Soft Computing

, Volume 21, Issue 21, pp 6531–6554 | Cite as

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

  • Xiao-Ning Shen
  • Ying Han
  • Jing-Zhi Fu
Methodologies and Application


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.


Metaheuristics Robust scheduling Multi-objective optimization evolutionary algorithms Robust measures 



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.

Compliance with ethical standards

Conflict of interest

Disclosure of potential conflicts of interest.

Humans and animal rights

Research involving human participants and/or animals.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.B-DAT, CICAEET, School of Information and ControlNanjing University of Information Science and TechnologyNanjingChina

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