An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility

Xuewen Huang; Xiaotong Zhang; Sardar M. N. Islam; Carlos A. Vega-Mejía

doi:10.3934/jimo.2019088

Article Contents

2020, Volume 16, Issue 6: 2943-2969. Doi: 10.3934/jimo.2019088

This issue Previous Article Distributionally robust chance constrained problems under general moments information Next Article Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function

An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility

1.
Faculty of Management and Economics, Dalian University of Technology, Dalian, Liaoning 116023, China
2.
ISILC, Victoria University, Melbourne, Australia
3.
Operations & Supply Chain Management Research Group, Universidad de La Sabana, Bogotá, Colombia

^* Corresponding author: Sardar M. N. Islam
^* Corresponding author: Sardar M. N. Islam

Received: October 31, 2017

Revised: February 28, 2019

Early access: July 2019

Published: October 2020

Xuewen Huang is supported by the National Science and Technology Plan of China under Grant No. 2015BAF09B01 and the China Scholarship under Grant No. 201606060170

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Abstract

This paper considers the Flexible Job-shop Scheduling Problem with Operation and Processing flexibility (FJSP-OP) with the objective of minimizing the makespan. A Genetic Algorithm based approach is presented to solve the FJSP-OP. For the performance improvement, a new and concise Four-Tuple Scheme (FTS) is proposed for modeling a job with operation and processing flexibility. Then, with the FTS, an enhanced Genetic Algorithm employing a more efficient encoding strategy is developed. The use of this encoding strategy ensures that the classic genetic operators can be adopted to the utmost extent without generating infeasible offspring. Experiments have validated the proposed approach, and the results have shown the effectiveness and high performance of the proposed approach.

Keywords:

Mathematics Subject Classification: Primary: 90B35, 90C59; Secondary: 68M20.

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Figure 1. Alternative process plans networks

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Figure 2. An illustrative chromosome applying the hierarchical encoding approach

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Figure 3. Illustrative chromosomes applying the integrated encoding approach

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Figure 4. Algorithm GENERATE-PROCESS-PLAN

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Figure 5. A chromosome of the FJSP-OP

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Figure 6. Algorithm GENERATE-SCHEDULING

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Figure 7. Decoding a chromosome

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Figure 8. Crossover operations

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Figure 9. Mutation operations

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Figure 10. The Gantt chart of Experiment 1

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Figure 11. The Gantt chart of Experiment 3

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Figure 12. The Gantt chart of Experiment 4

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Figure 13. The Gantt chart of problem mk06 in Experiment 5

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Figure 14. The Gantt chart of Experiment 6(b)

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Figure 15. Performance curve of Experiment 4

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Figure A1. The data of Experiment 3

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Table 1. Comparison of results for Experiment 1

Solution approach	EA	Modified GA	PBHA	GA-OP
Makespan	16	14	14	14
Mean CPU time (ms)	N/A	N/A	N/A	191
¹ N/A means the result was not given by the author.

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Table 2. Parameters and comparison of results on Experiment 3

Solution approach	ALO	Modified GA	GA-OP
Parameters	N/A	$ PopSize=500 $	$ PopSize=50 $
Parameters	N/A	$ P_c=0.8,P_m=0.1,IterNo=100 $
Makespan	161	162	145
Mean CPU time (ms)	N/A	N/A	309

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Table 3. Parameters and comparison of results on Experiment 4

Solution approach	ALGA	GA-OP
Parameters	$ PopSize=400 $	$ PopSize=200 $
Parameters	$ P_c=0.8 $, $ P_m=0.1 $, $ IterNo=100 $
Makespan	188	181
Mean CPU time (ms)	N/A	2,907

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Table 4. Comparison of results for Experiment 5

