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An effective L-MONG algorithm for solving multi-objective flow-shop inverse scheduling problems

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Abstract

Generally, in handling traditional scheduling problems, ideal manufacturing system environments are assumed before determining effective scheduling. Unfortunately, “ideal environments” are not always possible. Real systems often encounter some uncertainties which will change the status of manufacturing systems. These may cause the original schedule to no longer to be optimal or even feasible. Traditional scheduling methods are not effective in coping with these cases. Therefore, a new scheduling strategy called “inverse scheduling” has been proposed to handle these problems. To the best of our knowledge, this research is the first to provide a comprehensive mathematical model for multi-objective permutation flow-shop inverse scheduling problem (PFISP). In this paper, first, a PFISP mathematical model is devised and an effective hybrid multi-objective evolutionary algorithm is proposed to handle uncertain processing parameters (uncertainties) and multiple objectives at the same time. In the proposed algorithm, we take an insert method NEH-based (Nawaz–Enscore–Ham) as a local improving procedure and propose several adaptations including efficient initialization, decimal system encoding, elitism and population diversity. Finally, 119 public problem instances with different scales and statistical performance comparisons are provided for the proposed algorithm. The results show that the proposed algorithm performs better than the traditional multi-objective evolution algorithm (MOEA) in terms of searching quality, diversity level and efficiency. This paper is the first to propose a mathematical model and develop a hybrid MOEA algorithm to solve PFISP in inverse scheduling domain.

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Acknowledgments

The authors would like to thank the editor and anonymous referees whose comments helped a lot in improving this paper. This research work was supported by the National Science Foundation of China (NSFC) under Grant Nos. 51375004 and 51121002; Independent Innovation Finance HUST support plan under Grant No. 2013TS021.

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Authors and Affiliations

  1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, Hubei, China

    Jianhui Mou, Xinyu Li, Liang Gao & Wenchao Yi

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  1. Jianhui Mou
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  2. Xinyu Li
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Corresponding author

Correspondence to Liang Gao.

Appendix

Appendix

See Tables 4, 5, 6 and 7.

Table 4 Comparison of \(I_\textit{IGD}\) between the L-MONG and NSGAII algorithms
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Table 5 Comparison of \(N_\textit{NDS}\) between the L-MONG and NSGAII algorithms
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Table 6 Comparison of \(R_\textit{NDS}\) between the L-MONG and NSGAII algorithms
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Table 7 Non-dominated solutions for benchmarks
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Mou, J., Li, X., Gao, L. et al. An effective L-MONG algorithm for solving multi-objective flow-shop inverse scheduling problems. J Intell Manuf 29, 789–807 (2018). https://doi.org/10.1007/s10845-015-1129-2

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