Soft Computing

, Volume 23, Issue 24, pp 13067–13083 | Cite as

Kalman filter and multi-stage learning-based hybrid differential evolution algorithm with particle swarm for a two-stage flow shops scheduling problem

  • Bing-hai ZhouEmail author
  • Xiu-mei Liao
  • Ke Wang
Methodologies and Application


Inspired by the advantages of hybrid intelligent optimization methods, this paper at first proposes a hybrid differential evolution with particle swarm optimization (DEPS) to solve a two-stage hybrid flow shops scheduling problem. On the basis of analyzing the convergence and optimization scheme of DEPS, the Kalman filter algorithm and a multi-stage learning strategy are then creatively fused into DEPS, namely KLDEPS, to enhance the running performance of the algorithm. The introduction of the Kalman filter enriches the diversity of individuals and enhances the neighborhood search ability of the algorithm, and the combination with the multi-stage learning strategy has beneficial effect on jumping out of the local optimal scheme. To make the proposed KLDEPS more suitable for a real manufacturing environment, the constraints of queueing time between two stages, different job sizes and processing time are imposed on the scheduling problem. The performance of the proposed KLDEPS is evaluated by comparing with two other high-performing intelligent optimization algorithms. The computational results reveal that the proposed KLDEPS outperforms the other two algorithms both in solutions’ quality and convergence rate.


Hybrid flow shops scheduling Particle swarm Differential evolution Kalman filter Multi-stage learning 



The authors appreciate the supports to this research from the National Natural Science Foundation of China under Grant Nos. 61273035, 71471135.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringTongji UniversityShanghaiPeople’s Republic of China

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