Multi-level teaching-learning-based optimization algorithm for green batch processing scheduling problem

doi:10.11772/j.issn.1001-9081.2025050652

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (6): 1922-1930.DOI: 10.11772/j.issn.1001-9081.2025050652

• Advanced computing • Previous Articles

Multi-level teaching-learning-based optimization algorithm for green batch processing scheduling problem

Youlian ZHENG¹^,², Yingkun CUI², Deming LEI³, Jing WANG²^,⁴()

^1.School of Computer Science，Hubei University，Wuhan Hubei 430062，China
^2.Hubei Key Laboratory of Modern Manufacturing Quality Engineering （Hubei University of Technology），Wuhan Hubei 430068，China
^3.School of Automation，Wuhan University of Technology，Wuhan Hubei 430070，China
^4.Yangtze River Shipping Development Research Center，Wuhan Hubei 430014，China

Received:2025-06-13 Revised:2025-09-25 Accepted:2025-09-29 Online:2025-10-17 Published:2026-06-10
Contact: Jing WANG
About author:ZHENG Youlian， born in 1972， Ph. D.， associate professor. Her research interests include intelligent optimization， production scheduling.
CUI Yingkun， born in 2005. Her research interests include industrial process control， intelligent optimization.
LEI Deming， born in 1968， Ph. D.， professor. His research interests include intelligent system optimization and control， intelligent computing.
First author contact:WANG Jing， born in 1996， Ph. D.， lecturer. Her research interests include deep reinforcement learning， intelligent algorithm optimization and scheduling.
Supported by:
Doctoral Research Start-up Foundation of Hubei University of Technology(XJ2024001902)

求解绿色批加工调度问题的多层教学优化算法

郑友莲¹^,², 崔樱堃², 雷德明³, 王静²^,⁴()

^1.湖北大学计算机学院，武汉 430062
^2.现代制造质量工程湖北省重点实验室（湖北工业大学），武汉 430068
^3.武汉理工大学自动化学院，武汉 430070
^4.长江航运发展研究中心，武汉 430014

通讯作者: 王静
作者简介:郑友莲（1972—），女，副教授，博士，主要研究方向：智能优化、生产调度
崔樱堃（2005—），女，山东青岛人，主要研究方向：工业过程控制、智能优化
雷德明（1968—），男，湖北荆州人，教授，博士，主要研究方向：智能系统优化与控制、智能计算
第一联系人：王静（1996—），女，湖北咸宁人，讲师，博士，主要研究方向：深度强化学习、智能算法优化与调度。
基金资助:
湖北工业大学博士科研启动基金资助项目(XJ2024001902)

Abstract

Abstract:

To address the green parallel Batch Processing Machine （BPM） scheduling problem with redyeing operations in textile factory dyeing workshops， a Multi-level Teaching-Learning-Based Optimization （MTLBO） algorithm was proposed to minimize makespan， total energy consumption， and total weighted advance/delay cost. Firstly， heuristic rules were employed to generate the initial population for improving the initial solution quality. Secondly， the population was divided into three layers — teacher group， elite class， and ordinary class through multi-level structure， with an inter-layer efficient communication mechanism designed for information sharing and knowledge inheritance. Finally， to enhance exploration ability of the population， and to avoid the algorithm from the local optimum， a diversity enhancement operator based on probability model was introduced to replace stagnant solutions. Test instances generated on the basis of industrial data were used to evaluate MTLBO’s performance， and it was compared with the algorithms such as Adaptive Shuffled Frog-Leaping Algorithm （ASFLA）， Multi- Objective Artificial Bee Colony （MOABC） algorithm， Fuzzy Genetic Algorithm （FGA）， and Non-dominated Sorting Genetic Algorithm-Ⅱ （NSGA-Ⅱ）. The experimental results indicate that on average， the MTLBO has the dominance relation of non-dominated solution set 81.92% higher， the coverage metric 97.58% lower， and the convergence metric 99.66% lower. The above verifies MTLBO’s superior exploration ability and stability in optimizing scheduling metrics， providing robust solutions with optimization efficiency for practical production decision-making.

Key words: green scheduling problem, Batch Processing Machine (BPM), redyeing operation, Teaching-Learning-Based Optimization (TLBO) algorithm, probability model

摘要：

针对纺织工厂染色车间里考虑重染工序的绿色并行批处理机（BPM）调度问题，提出一种多层教学优化（MTLBO）算法，以最小化最大完成时间、总能耗和总加权提前/拖期成本。首先，运用启发式规则生成初始种群提升初始解质量；其次，采用多层结构将种群划分为教师组、精英班和普通班这3层，并设计高效的层间通信机制，促进信息共享与知识传承；最后，为了增强种群探索能力，防止算法陷入局部最优，引入一种基于概率模型的多样性增强算子替换停滞解。基于工业数据生成测试实例评估MTLBO的性能，并将它与自适应混合蛙跳算法（ASFLA）、多目标人工蜂群（MOABC）算法、模糊遗传算法（FGA）和非支配排序遗传算法Ⅱ（NSGA-Ⅱ）等算法进行比较。实验结果表明，MTLBO的非劣解集的支配关系平均提高81.92%，覆盖度指标平均提高97.58%，且在收敛性指标平均减低99.66%，以上验证了MTLBO在优化调度指标上的更强寻优能力和更高稳定性，为实际生产决策提供了兼具鲁棒性与优化效能的调度方案。

关键词: 绿色调度问题, 批处理机, 重染工序, 教学优化算法, 概率模型

CLC Number:

TP273

Youlian ZHENG, Yingkun CUI, Deming LEI, Jing WANG. Multi-level teaching-learning-based optimization algorithm for green batch processing scheduling problem[J]. Journal of Computer Applications, 2026, 46(6): 1922-1930.

