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Robustness measures and robust scheduling for multi-objective stochastic flexible job shop scheduling problems

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Abstract

Flexible job shop scheduling in uncertain environments plays an important part in real-world manufacturing systems. With the aim of capturing the uncertain and multi-objective nature of flexible job shop scheduling, a mathematical model for the multi-objective stochastic flexible job shop scheduling problem (MOSFJSSP) is constructed, where three objectives of make-span, maximal machine workload, and robustness to uncertainties are considered simultaneously under a variety of practical constraints. Two new scenario-based robustness measures are defined based on statistical tools. To solve MOSFJSSP appropriately, a modified multi-objective evolutionary algorithm based on decomposition (m-MOEA/D) is developed for robust scheduling. The novelty of our approach is that it adopts a new subproblem update method which exploits the global information, allows the elitists kept in an archive to participate in the child generation, employs a subproblem selection and suspension strategy to focus more computational efforts on promising subproblems, and incorporates problem-specific genetic operators for variation. Extensive experimental results on 18 problem instances, including 8 total flexible and 10 partial flexible instances, show that the two new robustness measures are more effective than the existing scenario-based measures, in improving the schedule robustness to uncertainties and maintaining a small variance of disrupted objective values. Compared to the state-of-the-art multi-objective optimization evolutionary algorithms (MOEAs), our proposed m-MOEA/D-based robust scheduling approach achieves a much better convergence performance. Different trade-offs among the three objectives are also analyzed.

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Notes

  1. \(|{*}|\) denotes the size of the set \({*}\), and \(\lceil \cdot \rceil \) means the minimum integer value equal to or bigger than \(\cdot \).

  2. In our m-MOEA/D, when calculating the \(g^{te}\)function defined in (13), the normalized function value \(fno_j \) is used instead of \(f_j \).

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61502239 and 61503191, Natural Science Foundation of Jiangsu Province of China under Grant Nos. BK20150924 and BK20150933, and Qing Lan Project of Jiangsu Province of China.

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Authors and Affiliations

  1. B-DAT, CICAEET, School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xiao-Ning Shen, Ying Han & Jing-Zhi Fu

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  1. Xiao-Ning Shen
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  2. Ying Han
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  3. Jing-Zhi Fu
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Correspondence to Xiao-Ning Shen.

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Shen, XN., Han, Y. & Fu, JZ. Robustness measures and robust scheduling for multi-objective stochastic flexible job shop scheduling problems. Soft Comput 21, 6531–6554 (2017). https://doi.org/10.1007/s00500-016-2245-4

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  • DOI: https://doi.org/10.1007/s00500-016-2245-4

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