A Novel Fast Optimisation Algorithm Using Differential Evolution Algorithm Optimisation and Meta-Modelling Approach

  • Yang LiuEmail author
  • Alan Kwan
  • Yacine Rezgui
  • Haijiang Li
Part of the Studies in Computational Intelligence book series (SCI, volume 637)


Genetic algorithms (GAs), Particle Swarm Optimisation (PSO) and Differential Evolution (DE) have proven to be successful in engineering model calibration problems. In real-world model calibration problems, each model evaluation usually requires a large amount of computation time. The optimisation process usually needs to run the numerical model and evaluate the objective function thousands of times before converging to global optima. In this study, a computational framework, known as DE-RF, is presented for solving computationally expensive calibration problems. We have proposed a dynamic meta-modelling approach, in which Random Forest (RF) regression model was embedded into a differential evolution optimisation framework to replace time consuming functions or models. We describe the performance of DE and DE-RF when applied to a hard optimisation function and a rainfall-runoff model calibration problem. The simulation results suggest that the proposed optimisation framework is able to achieve good solutions as well as provide considerable savings of the function calls with a very small number of actual evaluations, compared to these traditional optimisation algorithms.


Differential evolution optimisation Meta-modelling Random forest regression Automatic model calibration 



The research reported in this paper was conducted as part of the “Developing a Real Time Abstraction & Discharge Permitting Process for Catchment Regulation and Optimised Water Management” project funded by EPSRC (Engineering Physical Sciences Research Council) and TSB (Technology Strategy Board) in the UK as part of the Water Security managed programme (TSB/EPSRC grant reference number: TS/K002805/1). This financial support is gratefully acknowledged.


  1. 1.
    Holland, H.J.: Adaptation in Natural and Artificial Systems, An Introductory Analysis with Application to Biology, Control and Artificial Intelligence. The University of Michigan Press, Ann Arbor (1975)Google Scholar
  2. 2.
    Storn, R., Price K.: Differential evolution: a simple and efficient adaptive scheme for global optimisation over continuous spaces. Technical Report TR-95-012, International Computer Science Institute, Berkley (1995)Google Scholar
  3. 3.
    Kennedy, J., Eberhart, R.: Particle Swarm Optimisation. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1945 (1995)Google Scholar
  4. 4.
    Liu, Y.: Automatic calibration of a Rainfall-Runoff model using a fast and elitist multi-objective particle swarm algorithm. Expert Syst. Appl. 36(5), 9533–9538 (2009)CrossRefGoogle Scholar
  5. 5.
    Liu, Y., Khu, S.T., Savic, D.A.: A fast hybrid optimisation method of multi-objective genetic algorithm and k-nearest neighbour classifier for hydrological model calibration. Lect. Notes Comput. Sci. 3177, 546–551 (2004)CrossRefGoogle Scholar
  6. 6.
    Liu, Y., Pender, G.: Automatic calibration of a rapid flood spreading model using multi-objective optimisations. Soft Comput. 17, 713–724 (2013)CrossRefGoogle Scholar
  7. 7.
    Yapo, P.O., Gupta, H.V., Sorooshian, S.: Multi-objective global optimisation for hydrologic models. J. Hydrol. 204, 83–97 (1998)CrossRefGoogle Scholar
  8. 8.
    Madsen, H.: Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. J. Hydrol. 235, 276–288 (2000)CrossRefGoogle Scholar
  9. 9.
    Jin, Y.: Comprehensive survey of fitness approximation in evolutionary computation. Soft Comput. 9, 3–12 (2005)CrossRefGoogle Scholar
  10. 10.
    Yan, S., Minsker, B.S.: A dynamic meta-model approach to genetic algorithm solution of a risk-based groundwater remediation design model. In: American Society of Civil Engineers (ASCE) Environmental & Water Resources Institute (EWRI) World Water & Environmental Resources Congress 2003 & Related Symposia, Philadelphia, PA (2003)Google Scholar
  11. 11.
    Jin, Y., Olhofer, M., Sendhoff, B.: On evolutionary optimisation with approximate fitness functions. In: Proceedings of the Genetic and Evolutionary Computation Conference (2000)Google Scholar
  12. 12.
    Sun, C.L., Zeng, J.C., Pan, J.Y., Xue, S.D., Jin, Y.C.: A new fitness estimation strategy for particle swarm optimization. Inf. Sci. 221, 355–370 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Jin, Y.C.: Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol. Comput. 1(2), 61–70 (2011)CrossRefGoogle Scholar
  14. 14.
    Nguyen, A.T., Reiter, S., Rigo, P.: A review on simulation-based optimization methods applied to building performance analysis. Appl. Energy 113, 1043–1058 (2014)CrossRefGoogle Scholar
  15. 15.
    Forrester, A.I.J., Keane, A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45(1–3), 50–79 (2009)CrossRefGoogle Scholar
  16. 16.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press (1995)Google Scholar
  17. 17.
    Schölkopf, B., Smola, A., Williamson, R., Bartlett, P.: New support vector algorithms. Neural Comput. 12, 1207–1245 (2000)CrossRefGoogle Scholar
  18. 18.
    Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Carolin, S., Malley, J., Tutz, G.: Supplement to an introduction to recursive partitioning: rational, application, and characteristics of classification and regression trees, bagging, and random forests (2010). doi: 10.1037/a0016973.supp. Accessed 11 Nov 2010
  20. 20.
    Sudhanshu, M.: Some new test functions for global optimization and performance of repulsive particle swarm method. Accessed 1 Aug 2009

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yang Liu
    • 1
    Email author
  • Alan Kwan
    • 1
  • Yacine Rezgui
    • 1
  • Haijiang Li
    • 1
  1. 1.School of EngineeringCardiff UniversityCardiffUK

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