郑友莲, 崔樱堃, 雷德明, 王静. 求解绿色批加工调度问题的多层教学优化算法[J]. 《计算机应用》唯一官方网站, 2026, 46(6): 1922-1930.

Figures/Tables 13

Tab. 1 Symbols and descriptions

符号	描述
$A v$	第 $v$ 类工件的集合
$w t ¯ v$	第 $v$ 类工件的重量
$p ¯ v k$	第 $v$ 类工件在机器 $M k$ 上的加工时间/h
$d ¯ v -$	第 $v$ 类工件的最早交货日期/h
$d ¯ v +$	第 $v$ 类工件的最晚交货日期/h
$w ¯ v e$	第 $v$ 类工件的早完工权重
$w ¯ v t$	第 $v$ 类工件的晚完工权重
$Q k$	机器 $M k$ 的容量
$q k$	机器 $M k$ 加工时每小时单位能耗/（kW·h）
$E s t$	机器 $M k$ 清洗时每小时单位能耗/（kW·h），下标st（setup time）表示准备时间/清洗时间
$s t v, g$	机器从颜色 $v$ 到 $g$ 之间的清洗时间/h
$η$	总批数
$B k, b$	机器 $M k$ 上的批 $b$
$b p k, b$	$B k, b$ 的加工时间/h
$X g . k, b$	如果 $B k, b$ 中工件属于颜色 $g$ 则为1，否则为0
$Y v, g$	如果从颜色 $v$ 切换到颜色 $g$ 则为1，否则为0

Tab. 1 Symbols and descriptions

符号	描述
$A v$	第 $v$ 类工件的集合
$w t ¯ v$	第 $v$ 类工件的重量
$p ¯ v k$	第 $v$ 类工件在机器 $M k$ 上的加工时间/h
$d ¯ v -$	第 $v$ 类工件的最早交货日期/h
$d ¯ v +$	第 $v$ 类工件的最晚交货日期/h
$w ¯ v e$	第 $v$ 类工件的早完工权重
$w ¯ v t$	第 $v$ 类工件的晚完工权重
$Q k$	机器 $M k$ 的容量
$q k$	机器 $M k$ 加工时每小时单位能耗/（kW·h）
$E s t$	机器 $M k$ 清洗时每小时单位能耗/（kW·h），下标st（setup time）表示准备时间/清洗时间
$s t v, g$	机器从颜色 $v$ 到 $g$ 之间的清洗时间/h
$η$	总批数
$B k, b$	机器 $M k$ 上的批 $b$
$b p k, b$	$B k, b$ 的加工时间/h
$X g . k, b$	如果 $B k, b$ 中工件属于颜色 $g$ 则为1，否则为0
$Y v, g$	如果从颜色 $v$ 切换到颜色 $g$ 则为1，否则为0

Tab. 2 Information related to eight jobs and five color families

$v$	$A v$	$w t ¯ v$	$p ¯ v 1$	$p ¯ v 2$	$p ¯ v 3$	$d ¯ v -$	$d ¯ v +$	$w ¯ v e$	$w ¯ v t$
1	${J 1, J 2}$	31	20	25	23	72	84	3	3
2	${J 3}$	36	11	26	28	48	84	2	3
3	${J 4, J 5}$	34	14	21	23	64	118	4	3
4	${J 6}$	58	12	23	23	48	64	4	4
5	${J 7, J 8}$	31	15	25	29	36	60	1	3

Tab. 2 Information related to eight jobs and five color families

$v$	$A v$	$w t ¯ v$	$p ¯ v 1$	$p ¯ v 2$	$p ¯ v 3$	$d ¯ v -$	$d ¯ v +$	$w ¯ v e$	$w ¯ v t$
1	${J 1, J 2}$	31	20	25	23	72	84	3	3
2	${J 3}$	36	11	26	28	48	84	2	3
3	${J 4, J 5}$	34	14	21	23	64	118	4	3
4	${J 6}$	58	12	23	23	48	64	4	4
5	${J 7, J 8}$	31	15	25	29	36	60	1	3