Problem	$ n \times m $	TABC	HGTS	MA2	HA	PSO	VNSGA	GA-OP
mk01	10x6	40	40	40	40	41	40	40
mk02	10x6	26	26	26	26	26	26	26
mk03	15x8	204	204	204	204	207	204	204
mk04	15x8	60	60	60	60	65	60	60
mk05	15x4	173	172	172	172	171	173	172
mk06	10x15	60	57	59	57	61	58	57
mk07	20x5	139	139	139	139	173	144	139
mk08	20x10	523	523	523	523	523	523	523
mk09	20x10	307	307	307	307	307	307	307
mk10	20x15	202	198	202	197	312	198	198

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Table 5. The experimental results (computational time in terms of seconds) of experiment 5

Problem	n x m	TABC	HGTS	MA2	HA	PSO	VNSGA	GA-OP
mk01	10x6	3.36	5	20.16	0.06	N/A	N/A	0.27
mk02	10x6	3.72	15	28.21	0.59	N/A	N/A	3.75
mk03	15x8	1.56	2	53.76	0.16	N/A	N/A	0.12
mk04	15x8	66.58	10	30.53	0.49	N/A	N/A	3.41
mk05	15x4	78.45	18	36.36	4.57	N/A	N/A	6.23
mk06	10x15	173.98	63	80.61	53.82	N/A	N/A	65.14
mk07	20x5	66.19	33	37.74	20.01	N/A	N/A	25.4
mk08	20x10	2.15	3	77.71	0.02	N/A	N/A	0.2
mk09	20x10	304.43	24	75.23	0.86	N/A	N/A	4.1
mk10	20x15	418.19	104	90.75	33.21	N/A	N/A	73.12

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Table 6. Comparison of results on Experiment 6

Solution approach	Experiment 6(a)		Experiment 6(b)
Solution approach	ACO	GA-OP	Enhanced ACO	GA-OP
Makespan	589	522	484	482
Mean CPU time (ms)	128,700	12,056	120534	12063

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Table A1. Alternative machines of each operation performed for each job

Operation	Job
Operation	1	2	3	4	5	6
1	2, 4	2, 4	3, 5	3, 5	2, 4	2, 4
2	7, 8	7, 8	4, 6	4, 6	3, 5	3, 5
3	1, 2	1, 2	2, 3, 5	2, 3, 5	1, 2, 6	1, 2, 6
4	8, 6	8, 6	6, 7	6, 7	6, 8	6, 8
5	3, 5	3, 5	1, 8	1, 8	1, 7	1, 7
6	1, 2, 4	1, 2, 4	1, 4	1, 4	1, 3	1, 3
7	5, 6	5, 6	6, 7	6, 7	6, 7	6, 7
8	1, 7	1, 7	5, 8	5, 8	5, 8	5, 8
9	3, 8	3, 8	4, 2	4, 2	4, 3	4, 3

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Table A2. Processing times on the alternative machines of each operation

Operation	Job
Operation	1	2	3	4	5	6
1	18, 22	18, 22	12, 15	12, 15	18, 22	18, 22
2	39, 36	39, 36	24, 23	24, 23	12, 15	12, 15
3	11, 10	37, 39	30, 31, 29	30, 31, 29	50, 52, 54	50, 52, 54
4	31, 34	20, 21	21, 22	21, 22	19, 21	53, 51
5	21, 23	21, 23	32, 30	32, 30	32, 31	22, 24
6	10, 12, 15	10, 12, 15	22, 25	22, 25	22, 25	22, 25
7	32, 30	36, 38	24, 22	42, 44	24, 22	24, 22
8	45, 44	45, 44	20, 19	41, 43	20, 18	20, 18
9	26, 24	26, 24	27, 22	27, 22	27, 22	27, 22

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Table A3. Transportation times between the machines

Machine number	1	2	3	4	5	6	7	8
1	0	3	7	10	3	5	8	12
2	3	0	4	7	5	3	5	8
3	7	4	0	3	8	5	3	5
4	10	7	3	0	10	8	5	3
5	3	5	8	10	0	3	7	10
6	5	3	5	8	3	0	4	7
7	8	5	3	5	7	4	0	3
8	12	8	5	3	10	7	3	0

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