈雷, 程江峰, 朱永怀, 等. 多任务纺织立库货位分配与任务序列优化方法[J]. 计算机集成制造系统, 2023, 29(4): 1371-1385.
	Chen Lei, Cheng Jiangfeng, Zhu Yonghuai, et al. Multi-task Textile Stereoscopic Warehouse Location Allocation and Task Sequence Optimization Method[J]. Computer Integrated Manufacturing Systems, 2023, 29(4): 1371-1385.
10	Yan Bo, Yan Chang, Long Feng, et al. Multi-objective Optimization of Electronic Product Goods Location Assignment in Stereoscopic Warehouse Based on Adaptive Genetic Algorithm[J]. Journal of Intelligent Manufacturing, 2018, 29(6): 1273-1285.
11	Hakim Nadir Bessenouci, Sari Zaki, Ghomri Latéfa. Metaheuristic Based Control of a Flow Rack Automated Storage Retrieval System[J]. Journal of Intelligent Manufacturing, 2012, 23(4): 1157-1166.
12	付建林, 丁国富, 张剑, 等. 基于响应面和NSGA-Ⅱ的AGV系统多目标优化配置[J]. 系统仿真学报, 2022, 34(5): 994-1002.
	Fu Jianlin, Ding Guofu, Zhang Jian, et al. Multi-objective Optimization Configuration of AGV System Based on Response Surface and NSGA-Ⅱ[J]. Journal of System Simulation, 2022, 34(5): 994-1002.
13	田彬, 吴颖颖, 吴耀华, 等. "四向车"拣选系统订单排序优化[J]. 机械工程学报, 2019, 55(18): 225-232.
	Tian Bin, Wu Yingying, Wu Yaohua, et al. Order Sequencing Optimization for "Four-way" Shuttle Based Order Picking System[J]. Journal of Mechanical Engineering, 2019, 55(18): 225-232.
14	何昕杰, 周少武, 张红强, 等. 基于改进遗传算法的四向穿梭车系统订单排序优化[J]. 系统仿真学报, 2021, 33(9): 2166-2179.
	He Xinjie, Zhou Shaowu, Zhang Hongqiang, et al. Order Sorting Optimization for Four-way Shuttle System Based on Improved Genetic Algorithm[J]. Journal of System Simulation, 2021, 33(9): 2166-2179.
15	袁福龙, 朱建平. 基于改进蚁群算法的移动机器人最优路径规划[J]. 现代制造工程, 2021(7): 38-47, 65.
	Yuan Fulong, Zhu Jianping. Optimal Path Planning of Mobile Robot Based on Improved Ant Colony Algorithm[J]. Modern Manufacturing Engineering, 2021(7): 38-47, 65.
16	蔡安江, 薛晓飞, 郭师虹, 等. 两端式自动化立体仓库布局堆垛机调度[J]. 中国机械工程, 2019, 30(6): 735-741.
	Cai Anjiang, Xue Xiaofei, Guo Shihong, et al. Stacker Scheduling of Layouts for Automatic Warehouses with Double Ended[J]. China Mechanical Engineering, 2019, 30(6): 735-741.
17	Ju Xinglong, Chen V C P, Rosenberger J M, et al. Fast Knot Optimization for Multivariate Adaptive Regression Splines Using Hill Climbing Methods[J]. Expert Systems with Applications, 2021, 171: 114565.
18	Yu Jingjing, Voß Stefan, Song Xiangqun. Multi-objective Optimization of Daily Use of Shore Side Electricity Integrated with Quayside Operation[J]. Journal of Cleaner Production, 2022, 351: 131406.
19	李树勋, 连超, 潘伟亮, 等. 基于改进NSGA-Ⅱ算法的安全阀动态特性分析及优化[J]. 振动与冲击, 2023, 42(13): 66-74.
	Li Shuxun, Lian Chao, Pan Weiliang, et al. Dynamic Characteristics Analysis and Optimization of Safety Valve Based on Improved NSGA-Ⅱ Algorithm[J]. Journal of Vibration and Shock, 2023, 42(13): 66-74.
20	唐艺军, 王艳灵, 孙浩强. 基于改进NSGA-Ⅱ算法的高维多目标柔性冲压车间生产调度优化[J]. 锻压技术, 2023, 48(11): 204-211.
	Tang Yijun, Wang Yanling, Sun Haoqiang. Production Scheduling Optimization on High Dimensional Multi-objective Flexible Stamping Workshop Based on Improved NSGA-Ⅱ Algorithm[J]. Forging & Stamping Technology, 2023, 48(11): 204-211.
21	付建林, 丁国富, 张剑, 等. 基于响应面和NSGA-Ⅱ的AGV系统多目标优化配置[J]. 系统仿真学报, 2022, 34(5): 994-1002.
	Fu Jianlin, Ding Guofu, Zhang Jian, et al. Multi-objective Optimization Configuration of AGV System Based on Response Surface and NSGA-Ⅱ[J]. Journal of System Simulation, 2022, 34(5): 994-1002.
22	邰彬, 黄杨珏, 沈开程, 等. 基于指标加权K-means++算法的分布式光伏功率波动平抑控制方法[J]. 武汉大学学报(工学版), 2023, 56(11): 1413-1424.
	Tai Bin, Huang Yangjue, Shen Kaicheng, et al. Smoothing Control Method of Distributed Photovoltaic Power Fluctuation Based on the Index Weighted K-means++ Algorithm[J]. Engineering Journal of Wuhan University, 2023, 56(11): 1413-1424.