Fig.1 Scheduling scheme of an instance

Fig.2 Encoding scheme

Tab. 3 Data related to n，G and Av

$n$	$G$	$A v$
$n$	$G$	$v = 1$	$v = 2$	$v = 3$	$v = 4$	$v = 5$	$v = 6$	$v = 7$	$v = 8$	$v = 9$	$v = 10$	$v = 11$	$v = 12$
$5 μ$	3	$2 μ$	$1 μ$	$2 μ$
$8 μ$	5	$2 μ$	$1 μ$	$2 μ$	$1 μ$	$2 μ$
$11 μ$	6	$2 μ$	$1 μ$	$2 μ$	$2 μ$	$2 μ$	$2 μ$
$13 μ$	8	$1 μ$	$2 μ$	$1 μ$	$3 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$
$17 μ$	10	$2 μ$	$1 μ$	$2 μ$	$3 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$
$19 μ$	12	$2 μ$	$1 μ$	$1 μ$	$2 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$	$3 μ$	$1 μ$	$2 μ$	$1 μ$

Tab. 3 Data related to n，G and Av

$n$	$G$	$A v$
$n$	$G$	$v = 1$	$v = 2$	$v = 3$	$v = 4$	$v = 5$	$v = 6$	$v = 7$	$v = 8$	$v = 9$	$v = 10$	$v = 11$	$v = 12$
$5 μ$	3	$2 μ$	$1 μ$	$2 μ$
$8 μ$	5	$2 μ$	$1 μ$	$2 μ$	$1 μ$	$2 μ$
$11 μ$	6	$2 μ$	$1 μ$	$2 μ$	$2 μ$	$2 μ$	$2 μ$
$13 μ$	8	$1 μ$	$2 μ$	$1 μ$	$3 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$
$17 μ$	10	$2 μ$	$1 μ$	$2 μ$	$3 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$
$19 μ$	12	$2 μ$	$1 μ$	$1 μ$	$2 μ$	$2 μ$	$1 μ$	$2 μ$	$1 μ$	$3 μ$	$1 μ$	$2 μ$	$1 μ$

Tab. 4 Levels of parameters

水平	$N$	$η$	$δ$	$R$	$α$	$β$
1	80	10	40	30	0.4	0.45
2	100	20	50	40	0.5	0.55
3	120	30	60	50	0.6	0.65

Tab. 4 Levels of parameters

水平	$N$	$η$	$δ$	$R$	$α$	$β$
1	80	10	40	30	0.4	0.45
2	100	20	50	40	0.5	0.55
3	120	30	60	50	0.6	0.65

Fig.3 Main effect plots of mean value ρ and average signal-to-noise ratio of ρ

Tab. 5 Key parameters and their values of comparison algorithms

对比算法	参数及取值
ASFLA	种群规模100；子群数8；局部搜索迭代次数30；停滞阈值20
MOABC	种群规模120；雇佣蜂比例0.5；邻域搜索范围参数60
FGA	种群规模80；交叉概率0.8；变异概率0.2
NSGA-Ⅱ	种群规模100；交叉概率为 0.9；变异概率为 0.1

Tab. 6 Results of five algorithms on metric ??

$n × G × m$	$C (M T L B O, A S F L A)$	$C (A S F L A, M T L B O)$	$C (M T L B O, M O A B C)$	$C (M O A B C, M T L B O)$	$C (M T L B O, F G A)$	$C (F G A, M T L B O)$	$C (M T L B O, N S G A ‑ Ⅱ)$	$C (N S G A ‑ Ⅱ, M T L B O)$
平均值	0.805	0.098	0.541	0.197	0.722	0.156	0.837	0.074
5×3×2	1.000	1.000	1.000	0.444	1.000	0.926	1.000	0.370
8×5×2	0.545	0.222	0.769	0.444	0.750	0.389	0.625	0.222
10×3×6	0.611	0.373	0.588	0.039	0.571	0.529	0.286	0.098
11×6×3	0.438	0.188	0.231	0.625	0.750	0.188	0.600	0.250
13×8×3	0.071	0.450	0.300	0.600	1.000	0.000	0.333	0.450
16×5×5	0.692	0.250	0.154	0.438	0.762	0.313	0.600	0.063
17×10×4	0.600	0.000	0.545	0.000	0.409	0.118	0.000	0.353
19×12×4	1.000	0.000	0.958	0.000	0.125	0.429	1.000	0.000
20×3×6	0.957	0.036	0.625	0.036	0.278	0.464	1.000	0.000
22×6×5	1.000	0.000	0.000	1.000	0.667	0.000	1.000	0.000
26×8×5	1.000	0.000	0.000	0.111	1.000	0.000	1.000	0.000
32×5×8	1.000	0.000	0.833	0.000	1.000	0.000	1.000	0.000
34×10×6	0.333	0.000	1.000	0.000	1.000	0.000	1.000	0.000
38×12×6	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000
40×3×10	0.700	0.063	0.852	0.063	0.951	0.063	0.750	0.000
44×6×8	0.429	0.100	0.667	0.100	0.609	0.000	0.800	0.000
52×8×7	1.000	0.000	0.421	0.174	0.520	0.630	1.000	0.000
64×5×10	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000
68×10×8	0.167	0.250	0.100	0.417	0.720	0.333	0.111	0.417
76×12×6	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000
80×3×11	0.950	0.000	0.818	0.333	1.000	0.000	1.000	0.000
88×6×10	1.000	0.000	0.083	0.393	0.597	0.071	1.000	0.000
104×8×10	1.000	0.000	0.000	0.246	0.500	0.193	1.000	0.000
128×5×11	0.667	0.000	0.455	0.000	0.417	0.000	1.000	0.000
136×10×9	1.000	0.000	0.640	0.000	0.778	0.000	1.000	0.000
152×12×10	1.000	0.000	0.600	0.222	1.000	0.000	1.000	0.000
176×6×11	1.000	0.000	0.000	0.231	0.917	0.038	1.000	0.000
208×8×12	1.000	0.000	0.591	0.000	0.393	0.000	1.000	0.000
272×10×11	1.000	0.000	0.591	0.000	0.520	0.000	1.000	0.000
304×12×10	1.000	0.000	0.407	0.000	0.435	0.000	1.000	0.000

