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Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (8): 1598-1607    DOI: 10.3785/j.issn.1008-973X.2025.08.006
    
Improved migrating bird algorithm for re-entrant hybrid flowshop scheduling problem with lot streaming
Yabo LUO(),Shaolong YU,Feng ZHANG*(),Cunrong LI
School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China
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Abstract  

A re-entrant hybrid flowshop scheduling problem with lot streaming (RHFSP-LS) model was constructed in view of the difficulty of manual scheduling in array workshops to adapt to complex and variable production demands. An improved multi-objective migrating birds optimization algorithm was proposed for solving the model. A multi-objective migrating birds optimization algorithm based on non-dominated sorting, weighted sum, and external archive set was designed. The quality of the initial population was improved by using Logistic chaotic mapping and the NEH algorithm. A "sub-lot priority" + "batch priority" decoding strategy was proposed to enhance the algorithm’s solving capacity for special problems. A neighborhood search based on individual age was introduced to optimize the population’s neighborhood search direction. An escape mechanism combined with an external archive set was proposed to enhance the algorithm’s global search capability. The proposed strategies and algorithms were experimentally verified for the effectiveness and superiority in solving RHFSP-LS, ensuring an effective balance between the overall production cycle and the delivery deadlines of each process batch.



Key wordsre-entrant hybrid flowshop      lot streaming      migrating bird optimization algorithm      multi-objective optimization      production scheduling     
Received: 25 September 2024      Published: 28 July 2025
CLC:  TH 166  
Fund:  国家自然科学基金资助项目(51875430).
Corresponding Authors: Feng ZHANG     E-mail: luoyabo@whut.edu.cn;zhangfengie@whut.edu.cn
Cite this article:

Yabo LUO,Shaolong YU,Feng ZHANG,Cunrong LI. Improved migrating bird algorithm for re-entrant hybrid flowshop scheduling problem with lot streaming. Journal of ZheJiang University (Engineering Science), 2025, 59(8): 1598-1607.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.08.006     OR     https://www.zjujournals.com/eng/Y2025/V59/I8/1598


改进候鸟算法求解可重入混流车间批量流调度

鉴于阵列车间手工排产难以适应复杂多变的生产需求,构建可重入混合流水车间批量流调度问题(RHFSP-LS)模型,提出改进多目标候鸟优化算法进行求解. 设计基于非支配排序、加权总和与外部档案集的多目标候鸟优化算法. 利用Logistic混沌映射和NEH算法,提高了初始种群的质量. 提出“子批优先”+“批次优先”的解码策略,提升了算法对于特殊问题的求解能力. 提出基于个体年龄的邻域搜索,优化了种群的邻域搜索方向. 提出结合外部档案集的逃逸机制,提升了算法的全局搜索能力. 通过实验验证了所提策略及算法在解决RHFSP-LS上的有效性与优越性,保证了整体生产周期与各工艺批次交货期限的有效平衡.


