基于动态储位分配策略的自动化立库多目标优化

doi:10.16182/j.issn1004731x.joss.24-0210

摘要/Abstract

摘要：

基于动态储位分配策略，以整库为优化主体，以满足安全性、合理性的货位分配目标，以满足各堆垛机作业时间最短、作业能耗最低的调度目标，构建二阶段优化模型。上下层均为典型多目标优化问题，上层模型的理想解将作为下层模型的初始条件。采用多目标遗传算法求解优化模型的理想解，并通过熵权法对各个目标分配权重。结果表明：在货物离散排布状态下动静态分配策略无明显差异，但聚合排布状态下动态分配策略对货位分配与堆垛机调度的综合优化效果明显优于静态分配，且货物质量影响整体优化效果；大质量情况下安全性优化效果更为显著而较小质量情况下合理性与堆垛机调度优化效果更为明显。

关键词: 自动化立体库, 货位分配, 调度优化, 多目标优化, 多目标遗传算法

Abstract:

Based on the dynamic storage allocation strategy, the two-stage optimization model is constructed with the whole warehouse as the main optimization body, in order to meet the safety and rationality of the storage allocation goals, and to meet the dispatching goals of the shortest operation time and the lowest energy consumption of each stacke. The upper and lower levels of the model are typical multi-objective optimization problems, and the ideal solution of the upper level model will be the initial condition of the lower level model. The multi-objective genetic algorithm is used to solve the ideal solution of the optimization model, and the entropy weight method is used to assign weights to each objective. The final results show that there is no significant difference between dynamic and static allocation strategies under the discrete arrangement of goods, but the comprehensive optimization effect of dynamic allocation strategy on cargo location allocation and stacker scheduling under the aggregate arrangement is significantly better than that of static allocation, and the quality of goods affects the overall optimization effect. In the case of large mass, the safety optimization effect is more obvious, while in the case of small mass, the rationality and the optimization effect of stacker scheduling are more obvious.

Key words: automatic stereoscopic library, space allocation, scheduling optimization, multi-objective optimization, multi-objective genetic algorithm

中图分类号:

TP391.9

陈娟,郑旺,刘倩倩等 . 基于动态储位分配策略的自动化立库多目标优化[J]. 系统仿真学报, 2025, 37(6): 1435-1448.

Chen Juan,Zheng Wang,Liu Qianqian,et al . Automatic Multi-objective Optimization Based on Dynamic Storage Location Allocation Strategy[J]. Journal of System Simulation, 2025, 37(6): 1435-1448.

图/表 15

图1

图2

图3

图4

图5

表1

货架规格与堆垛机运行参数

名称	数值
单排货架列数b	10
单排货架层数c	6
单个货格长度 $l y / m$	1.2
单个货格高度 $l z / m$	1.2
货架通道宽度/m	1.5
堆垛机水平方向额定速度 $v y$ $/ (m ⋅ s - 1)$	0.4
堆垛机竖直方向额定速度 $v z$ $/ (m ⋅ s - 1)$	0.4
堆垛机电机水平运行额定功率 $P y$ /kW	30
堆垛机电机竖直运行额定功率 $P z$ /kW	40

表1

图6

表2

表3

原始数据在各个权重下的目标函数值与熵权值

权重				较小质量目标函数值				较大质量目标函数值
$u 1$	$u 2$	$u 3$	$u 4$	$f 1$	$f 2$	$f 3$	$f 4$	$f 1$	$f 2$	$f 3$	$f 4$
1	0	0	0	19.211	54.303	362	53.726	19.212	59.982	4 420	5.784
0	1	0	0	23.529	22.946	552	53.208	23.713	22.936	5 375	5.310
0	0	1	0	23.545	64.821	2	58.568	23.651	66.072	0	5.601
0	0	0	1	21.252	25.582	487	48.822	21.371	25.547	1 475	4.869
0.5	0.5	0	0	21.000	23.594	657	51.439	21.060	23.502	5 465	5.098
0.5	0	0.5	0	19.459	69.394	2	58.227	19.262	62.866	10	5.856
0.5	0	0	0.5	19.360	67.506	2	55.460	19.214	44.406	5 010	5.122
0	0.5	0.5	0	23.962	23.207	3	54.049	23.541	23.058	20	5.240
0	0.5	0	0.5	22.633	23.453	597	49.445	23.33	22.941	4 640	5.038
0	0	0.5	0.5	21.689	25.681	2	49.472	21.446	25.371	30	4.921
0.33	0.33	0.33	0	21.367	24.132	2	51.589	21.526	23.604	30	5.103
0.33	0.33	0	0.33	20.847	24.134	867	49.066	20.945	23.730	5 955	4.981
0.33	0	0.33	0.33	19.948	29.742	2	49.445	19.306	42.906	30	5.115
0	0.33	0.33	0.33	22.146	24.157	2	49.419	23.707	23.106	20	5.170
熵权值				0.287	0.272	0.207	0.234	0.385	0.183	0.279	0.153