Tab. 6 Results of five algorithms on metric ??

$n × G × m$	$C (M T L B O, A S F L A)$	$C (A S F L A, M T L B O)$	$C (M T L B O, M O A B C)$	$C (M O A B C, M T L B O)$	$C (M T L B O, F G A)$	$C (F G A, M T L B O)$	$C (M T L B O, N S G A ‑ Ⅱ)$	$C (N S G A ‑ Ⅱ, M T L B O)$
平均值	0.805	0.098	0.541	0.197	0.722	0.156	0.837	0.074
5×3×2	1.000	1.000	1.000	0.444	1.000	0.926	1.000	0.370
8×5×2	0.545	0.222	0.769	0.444	0.750	0.389	0.625	0.222
10×3×6	0.611	0.373	0.588	0.039	0.571	0.529	0.286	0.098
11×6×3	0.438	0.188	0.231	0.625	0.750	0.188	0.600	0.250
13×8×3	0.071	0.450	0.300	0.600	1.000	0.000	0.333	0.450
16×5×5	0.692	0.250	0.154	0.438	0.762	0.313	0.600	0.063
17×10×4	0.600	0.000	0.545	0.000	0.409	0.118	0.000	0.353
19×12×4	1.000	0.000	0.958	0.000	0.125	0.429	1.000	0.000
20×3×6	0.957	0.036	0.625	0.036	0.278	0.464	1.000	0.000
22×6×5	1.000	0.000	0.000	1.000	0.667	0.000	1.000	0.000
26×8×5	1.000	0.000	0.000	0.111	1.000	0.000	1.000	0.000
32×5×8	1.000	0.000	0.833	0.000	1.000	0.000	1.000	0.000
34×10×6	0.333	0.000	1.000	0.000	1.000	0.000	1.000	0.000
38×12×6	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000
40×3×10	0.700	0.063	0.852	0.063	0.951	0.063	0.750	0.000
44×6×8	0.429	0.100	0.667	0.100	0.609	0.000	0.800	0.000
52×8×7	1.000	0.000	0.421	0.174	0.520	0.630	1.000	0.000
64×5×10	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000
68×10×8	0.167	0.250	0.100	0.417	0.720	0.333	0.111	0.417
76×12×6	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000
80×3×11	0.950	0.000	0.818	0.333	1.000	0.000	1.000	0.000
88×6×10	1.000	0.000	0.083	0.393	0.597	0.071	1.000	0.000
104×8×10	1.000	0.000	0.000	0.246	0.500	0.193	1.000	0.000
128×5×11	0.667	0.000	0.455	0.000	0.417	0.000	1.000	0.000
136×10×9	1.000	0.000	0.640	0.000	0.778	0.000	1.000	0.000
152×12×10	1.000	0.000	0.600	0.222	1.000	0.000	1.000	0.000
176×6×11	1.000	0.000	0.000	0.231	0.917	0.038	1.000	0.000
208×8×12	1.000	0.000	0.591	0.000	0.393	0.000	1.000	0.000
272×10×11	1.000	0.000	0.591	0.000	0.520	0.000	1.000	0.000
304×12×10	1.000	0.000	0.407	0.000	0.435	0.000	1.000	0.000

