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Mathematics 2019, 7(4), 318; https://doi.org/10.3390/math7040318

Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling

1, 2,3,4,*, 2,4 and 3,5
1
School of Software, Dalian University of Technology, Dalian 116620, China
2
DUT-RU Inter. School of Information Science & Engineering, Dalian University of Technology, Dalian 116620, China
3
Fuzzy Logic Systems Institute, 820-0067 Fukuoka, Japan
4
Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, Dalian University of Technology, Dalian 116620, China
5
Department of Management Engineering, Tokyo University of Science, 163-8001 Tokyo, Japan
*
Author to whom correspondence should be addressed.
Received: 30 January 2019 / Revised: 20 March 2019 / Accepted: 22 March 2019 / Published: 28 March 2019
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Abstract

Flexible job shop scheduling is an important issue in the integration of research area and real-world applications. The traditional flexible scheduling problem always assumes that the processing time of each operation is fixed value and given in advance. However, the stochastic factors in the real-world applications cannot be ignored, especially for the processing times. We proposed a hybrid cooperative co-evolution algorithm with a Markov random field (MRF)-based decomposition strategy (hCEA-MRF) for solving the stochastic flexible scheduling problem with the objective to minimize the expectation and variance of makespan. First, an improved cooperative co-evolution algorithm which is good at preserving of evolutionary information is adopted in hCEA-MRF. Second, a MRF-based decomposition strategy is designed for decomposing all decision variables based on the learned network structure and the parameters of MRF. Then, a self-adaptive parameter strategy is adopted to overcome the status where the parameters cannot be accurately estimated when facing the stochastic factors. Finally, numerical experiments demonstrate the effectiveness and efficiency of the proposed algorithm and show the superiority compared with the state-of-the-art from the literature. View Full-Text
Keywords: MRF-based decomposition strategy; stochastic scheduling; flexible job shop scheduling; cooperative co-evolution algorithm MRF-based decomposition strategy; stochastic scheduling; flexible job shop scheduling; cooperative co-evolution algorithm
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Sun, L.; Lin, L.; Li, H.; Gen, M. Cooperative Co-Evolution Algorithm with an MRF-Based Decomposition Strategy for Stochastic Flexible Job Shop Scheduling. Mathematics 2019, 7, 318.

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