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Differential evolution algorithm with ensemble of populations for global numerical optimization

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Abstract

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving global optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE to handle a specific problem crucially depends on the proper choice of various parameters including the size of the population. Employing the trial and error scheme to search for the most suitable parameter settings requires high computational costs. In this paper, we propose a DE algorithm with an ensemble of parallel populations in which the number of function evaluations allocated to each population is self-adapted by learning from their previous experiences in generating superior solutions. Consequently, a more suitable population size takes most of the function evaluations adaptively to match different phases of the search process/evolution. Although the evolutionary algorithms have been investigated for about five decades, to our best of knowledge so far no effective population adaptation scheme has been proposed. The performance of the DE algorithm with an ensemble of parallel populations is extensively evaluated on a suite of 14 bound-constrained numerical optimization problems and compares favorably with the conventional DE with different single population sizes.

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References

  1. Storn, R., Price, K.V.: Differential evolution-A simple and efficient heuristic for global optimization over continuous Spaces. Journal of Global Optimization, 11, pp. 341–359 (1997)

    Article  Google Scholar 

  2. Rogalsky, T., Derksen, R.W., Kocabiyik, S.: Differential evolution in aerodynamic optimization. In Proc. of 46th Annual Conf. of Canadian Aeronautics and Space Institute, Montreal, Quebec, pp. 29–36 (May 1999)

  3. Joshi, R., Sanderson, A.C.: Minimal representation multisensor fusion using differential evolution. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29(1), 63–76 (1999)

    Article  Google Scholar 

  4. Storn, R.: On the usage of differential evolution for function optimization. In Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS 1996), Berkeley, pp. 519–523

  5. Ilonen, J., Kamarainen, J.-K., Lampinen, J., Differential evolution training algorithm for feed-forward neural networks. Neural Processing Letters, 7(1), 93–105 (2003)

    Article  Google Scholar 

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

    Google Scholar 

  7. Lampinen, J., Zelinka, I.: On stagnation of the differential evolution algorithm. in Ošmera P.(ed), Proc. of MENDEL 2000, 6th International Mendel Conference on Soft Computing, pp. 76–83 (2002)

  8. Gämperle, R., Müller, S.D., Koumoutsakos, P.: A parameter study for differential evolution. In Grmela, A., Mastorakis, N.E. editors, Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation, Interlaken, Switzerland, WSEAS Press, pp. 293–298 (2002)

    Google Scholar 

  9. Zaharie, D., Control of population diversity and adaptation in differential evolution algorithms. In Matousek, R., Osmera, P. (eds.) Proc. of Mendel 2003, 9th International Conference on Soft Computing, Brno, Czech Republic, pp. 41–46 (June 2003)

  10. Das, S., Konar, A., Chakraborty, U.K.: Two improved differential evolution schemes for faster global search. In ACM-SIGEVO Proceedings of Genetic and Evolutionary Computation Conference (GECCO-2005), Washington DC, USA, pp. 991–998

  11. Storn, R., Price, K., Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012,ICSI, http://http.icsi.berkeley.edu/~storn/litera.html (1995)

  12. Price, K. V., An introduction to differential evolution. In: Corne, D., Dorigo, M., and Glover, F. (eds.): New Ideas in Optimization. McGraw-Hill, London (UK) 79–108 (1999)

    Google Scholar 

  13. Rönkkönen, J., Kukkonen, S., Price, K.V.: Real-parameter optimization with differential evolution. In 2005 IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, Scotland, IEEE Press, pp. 506–513 (Sept. 2005)

    Chapter  Google Scholar 

  14. Qin, A.K., Suganthan, P.N., Self-adaptive differential evolution algorithm for numerical optimization. in IEEE Congress on Evolutionary Computation (CEC 2005) Edinburgh, Scotland, IEEE Press, pp. 1785–1791 (Sept. 2005)

    Chapter  Google Scholar 

  15. Hansen, N.: Compilation of results on the 2005 CEC benchmark function set,” May 4, 2006. http://www.ntu.edu.sg/home/epnsugan/index_files/CEC-05/compareresults.pdf

  16. Liang, J.J., Suganthan, P.N., Deb, K.: Novel composition test functions for numerical global optimization. In IEEE Swarm Intelligence Symposium 2005, Pasadena, California, pp. 68–75 (June 2005)

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  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    R. Mallipeddi & P. N. Suganthan

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  1. R. Mallipeddi
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  2. P. N. Suganthan
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Correspondence to R. Mallipeddi.

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Mallipeddi, R., Suganthan, P.N. Differential evolution algorithm with ensemble of populations for global numerical optimization. OPSEARCH 46, 184–213 (2009). https://doi.org/10.1007/s12597-009-0012-3

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