Tab. 7 Results of five algorithms on metrics ρ and DIR

$n × G × m$	ρ					$D I R$
$n × G × m$	MTLBO	ASFLA	NSGA-Ⅱ	MOABC	FGA	MTLBO	ASFLA	NSGA-Ⅱ	MOABC	FGA
平均值	0.920	0.065	0.017	0.024	0.004	0.228	28.711	42.647	73.625	122.888
5×3×2	1.000	0.333	0.148	0.222	0.000	0.000	0.877	7.209	3.025	11.478
8×5×2	0.762	0.381	0.048	0.000	0.000	0.321	0.699	1.394	1.315	3.390
10×3×6	1.000	0.000	0.000	0.000	0.000	0.000	18.829	26.343	14.047	100.650
11×6×3	0.833	0.056	0.000	0.000	0.111	0.501	12.210	25.823	12.291	6.517
13×8×3	0.867	0.067	0.067	0.000	0.000	0.420	18.883	34.255	83.625	97.094
16×5×5	0.700	0.300	0.000	0.000	0.000	0.208	12.745	24.951	64.298	86.961
17×10×4	0.850	0.150	0.000	0.000	0.000	1.184	7.370	42.685	37.716	140.560
19×12×4	0.955	0.045	0.000	0.000	0.000	0.596	32.391	77.880	20.309	244.990
20×3×6	0.900	0.067	0.000	0.033	0.000	0.455	4.557	12.465	15.471	40.223
22×6×5	1.000	0.000	0.000	0.000	0.000	0.000	43.412	49.776	149.500	184.200
26×8×5	1.000	0.000	0.000	0.000	0.000	0.000	5.180	29.634	54.118	157.660
32×5×8	1.000	0.000	0.000	0.000	0.000	0.000	13.325	61.077	258.770	378.680
34×10×6	0.826	0.130	0.043	0.000	0.000	0.149	1.855	3.147	15.351	29.329
38×12×6	1.000	0.000	0.000	0.000	0.000	0.000	144.670	81.741	418.520	450.610
40×3×10	1.000	0.000	0.000	0.000	0.000	0.000	11.159	23.435	11.754	30.407
44×6×8	0.714	0.214	0.071	0.000	0.000	1.325	25.039	27.729	56.608	78.543
52×8×7	1.000	0.000	0.000	0.000	0.000	0.000	40.971	44.476	70.042	87.787
64×5×10	0.957	0.043	0.000	0.000	0.000	0.096	14.426	21.443	47.243	133.560
68×10×8	0.750	0.167	0.083	0.000	0.000	0.118	2.928	3.303	9.929	13.699
76×12×6	1.000	0.000	0.000	0.000	0.000	0.000	169.680	325.430	529.310	847.300
80×3×11	1.000	0.000	0.000	0.000	0.000	0.000	20.358	45.022	23.297	105.100
88×6×10	0.963	0.000	0.037	0.000	0.000	0.071	28.571	13.395	47.287	61.675
104×8×10	1.000	0.000	0.000	0.000	0.000	0.000	13.048	28.414	29.930	35.363
128×5×11	1.000	0.000	0.000	0.000	0.000	0.000	14.159	18.014	23.790	27.098
136×10×9	0.526	0.000	0.000	0.474	0.000	1.405	17.979	26.513	1.026	42.296
152×12×10	1.000	0.000	0.000	0.000	0.000	0.000	66.410	85.830	63.930	131.700
176×6×11	1.000	0.000	0.000	0.000	0.000	0.000	9.976	12.211	11.201	12.483
208×8×12	1.000	0.000	0.000	0.000	0.000	0.000	35.530	39.478	45.208	50.623
272×10×11	1.000	0.000	0.000	0.000	0.000	0.000	29.788	36.446	36.709	43.936
304×12×10	1.000	0.000	0.000	0.000	0.000	0.000	44.302	49.885	53.124	52.728

Tab. 7 Results of five algorithms on metrics ρ and DIR

$n × G × m$	ρ					$D I R$
$n × G × m$	MTLBO	ASFLA	NSGA-Ⅱ	MOABC	FGA	MTLBO	ASFLA	NSGA-Ⅱ	MOABC	FGA
平均值	0.920	0.065	0.017	0.024	0.004	0.228	28.711	42.647	73.625	122.888
5×3×2	1.000	0.333	0.148	0.222	0.000	0.000	0.877	7.209	3.025	11.478
8×5×2	0.762	0.381	0.048	0.000	0.000	0.321	0.699	1.394	1.315	3.390
10×3×6	1.000	0.000	0.000	0.000	0.000	0.000	18.829	26.343	14.047	100.650
11×6×3	0.833	0.056	0.000	0.000	0.111	0.501	12.210	25.823	12.291	6.517
13×8×3	0.867	0.067	0.067	0.000	0.000	0.420	18.883	34.255	83.625	97.094
16×5×5	0.700	0.300	0.000	0.000	0.000	0.208	12.745	24.951	64.298	86.961
17×10×4	0.850	0.150	0.000	0.000	0.000	1.184	7.370	42.685	37.716	140.560
19×12×4	0.955	0.045	0.000	0.000	0.000	0.596	32.391	77.880	20.309	244.990
20×3×6	0.900	0.067	0.000	0.033	0.000	0.455	4.557	12.465	15.471	40.223
22×6×5	1.000	0.000	0.000	0.000	0.000	0.000	43.412	49.776	149.500	184.200
26×8×5	1.000	0.000	0.000	0.000	0.000	0.000	5.180	29.634	54.118	157.660
32×5×8	1.000	0.000	0.000	0.000	0.000	0.000	13.325	61.077	258.770	378.680
34×10×6	0.826	0.130	0.043	0.000	0.000	0.149	1.855	3.147	15.351	29.329
38×12×6	1.000	0.000	0.000	0.000	0.000	0.000	144.670	81.741	418.520	450.610
40×3×10	1.000	0.000	0.000	0.000	0.000	0.000	11.159	23.435	11.754	30.407
44×6×8	0.714	0.214	0.071	0.000	0.000	1.325	25.039	27.729	56.608	78.543
52×8×7	1.000	0.000	0.000	0.000	0.000	0.000	40.971	44.476	70.042	87.787
64×5×10	0.957	0.043	0.000	0.000	0.000	0.096	14.426	21.443	47.243	133.560
68×10×8	0.750	0.167	0.083	0.000	0.000	0.118	2.928	3.303	9.929	13.699
76×12×6	1.000	0.000	0.000	0.000	0.000	0.000	169.680	325.430	529.310	847.300
80×3×11	1.000	0.000	0.000	0.000	0.000	0.000	20.358	45.022	23.297	105.100
88×6×10	0.963	0.000	0.037	0.000	0.000	0.071	28.571	13.395	47.287	61.675
104×8×10	1.000	0.000	0.000	0.000	0.000	0.000	13.048	28.414	29.930	35.363
128×5×11	1.000	0.000	0.000	0.000	0.000	0.000	14.159	18.014	23.790	27.098
136×10×9	0.526	0.000	0.000	0.474	0.000	1.405	17.979	26.513	1.026	42.296
152×12×10	1.000	0.000	0.000	0.000	0.000	0.000	66.410	85.830	63.930	131.700
176×6×11	1.000	0.000	0.000	0.000	0.000	0.000	9.976	12.211	11.201	12.483
208×8×12	1.000	0.000	0.000	0.000	0.000	0.000	35.530	39.478	45.208	50.623
272×10×11	1.000	0.000	0.000	0.000	0.000	0.000	29.788	36.446	36.709	43.936
304×12×10	1.000	0.000	0.000	0.000	0.000	0.000	44.302	49.885	53.124	52.728