关键词: 可重入混合流水车间,  批量流,  候鸟优化算法,  多目标优化,  生产调度 
Fig.1 Schematic diagram of RHFSP-LS
Fig.2 Schematic of MBO multi-objective optimization
Fig.3 Flow chart of IMO-MBO
Fig.4 Gantt chart of special problem scheduling
Fig.5 Schematic of order crossover
参数小规模大规模
工艺批次数量[5, 10][10, 20]
加工子批数量[1, 5][1, 10]
重入层数[1, 2][1, 4]
加工阶段数量[4, 6][6, 10]
每个阶段并行机数量[1, 3][1, 6]
加工时间[5, 30]
工艺批次交货期限$ [0.7{\mathrm{ATPT}},0.7 \mathrm{max}\;({\mathrm{{P}{T}}})] $
Tab.1 Range of values of parameters required to generate set of example
参数水平参数
$ {P}_{\mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e}} $$ G $$ [{P}_{\mathrm{f}},{P}_{\mathrm{u}}] $$ [{A}_{\mathrm{m}\mathrm{i}\mathrm{n}},{A}_{\mathrm{m}\mathrm{a}\mathrm{x}}] $$ {A}_{\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{t}} $
Level1313[0.1, 0.9][2,4]8
Level2515[0.2, 0.8][3,5]10
Level3818[0.3, 0.7][4,6]13
Level410110[0.4, 0.6][5,7]15
Tab.2 Value of parameter level in orthogonal experiment
实验
编号
参数IGD
平均值
$ {P}_{\mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e}} $$ G $$ [{P}_{\mathrm{f}},{P}_{\mathrm{u}}] $$ [{A}_{\mathrm{m}\mathrm{i}\mathrm{n}}, $$ {A}_{\mathrm{m}\mathrm{a}\mathrm{x}}] $$ {A}_{\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{t}} $
1313[0.1, 0.9][2, 4]870.4741
2315[0.2, 0.8][3, 5]1076.5185
3318[0.3, 0.7][4, 6]1362.2106
43110[0.4, 0.6][5, 7]1566.1984
5513[0.2, 0.8][4, 6]1579.3679
6515[0.1, 0.9][5, 7]1387.6653
7518[0.4, 0.6][2, 4]1080.1016
85110[0.3, 0.7][3, 5]877.2222
9813[0.3, 0.7][5, 7]10102.1428
10815[0.4, 0.6][4, 6]894.7215
11818[0.1, 0.9][3, 5]15105.5816
128110[0.2, 0.8][2, 4]1398.6123
131013[0.4, 0.6][3, 5]13111.7112
141015[0.3, 0.7][2, 4]15102.2907
151018[0.2, 0.8][5, 7]8107.0169
1610110[0.1, 0.9][4, 6]10103.5490
Tab.3 Result of orthogonal experiment
水平$ {P}_{\mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e}} $$ G $$ [{P}_{\mathrm{f}},{P}_{\mathrm{u}}] $$ [{A}_{\mathrm{m}\mathrm{i}\mathrm{n}}, $$ {A}_{\mathrm{m}\mathrm{a}\mathrm{x}}] $$ {A}_{\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{t}} $
Level168.850490.924091.817587.869787.3586
Level281.089290.299090.378992.758490.5780
Level3100.264588.727785.966684.962290.0498
Level4106.141986.395488.183190.755888.3596
Delta37.29154.52865.85097.79623.2194
排秩14331
Tab.4 Ordering of parameter level value
算法解码策略种群初始化基于个体年龄
的邻域搜索
逃逸策略
IMO-MBO1$ a $
MBO12$ a $
MBO23$ a $
MBO31$ b $
MBO41$ c $
MBO51$ d $
MBO61$ a $
MBO71$ a $
MBO82$ d $
Tab.5 Strategy setting of ablation study
算例IGD
IMO-MBOMBO1MBO2MBO3MBO4MBO5MBO6MBO7MBO8
N8M5R225.3812+25.423120.607729.3766*26.320630.905526.780029.144333.3299
N10M6R227.9043+27.182030.535340.7840*28.347641.564629.191430.393241.7358
N7M4R13.8630+4.74566.52115.0911*4.41045.45494.21364.65575.8562
N6M6R223.9847+23.650732.073828.4261*24.009130.571025.290424.727630.5995
N7M6R120.729522.413213.094223.3739*20.5896+24.166822.413223.202226.3538
N18M6R259.9558+52.0587157.0559155.0430*59.9601180.500164.428077.2802249.7320
N16M6R4121.2070129.938360.9170177.7854120.8587+157.4509*130.2013122.9012159.7152
N17M8R363.6715+82.4753151.6475181.593165.3661165.8053*70.860368.0615161.3383
N11M7R234.9560+39.233036.7736203.2538*37.1728204.904536.541835.9319182.8789
N13M6R145.6521+48.195169.188362.609246.807262.0986*48.774051.267666.0469
Tab.6 Comparison of IGD metrics for IMO-MBO and variant algorithms
对比算法p对比算法p
IMO-MBO vs. MBO10.139MBO2 vs. IMO-MBO0.285
IMO-MBO vs. MBO50.005MBO2 vs. MBO10.445
IMO-MBO vs. MBO60.005IMO-MBO vs. MBO30.037
IMO-MBO vs. MBO70.005IMO-MBO vs. MBO40.005
IMO-MBO vs. MBO80.005MBO3 vs. MBO50.386
Tab.7 Wilcoxon signed rank test for IMO-MBO and variant algorithms
Fig.6 Pareto frontier comparison of $ \varepsilon $-constraint method and different decoding method
算法参数数值
NSGA-II种群大小100
交叉概率0.8
变异概率0.2
MOPSO粒子群规模50
惯性权重0.2
个体学习因子0.4
群体学习因子0.8
Tab.8 Partial parameter value for NSGA-II and MOPSO
算法IGD
N8M5R2N10M6R2N7M4R1N6M6R2N7M6R1N18M6R2N16M6R4N17M8R3N11M7R2N13M6R1
IMO-MBO20.512445.89501.562327.958724.561456.811786.990770.735721.800832.7284
NSGA-II28.958869.12796.363038.785932.5824416.8008276.4641166.672359.193765.9818
MOPSO21.774670.04099.183636.893637.7266350.0761348.5028134.274836.371966.4674
MOHGA22.050852.83022.195229.049226.039251.2483105.556977.648730.706135.0671
HDABC21.592355.83073.008027.980728.2604248.0519181.2737155.648245.966652.1716
Tab.9 Comparison of IGD indicator for IMO-MBO and contrast algorithm
对比算法p
IMO-MBO vs. NSGA-II0.005
IMO-MBO vs. MOPSO0.005
IMO-MBO vs. MOHGA0.028
IMO-MBO vs. HDABC0.005
Tab.10 Wilcoxon signed rank test for IMO-MBO with contrast algorithms
Fig.7 Normalized result of IGD indicator
Fig.8 Pareto frontier comparison of N6M6R2 and N17M8R3
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