A Modified Migrating Birds Optimization for Multi-Objective Lot Streaming Hybrid Flowshop Scheduling

doi:10.16183/j.cnki.jsjtu.2020.435

Abstract

Abstract:

This paper proposes an adaptive migrating birds optimization (AMBO) method based on variable neighborhood search to solve the inequal lot streaming hybrid flowshop scheduling problem (ILS-HFSP) for a 2+1+1 hybrid flowshop, which realizes multi-objective optimization of minimizing makespan and minimum average work in process. Compared with the original migrating birds optimization, the AMBO algorithm adopts the variable neighborhood search strategy with an adaptive selection probability of neighborhood operator that is adaptively adjusted with the number of iterations. Besides, a time-window operator is adopted to improve the search performance of exchange operators and convergence rate. Several orders of different scales generated randomly are studied, and the results show that the AMBO algorithm has a higher solution quality and a better convergence performance than the migrating birds optimization algorithm and the genetic algorithm, thereby verifying the effectiveness of the AMBO algorithm.

Key words: lot streaming problem, hybrid flowshop scheduling problem, variable neighborhood search, adaptive migrating birds optimization (AMBO), time window operation

CLC Number:

TH166

TANG Hongtao, WANG Dannan, SHAO Yiping, ZHAO Wenbin, JIANG Weiguang, CHEN Qingfeng. A Modified Migrating Birds Optimization for Multi-Objective Lot Streaming Hybrid Flowshop Scheduling[J]. Journal of Shanghai Jiao Tong University, 2022, 56(2): 201-213.

Figures/Tables 15

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Tab.7

Comparison of RPI among GA, MBO, and AMBO algorithms at ρ=10,20, and 30

任务规模	算法	ρ=10		ρ=20		ρ=30
任务规模	算法	$x -$ /%	s	$x -$ /%	s	$x -$ /%	s
60	GA	5.78	4.78	8.15	4.32	13.01	3.81
	MBO	12.21	3.79	11.06	3.64	8.70	3.43
	AMBO	3.37	2.78	2.84	2.57	2.61	2.44
80	GA	3.73	5.24	7.27	4.71	11.42	4.29
	MBO	11.93	4.13	10.38	3.81	7.94	3.72
	AMBO	3.54	3.11	3.13	2.79	2.89	2.58
100	GA	2.41	5.67	5.61	5.12	7.56	4.52
	MBO	12.71	4.85	10.47	4.45	7.46	4.23
	AMBO	5.74	3.43	3.74	3.12	3.31	2.88

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产品数量范围	订单数比例/%	产品总数比例/%
1×10³~3×10³	80	50
3×10³~1×10⁴	15	30
1×10⁴~2×10⁴	5	20

水平	α	ω	m	g
1	0.08283	0.08393	0.08437	0.0818
2	0.08163	0.0813	0.08367	0.08533
3	0.08837	0.0876	0.0848	0.0857
Δ	0.00673	0.0063	0.00113	0.0039
排序	1	2	4	3

序号	AMBO		MBO		GA
序号	最优解均值	标准偏差	最优解均值	标准偏差	最优解均值	标准偏差
1	0.0649	0.00384	0.0653	0.00404	0.0664	0.00684
2	0.0625	0.00335	0.0626	0.00334	0.0642	0.00759
3	0.0683	0.00354	0.0726	0.00369	0.0764	0.00795
4	0.0686	0.00284	0.0784	0.00365	0.0814	0.00718
5	0.0748	0.00321	0.0765	0.00364	0.0787	0.00768
6	0.0646	0.00322	0.0795	0.00342	0.0834	0.00747
7	0.0706	0.00317	0.0796	0.00391	0.0777	0.00734
8	0.0715	0.00336	0.0771	0.00387	0.0804	0.00847
9	0.0673	0.00341	0.0715	0.00405	0.0761	0.00757
10	0.0711	0.00371	0.0826	0.00367	0.0817	0.00754
11	0.0621	0.00315	0.0645	0.00378	0.0794	0.00781
12	0.0733	0.00344	0.0799	0.00363	0.0844	0.00759
13	0.0875	0.00334	0.0884	0.00413	0.0919	0.00763
15	0.0865	0.00325	0.0886	0.00357	0.0884	0.00804
14	0.0686	0.00311	0.0726	0.00398	0.0757	0.00725
16	0.0639	0.00324	0.0709	0.00338	0.0704	0.00737
17	0.0716	0.00315	0.0719	0.00401	0.0717	0.00794
18	0.0639	0.00341	0.0656	0.00387	0.0732	0.00781
19	0.0723	0.00331	0.0695	0.00348	0.0774	0.00765
20	0.0633	0.00345	0.0644	0.00367	0.0706	0.00742
21	0.0643	0.00344	0.0684	0.00379	0.0704	0.00806
22	0.0659	0.00339	0.0724	0.00344	0.0722	0.00774
23	0.0665	0.00338	0.0726	0.00404	0.0719	0.00735
24	0.0649	0.00326	0.0686	0.00367	0.0704	0.00784
25	0.0685	0.00328	0.0699	0.00421	0.0717	0.00785
26	0.0696	0.00285	0.0699	0.00368	0.0707	0.00752
27	0.0724	0.00324	0.0726	0.00354	0.0731	0.00728
28	0.0624	0.00337	0.0679	0.00364	0.0695	0.00838
29	0.0688	0.00315	0.0695	0.00392	0.0714	0.00763
30	0.0691	0.00308	0.0719	0.00390	0.0737	0.00734
均值	0.0690	0.00330	0.0731	0.00375	0.0758	0.00764

算法	最优解均值	解的标准偏差	平均收敛迭代次数	算法平均运行时间/s
GA	0.0758	0.00764	88	263.13
MBO	0.0731	0.00375	76	335.24
AMBO	0.0690	0.00330	56	358.12

任务规模	算法	最优解均值	解的标准偏差	平均收敛迭代次数/次	算法平均收敛时间/s
30	GA	0.0771	0.00798	128	362.24
	MBO	0.0748	0.00384	112	466.25
	AMBO	0.0706	0.00376	87	493.46
40	GA	0.0778	0.00784	167	560.32
	MBO	0.0752	0.00391	154	650.21
	AMBO	0.0714	0.00364	125	708.72
50	GA	0.0806	0.00814	205	780.32
	MBO	0.0766	0.00414	179	920.31
	AMBO	0.0721	0.00385	162	994.63