Fig.4 Convergence curves of five algorithms

Tab. 8 Wilcoxon signed rank test results of five algorithms on metrics ??， ρ and DIR

MTLBO的对比算法	不同指标的p值
MTLBO的对比算法	$C$	$ρ$	$D I R$
ASFLA	0.000	0.001	0.000
NSGA-Ⅱ	0.000	0.000	0.000
MOABC	0.000	0.000	0.003
FGA	0.000	0.000	0.000

Tab. 8 Wilcoxon signed rank test results of five algorithms on metrics ??， ρ and DIR

MTLBO的对比算法	不同指标的p值
MTLBO的对比算法	$C$	$ρ$	$D I R$
ASFLA	0.000	0.001	0.000
NSGA-Ⅱ	0.000	0.000	0.000
MOABC	0.000	0.000	0.003
FGA	0.000	0.000	0.000

Tab. 9 Performance data for five hundred iterations on six instances with different scales

实例	算法	$D I R$	平均运行时间/s	实例	算法	$D I R$	平均运行时间/s
5×3×2	MTLBO	0.912	3.2	136×10×9	MTLBO	18.532	87.6
	ASFLA	3.215	2.8		ASFLA	27.041	81.2
	MOABC	11.893	4.1		MOABC	85.217	98.5
	FGA	16.027	5.3		FGA	98.362	105.4
	NSGA-Ⅱ	19.206	2.5		NSGA-Ⅱ	1.153	50.5
32×5×8	MTLBO	13.521	21.7	208×8×12	MTLBO	36.015	152.3
	ASFLA	62.103	19.5		ASFLA	40.217	148.9
	MOABC	259.872	28.9		MOABC	410.258	169.2
	FGA	380.156	35.2		FGA	510.364	127.6
	NSGA-Ⅱ	260.154	13.3		NSGA-Ⅱ	46.012	160.7
64×5×10	MTLBO	14.862	43.2	304×12×10	MTLBO	45.021	266.7
	ASFLA	22.015	39.8		ASFLA	50.526	219.8
	MOABC	65.321	51.7		MOABC	530.621	241.5
	FGA	135.624	60.3		FGA	620.478	258.9
	NSGA-Ⅱ	48.012	35.6		NSGA-Ⅱ	54.218	181.5

Tab. 9 Performance data for five hundred iterations on six instances with different scales

实例	算法	$D I R$	平均运行时间/s	实例	算法	$D I R$	平均运行时间/s
5×3×2	MTLBO	0.912	3.2	136×10×9	MTLBO	18.532	87.6
	ASFLA	3.215	2.8		ASFLA	27.041	81.2
	MOABC	11.893	4.1		MOABC	85.217	98.5
	FGA	16.027	5.3		FGA	98.362	105.4
	NSGA-Ⅱ	19.206	2.5		NSGA-Ⅱ	1.153	50.5
32×5×8	MTLBO	13.521	21.7	208×8×12	MTLBO	36.015	152.3
	ASFLA	62.103	19.5		ASFLA	40.217	148.9
	MOABC	259.872	28.9		MOABC	410.258	169.2
	FGA	380.156	35.2		FGA	510.364	127.6
	NSGA-Ⅱ	260.154	13.3		NSGA-Ⅱ	46.012	160.7
64×5×10	MTLBO	14.862	43.2	304×12×10	MTLBO	45.021	266.7
	ASFLA	22.015	39.8		ASFLA	50.526	219.8
	MOABC	65.321	51.7		MOABC	530.621	241.5
	FGA	135.624	60.3		FGA	620.478	258.9
	NSGA-Ⅱ	48.012	35.6		NSGA-Ⅱ	54.218	181.5