参数	值
货架列数/排数/层数	10/10/8
货位长度/宽度/高度/m	1/1/1
各层穿梭车的数量	4
提升机平均提升速度/(m/s)	1.2
穿梭车平均行驶速度/(m/s)	1.5
四向穿梭车装载时间/s	5
四向穿梭车卸载时间/s	3
第z层入库平台1坐标	(0，4，z)
第z层入库平台2坐标	(0，8，z)
第z层出库平台1坐标	(11，8，z)
第z层出库平台2坐标	(11，8，z)

序号	设备使用均衡	货架稳定性	出入库效率	序号	设备使用均衡	货架稳定性	出入库效率
1	27.12	2.77	3 680.25	14	26.24	2.69	3 726.05
2	26.15	2.71	3 700.34	15	26.77	2.70	3 717.21
3	26.15	2.70	3 709.28	16	26.96	2.73	3 688.78
4	26.38	2.67	3 741.72	17	26.46	2.73	3 684.76
5	26.46	2.76	3 676.91	18	26.38	2.74	3 680.15
6	26.84	2.79	3 662.09	19	26.69	2.76	3 668.12
7	27.10	2.80	3 669.28	20	26.91	2.77	3 663.03
8	26.32	2.78	3 654.04	21	26.32	2.77	3 659.02
9	26.91	2.79	3 659.93	22	26.91	2.77	3 666.53
10	26.64	2.79	3 650.43	23	★26.15	2.72	3 679.32
11	26.53	2.73	3 694.71	24	26.64	2.80	★3 647.74
12	26.53	2.74	3 688.33	25	26.22	★2.66	3 744.17
13	26.31	2.67	3 733.06

方案	设备使用均衡	货架稳定性	出入库效率
优化/%	3.1	4.5	3.4
Pareto(2)	26.15	2.71	3 700.34
目标权重	26.98	2.84	3 832.31

货物数量	算例编号	NSGA-II				NSGAII-HC-K-means
货物数量	算例编号	F₁	F₂	F₃	T/s	F₁	P₁/%	F₂	P₂/%	F₃	P₃/%	T/s
150	1	28.32	2.78	3 868.40	8.99	28.21	0.40	2.50	10.17	3 607.12	6.75	7.27
	2	28.76	2.47	3 860.92	9.32	27.30	5.06	2.36	4.41	3 514.57	8.97	7.09
	3	28.10	2.60	3 974.07	8.91	26.96	4.07	2.49	4.14	3 581.40	9.88	7.27
	4	29.45	2.69	3 872.53	10.07	27.01	8.27	2.55	5.15	3 708.65	4.23	6.74
	5	27.38	3.08	4 120.30	9.69	25.54	6.71	2.69	12.77	3 725.49	9.58	6.92
	平均	29.02	2.72	3 939.24	9.39	27.00	6.96	2.52	7.35	3 627.45	7.91	7.06
250	1	37.87	3.02	6 893.69	23.90	35.59	6.02	2.66	12.01	6 206.25	9.97	19.13
	2	36.03	3.05	7 182.01	22.86	34.83	3.34	2.85	6.59	6 392.46	10.99	18.48
	3	35.90	3.20	7 089.62	22.93	34.16	4.86	2.86	10.67	6 484.02	8.54	18.20
	4	32.31	3.48	7 170.92	24.96	30.87	4.46	3.07	11.79	6 597.85	7.99	18.76
	5	36.55	3.08	6 584.00	25.35	35.45	3.01	2.91	5.38	6 383.47	3.05	18.66
	平均	35.82	3.17	6 984.05	24.00	34.18	4.58	2.87	9.46	6 412.81	8.18	18.65
400	1	44.35	3.32	11 028.44	39.75	41.09	7.35	3.12	6.13	10 837.76	1.73	28.24
	2	49.45	3.61	10 979.17	35.05	45.34	8.31	3.16	12.47	10 905.67	0.67	28.08
	3	42.60	3.62	11 252.15	40.95	39.31	7.73	3.38	6.74	11 186.12	0.59	28.40
	4	49.83	3.17	10 880.54	41.69	47.61	4.46	3.13	1.12	10 865.10	0.14	28.42
	5	49.84	3.10	11 896.61	40.46	46.70	6.30	3.05	1.75	10 738.75	9.73	28.42
	平均	47.43	3.36	11 207.38	39.58	44.01	7.21	3.17	5.65	10 906.68	2.68	28.31

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