表3

图7

图8

图9

表4

表5

表6

参考文献 13

1	刘恺文, 曹政才. 基于改进灰狼优化算法的自动化立体仓库作业能量优化调度[J]. 计算机集成制造系统, 2020, 26(2): 376-383.
	Liu Kaiwen, Cao Zhengcai. Energy-optimized Task Scheduling of Automated Warehouse Based on Improved Grey Wolf Optimizer[J]. Computer Integrated Manufacturing Systems, 2020, 26(2): 376-383.
2	蔺一帅, 李青山, 陆鹏浩, 等. 智能仓储货位规划与AGV路径规划协同优化算法[J]. 软件学报, 2020, 31(9): 2770-2784.
	Lin Yishuai, Li Qingshan, Lu Penghao, et al. Shelf and AGV Path Cooperative Optimization Algorithm Used in Intelligent Warehousing[J]. Journal of Software, 2020, 31(9): 2770-2784.
3	李珍萍, 卜晓奇, 陈星艺. 基于商品关联度的智能仓库储位分配问题研究[J]. 数学的实践与认识, 2020, 50(5): 23-31.
	Li Zhenping, Bu Xiaoqi, Chen Xingyi. Research on Storage Allocation Problem of Intelligent Warehouse Based on Correlation Degree of Items[J]. Mathematics in Practice and Theory, 2020, 50(5): 23-31.
4	姜良重, 雷航, 李贞昊, 等. 采用自适应优化权重的出库货位优化方法研究[J]. 计算机工程与应用, 2021, 57(15): 271-278.
	Jiang Liangzhong, Lei Hang, Li Zhenhao, et al. Research on Outbound Slotting Optimization Method by Using Adaptive Optimization Weights[J]. Computer Engineering and Applications, 2021, 57(15): 271-278.
5	唐文献, 彭伟, 苏世杰, 等. 面向船舶行业的多巷道自动化立体仓库货位优化[J]. 计算机集成制造系统, 2020, 26(2): 384-392.
	Tang Wenxian, Peng Wei, Su Shijie, et al. Slotting Optimization of Multi-roadway Automated High-rise Warehouse for Shipping Industry[J]. Computer Integrated Manufacturing Systems, 2020, 26(2): 384-392.
6	Lee I G, Chung S H, Yoon S W. Two-stage Storage Assignment to Minimize Travel Time and Congestion for Warehouse Order Picking Operations[J]. Computers & Industrial Engineering, 2020, 139: 106129.
7	李博文, 李建国, 常立丹. 基于遗传-集束搜索的立体车库堆垛机运行路径优化[J]. 科学技术与工程, 2019, 19(31): 233-238.
	Li Bowen, Li Jianguo, Chang Lidan. Operation Path Optimization of Stereo Garage Stacker Based on Genetic-beam Search Hybrid Algorithm[J]. Science Technology and Engineering, 2019, 19(31): 233-238.
8	邹霞, 吴耀华, 李毅超, 等. 随机订单驱动的集中式和分散式AS/RS建模及仿真[J]. 计算机集成制造系统, 2017, 23(12): 2778-2786.
	Zou Xia, Wu Yaohua, Li Yichao, et al. Modeling and Simulation of Centralized and Decentralized AS/RS Driven by Random Orders[J]. Computer Integrated Manufacturing Systems, 2017, 23(12): 2778-2786.
9	夏绪辉, 朱强, 王蕾, 等. 考虑时间和能耗的立体仓库三维空间路径优化[J]. 武汉科技大学学报, 2018, 41(6): 465-472.
	Xia Xuhui, Zhu Qiang, Wang Lei, et al. Three-dimensional Spatial Path Optimization of Automatic Storage and Retrieval System Considering Time and Energy Consumption[J]. Journal of Wuhan University of Science and Technology, 2018, 41(6): 465-472.
10	Bortolini Marco, Faccio Maurizio, Ferrari Emilio, et al. Design of Diagonal Cross-aisle Warehouses with Class-based Storage Assignment Strategy[J]. The International Journal of Advanced Manufacturing Technology, 2019, 100(9): 2521-2536.
11	Silva Allyson, Coelho Leandro C, Darvish Maryam, et al. Integrating Storage Location and Order Picking Problems in Warehouse Planning[J]. Transportation Research Part E: Logistics and Transportation Review, 2020, 140: 102003.
12	方磊, 吉卫喜, 彭威, 等. 动态储位分配策略下仓储作业能耗优化调度[J]. 计算机工程与应用, 2023, 59(4): 303-311.
	Fang Lei, Ji Weixi, Peng Wei, et al. Optimal Scheduling of Storage Energy Consumption Under Dynamic Storage Allocation Strategy[J]. Computer Engineering and Applications, 2023, 59(4): 303-311.
13	吴婷. 基于遗传算法的仓储系统多目标货位优化的研究[D]. 武汉: 武汉理工大学, 2011.
	Wu Ting. Study on Warehouse Slotting Optimization of Multi-objective Based on Genetic Algorithm[D]. Wuhan: Wuhan University of Technology, 2011.