References 28

[1]	FENG L， CHEN G， ZHOU S， et al. An energy-efficient unrelated parallel machine scheduling problem with batch processing and time-of-use electricity prices［J］. Mathematics， 2024， 12（3）： No.376.
[2]	LEI D， HEEN L. A cooperated imperialist competitive algorithm for unrelated parallel batch machine scheduling problem ［J］. Computers， Materials and Continua， 2024， 79（2）： 1855-1874.
[3]	ZHENG S， XIE N， WU Q， et al. Novel mathematical formulations for parallel-batching processing machine scheduling problems［J］. Computers and Operations Research， 2025， 173： No.106859.
[4]	ZHOU S， JIA Z， JIN M， et al. Minimizing makespan on parallel batch processing machines with two-dimensional rectangular jobs［J］. Computers and Industrial Engineering， 2022， 169： No.108167.
[5]	ZHANG W， TANG H， WANG W， et al. A multi-objective hybrid algorithm for the casting scheduling problem with unrelated batch processing machine［J］. Complex System Modeling and Simulation， 2024， 4（3）： 236-257.
[6]	SÁENZ-ALANÍS C A， JOBISH V D， SALAZAR-AGULLAR M A， et al. A parallel machine batch scheduling problem in a brewing company［J］. The International Journal of Advanced Manufacturing Technology， 2016， 87（1/2/3/4）： 65-75.
[7]	GHALEB M， TAGHIPOUR S. Dynamic shop-floor scheduling using real-time information： a case study from the thermoplastic industry［J］. Computers and Operations Research， 2023， 152： No.106134.
[8]	HU K X， CHE Y X， NG T S， et al. Unrelated parallel batch processing machine scheduling with time requirements and two-dimensional packing constraints［J］. Computers and Operations Research， 2024， 162： No.106474.
[9]	FU L L， ALOULOU M A， TRIKI C. Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows［J］. International Journal of Production Research， 2017， 55（20）： 5942-5957.
[10]	ZHANG R， CHANG P C， SONG S， et al. A multi-objective artificial bee colony algorithm for parallel batch-processing machine scheduling in fabric dyeing processes［J］. Knowledge-Based Systems， 2017， 116： 114-129.
[11]	LI D， WANG J， QIANG R， et al. A hybrid differential evolution algorithm for parallel machine scheduling of lace dyeing considering colour families， sequence-dependent setup and machine eligibility［J］. International Journal of Production Research， 2021， 59（9）： 2722-2738.
[12]	HUYNH N T， CHIEN C F. A hybrid multi-subpopulation genetic algorithm for textile batch dyeing scheduling and an empirical study［J］. Computers and Industrial Engineering， 2018， 125： 615-627.
[13]	LI K， ZHANG H， CHU C， et al. A bi-objective evolutionary algorithm for minimizing maximum lateness and total pollution cost on non-identical parallel batch processing machines［J］. Computers and Industrial Engineering， 2022， 172（Pt A）： No.108608.
[14]	DED K， PRATAP A， AGARWAL S， et al. A fast and elitist multiobjective genetic algorithm： NSGA-Ⅱ［J］. IEEE Transactions on Evolutionary Computation， 2002， 6（2）： 182-197.
[15]	DEMİR Y. An efficient lexicographic approach to solve multi-objective multi-port fabric dyeing machine planning problem［J］. Applied Soft Computing， 2023， 144： No.110541.
[16]	SRINATH N， YILMARLAR I O， KURZ M E， et al. Hybrid multi-objective evolutionary meta-heuristics for a parallel machine scheduling problem with setup times and preferences［J］. Computers and Industrial Engineering， 2023， 185： No.109675.
[17]	LEI D， DAI T. An adaptive shuffled frog-leaping algorithm for parallel batch processing machines scheduling with machine eligibility in fabric dyeing process［J］. International Journal of Production Research， 2024， 62（21）： 7704-7721.
[18]	WANG J， LI D， TANG H， et al. A dynamical teaching-learning-based optimization algorithm for fuzzy energy-efficient parallel batch processing machines scheduling in fabric dyeing process［J］. Applied Soft Computing， 2024， 167（Pt C）： No.112413.
[19]	ZHANG R， CHANG P C， SONG S， et al. Local search enhanced multi-objective PSO algorithm for scheduling textile production processes with environmental considerations［J］. Applied Soft Computing， 2017， 61： 447-467.
[20]	WANG X， ZHU S， CHEN Q. Unrelated parallel machine scheduling with random rework and limited preemption［J］. Computers and Operations Research， 2025， 177： No.106968.
[21]	WANG F， SU Y， JU F， et al. Fast schedule recovery method for semiconductor packaging lines with machine failures and constrained time windows［J］. IEEE Transactions on Automation Science and Engineering， 2025， 22： 18076-18087.
[22]	陈海洋，柴冰，王瑞兰，等. 基于时间窗的SVDBN 近似推理算法研究［J］. 系统仿真学报， 2020， 32（2）： 217-228.
	CHEN H Y， CHAI B， WANG R L， et al. Research on approximate reference algorithm of SVDBN based on sliding window［J］. Journal of System Simulation， 2020， 32（2）： 217-228.
[23]	LEI D， SU B， LI M. Cooperated teaching-learning-based optimisation for distributed two-stage assembly flow shop scheduling［J］. International Journal of Production Research， 2021， 59（23）： 7232-7245.
[24]	ZHENG J， WANG L， WANG J J. A cooperative coevolution algorithm for multi-objective fuzzy distributed hybrid flow shop［J］. Knowledge-based Systems， 2022， 194： No.105536.
[25]	LI K， XU L， ZHANG H， et al. A genetic algorithm for fuzzy identical parallel machine scheduling of minimising total weighted tardiness under resource constrain［J］. International Journal of Production Research， 2024， 62（21）： 7619-7643.
[26]	LEI D. Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems［J］. The International Journal of Advanced Manufacturing Technology， 2008， 37（1/2）： 157-165.
[27]	PAN Q K， WANG L， QIAN B. A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems［J］. Computers and Operations Research， 2009， 36（8）： 2498-2511.
[28]	ZITZLER E， THIELE L. Multiobjective evolutionary algorithms： a comparative case study and the strength Pareto approach［J］. IEEE Transactions on Evolutionary Computation， 1999， 3（4）： 257-271.

