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

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doi: 10.3934/jimo.2019088

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

Xuewen Huang ^1, , Xiaotong Zhang ^1, , Sardar M. N. Islam ^2,, and Carlos A. Vega-Mejía ^2,3,

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

Received November 2017 Revised March 2019 Published July 2019

Fund Project: 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.

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: IPPS, flexible job-shop scheduling, operation flexibility, processing flexibility, Genetic Algorithm.

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

Citation: Xuewen Huang, Xiaotong Zhang, Sardar M. N. Islam, Carlos A. Vega-Mejía. An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019088

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Figure 1. Alternative process plans networks

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.

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

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

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

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

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

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

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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American Institute of Mathematical Sciences

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

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