货号	周转率/%	较小质量/kg	较大质量/kg
121	59	120	1 200
122	44	110	1 100
123	64	80	800
124	51	90	900
125	27	90	900
126	47	90	900
127	45	160	1 600
128	8	110	1 100
129	57	100	1 000
130	11	70	700
131	56	90	900
132	22	110	1 100
133	69	75	755
134	60	205	2 055
135	12	95	955
136	47	155	1 555
137	45	135	1 355
138	18	115	1 155
139	57	145	1 455
140	19	75	755
141	64	125	1 255
142	45	115	1 155
143	60	155	1 555
144	57	145	1 455

不同载货质量优化目标		初始状态静态分配	初始状态动态分配	优化比例/%	初分配状态静态分配	初分配状态动态分配	优化比例/%
较小质量	f₁	21.155	20.691	2.19	22.776	17.630	22.60
	f₂	24.400	24.471	-0.29	10.315	9.876	4.26
	f₃	2(极为安全)	2(极为安全)		4(极为安全)	4(极为安全)
	f₄	49.481	49.299	0.37	40.493	35.947	11.23
大质量	f₁	20.561	20.400	0.78	20.393	16.540	18.89
	f₂	24.927	24.861	0.26	14.047	11.343	19.25
	f₃	10(极为安全)	20(极为安全)		20(极为安全)	35(极为安全)
	f₄	4.983	5.017	-0.682	4.544	4.172	8.19

载货质量	目标函数	u₁/u₂											熵权值
载货质量	目标函数	1/0	0.9/0.1	0.8/0.2	0.7/0.3	0.6/0.4	0.5/0.5	0.4/0.6	0.3/0.7	0.2/0.8	0.1/0.9	0/1	熵权值
较小	F₁	378	375	375	381	390	375	384	381	375	387	372	0.511
较小	F₂	15 700	15 600	15 500	15 500	15 700	15 500	15 500	15 850	15 700	15 700	15 600	0.489
较大	F₁	378	375	378	384	381	381	381	381	387	381	381	0.489
较大	F₂	15 550	15 400	15 500	15 500	15 800	15 500	15 700	15 700	15 400	15 500	15 500	0.511

载货质量	目标函数	堆垛机号	初始状态(离散状态)			初分配优化状态(聚合状态)
载货质量	目标函数	堆垛机号	静态分配目标函数值	动态分配目标函数值	优化效果/%	静态分配目标函数值	动态分配目标函数值	优化效果/%
较小	F₁	1	375	369		429	309
		2	384	387		357	297
		3	345	360		288	294
		综合	1 104	1 116	-1.09	1 074	900	16.2
	F₂	1	15 550	15 550		18 000	12 350
		2	16 650	16 350		15 550	13 050
		3	16 100	16 100		12 200	12 200
		综合	48 300	48 000	0.62	45 750	37 600	17.8
较大	F₁	1	378	393		210	222
		2	390	378		408	360
		3	351	381		309	240
		综合	1 119	1 152	-2.95	927	822	11.33
	F₂	1	15 400	15 400		9 500	9 850
		2	16 500	16 350		17 800	15 550
		3	16 100	16 100		13 700	10 350
		综合	48 000	47 850	0.31	41 000	35 750	12.8

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