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(Non) convergence results for the differential evolution method

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Abstract

In this paper we deal with the convergence properties of the differential evolution (DE) algorithm, a rather popular stochastic method for solving global optimization problems. We are going to show there exist instances for which the basic version of DE has a positive probability not to converge (stagnation might occur), or converges to a single point which is not a local minimizer of the objective function, even when the objective function is convex. Next, some minimal corrections of the basic DE scheme are suggested in order to recover convergence with probability one to a local minimizer at least in the case of strictly convex functions.

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References

  1. Ali, M.: Differential evolution with preferential crossover. Eur. J. Oper. Res. 181, 1137–1147 (2007)

    Article  MATH  Google Scholar 

  2. Braak, C.T.: A Markov Chain Monte Carlo version of the genetic algorithm differential evolution: easy bayesian computing for real parameter spaces. Stat. Comput. 16, 239–249 (2006)

    Article  MathSciNet  Google Scholar 

  3. Chakraborty, U.K. (ed.): Advances in Differential Evolution. Springer, Berlin (2008)

    MATH  Google Scholar 

  4. Das, S., Suganthan, P.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15, 4–31 (2011)

    Article  Google Scholar 

  5. Kolda, T., Lewis, R., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385–482 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lampinen, J., Zelinka, I.: On stagnation of the differential evolution algorithm. In: Proceedings of the 6th international conference on soft computing MENDEL, pp. 76–83. Brno, Czech Republic (2000)

  7. Price, K., Storn, R., Lampinen, J.: Differential Evolution. A Practical Approach to Global Optimization. Springer, Berlin (2005)

    MATH  Google Scholar 

  8. Rudolph, G.: Convergence of evolutionary algorithms in general search space. In: Proceedings of the IEEE International Conference On Evolutionary Computation. Nagoya, Japan (1996)

  9. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Storn, R., Price, K.V.: Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces (TR-95-012). ICSI, USA (1995)

  11. Torczon, V.: On the convergence of pattern search algorithms. SIAM J. Optim. 7, 1–25 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Vasile, M., Minisci, E., Locatelli, M.: An inflationary differential evolution algorithm for space trajectory optimization. IEEE Trans. Evol. Comput. 15, 267–281 (2011)

    Article  Google Scholar 

  13. Zaharie, D.: Critical values for control parameters of differential evolution algorithm. In: Proceedings of 8th international conference on soft computing, mendel 2002, pp. 62–67 (2002)

  14. Zhigljavsky, A., Žilinskas, A.: Stochastic Global Optimization. Springer, Berlin (2008)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Parma, Via G.P. Usberti, 181/A, 43124 , Parma, Italy

    Marco Locatelli

  2. Department of Mechanical and Aerospace Engineering, University of Strathclyde, 75 Montrose Street, Glasgow, Scotland, G1 1XJ, UK

    Massimiliano Vasile

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  1. Marco Locatelli
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  2. Massimiliano Vasile
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Correspondence to Marco Locatelli.

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Locatelli, M., Vasile, M. (Non) convergence results for the differential evolution method. Optim Lett 9, 413–425 (2015). https://doi.org/10.1007/s11590-014-0816-9

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  • DOI: https://doi.org/10.1007/s11590-014-0816-9

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