Multi-level teaching-learning-based optimization algorithm for green batch processing scheduling problem

求解绿色批加工调度问题的多层教学优化算法

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 13

References 28

Related Articles 14

Recommended Articles

Metrics

[1]	Shanglong LI, Jianhua LIU, Heming JIA. Reptile search algorithm based on multi-hunting coordination strategy [J]. Journal of Computer Applications, 2024, 44(9): 2818-2828.
[2]	Hao GAO, Qingke ZHANG, Xianglong BU, Junqing LI, Huaxiang ZHANG. Teaching-learning-based optimization algorithm based on cooperative mutation and Lévy flight strategy and its application [J]. Journal of Computer Applications, 2023, 43(5): 1355-1364.
[3]	ZHANG Jie, CHANG Tianqing, DAI Wenjun, GUO Libin, ZHANG Lei. Object tracking algorithm based on correlation filtering and color probability model [J]. Journal of Computer Applications, 2020, 40(6): 1774-1782.
[4]	TONG Nan, FU Qiang, ZHONG Caiming. Improved teaching-learning-based optimization algorithm based on self-learning mechanism [J]. Journal of Computer Applications, 2018, 38(2): 443-447.
[5]	YANG Tianpeng, CHEN Lifei. Probability model-based algorithm for non-uniform data clustering [J]. Journal of Computer Applications, 2018, 38(10): 2844-2849.
[6]	HUANG Hainan, LI Xiaofeng, LIAN Peikun, RONG Jian. Trigger probability model of transit signal priority strategies based on signal timing [J]. Journal of Computer Applications, 2018, 38(10): 3025-3029.
[7]	ZHU Jie, CHEN Lifei. Bayesian clustering algorithm for categorical data [J]. Journal of Computer Applications, 2017, 37(4): 1026-1031.
[8]	YANG Peng, ZHAO Hui, BAO Zhonggui. Research on properties of shared resource matrix method based on double cross linked list [J]. Journal of Computer Applications, 2016, 36(3): 653-656.
[9]	HUANG Xiangdong, XIA Shixiong, NIU Qiang, ZHAO Zhijun. Improved teaching-learning-based optimization algorithm based on K-means [J]. Journal of Computer Applications, 2015, 35(11): 3126-3129.
[10]	YANG Guan-ci LI Shao-bo ZHONG Yong. Probability analysis of capturing specific objects in stratified sampling model [J]. Journal of Computer Applications, 2012, 32(08): 2209-2211.
[11]	HAN Xu YANG Yu-wang WANG Lei. Performance of network coding protocol based epidemic routing [J]. Journal of Computer Applications, 2012, 32(03): 791-794.
[12]	Li Xiao-Guang Peng Wang Wei Zhang Daling Wang. Study on Chinese-English corpus construction toward multiple-domain resources [J]. Journal of Computer Applications, 2008, 28(1): 146-148.
[13]	LI Jian-zhong,SHI Sheng-fei,WANG Chao-kun. Sampling and scheduling algorithm for wireless sensor networks based on sample data probability model [J]. Journal of Computer Applications, 2005, 25(09): 1982-1985.
[14]	LIU Ping, CHEN Bin, FU Zhong-liang. Modeling perspective image and its optimized segmentation [J]. Journal of Computer Applications, 2005, 25(05): 1084-1086.