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On the adaptation of the mutation scale factor in differential evolution

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Abstract

Differential evolution (DE) is a simple yet effective metaheuristic specially suited for real-parameter optimization. The most advanced DE variants take into account the feedback obtained in the self-optimization process to modify their internal parameters and components dynamically. In recent years, some controversies have arisen regarding the adaptive schemes that incorporate feedback from the search process to guide the adaptation of the mutation scale factor. Some researchers have claimed that no significant benefits are obtained with these kinds of schemes. However, other studies have shown that they are highly effective. In this paper, we show that there is a relationship between the effectiveness of these adaptive schemes and the balance between exploration and exploitation induced by the trial vector generation strategy considered. State-of-the-art adaptive schemes are not useful for the trial vector generation strategies with the highest levels of exploration, which in fact seems to be the reason behind the controversies of recent years.

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References

  1. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. Trans. Evol. Comput. 10(6), 646–657 (2006)

    Google Scholar 

  2. Das, S., Suganthan, P.: Differential evolution: a survey of the state-of-the-art 15(1), 4–31 (2011)

  3. LaTorre, A., Muelas, S., Pea, J.M.: A mos-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test. Soft Comput. 15(11), 2187–2199 (2011)

    Article  Google Scholar 

  4. Lozano, M., Molina, D., Herrera, F.: Editorial scalability of evolutionary algorithms and other metaheuristics for large-scale continuous optimization problems. Soft Comput. 15(11):2085-2087 (2011)

    Google Scholar 

  5. Mallipeddi, R., Suganthan, P., Pan, Q., Tasgetiren, M.: Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl. Soft Comput. 11(2), 1679–1696 (2011)

    Article  Google Scholar 

  6. Mezura-Montes, E., Velázquez-Reyes, J., Coello Coello, C.A. : A comparative study of differential evolution variants for global optimization. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation (GECCO’06), pp. 485–492. ACM, New York (2006)

  7. Neri, F., Tirronen, V.: Recent advances in differential evolution: a survey and experimental analysis. Artif. Intell. Rev. 33(1–2), 61–106 (2010)

    Article  Google Scholar 

  8. Price, K.: Differential evolution. In: Zelinka, I., Snás̆el, V., Abraham, A. (eds) Handbook of Optimization, Intelligent Systems Reference Library, vol. 38, pp. 187–214. Springer, Berlin Heidelberg (2013)

  9. Price, K., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization. Government Printing Office, Natural Computing Series. USA (2005)

  10. Qin, A.K., Huang, V.L., Suganthan, P.: Differential evolution algorithm with strategy adaptation for global numerical optimization. Trans. Evol. Comput. 13(2), 398–417 (2009)

    Google Scholar 

  11. Soliman, O.S., Bui, L.T., Abbass, H.A.: The effect of a stochastic step length on the performance of the differential evolution algorithm. In: 2007 IEEE Congress on Evolutionary Computation (CEC’07), pp. 2850–2857 (2007)

  12. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tvrdík, J., Poláková, R., Veselský, J., Bujok, P.: Adaptive variants of differential evolution: Towards control-parameter-free optimizers. In: Zelinka, I., Snás̆el, V., Abraham, A. (eds) Handbook of Optimization, Intelligent Systems Reference Library, vol. 38, pp. 423–449. Springer, Berlin Heidelberg (2013)

  14. Wang, Y., Cai, Z., Zhang, Q.: Differential evolution with composite trial vector generation strategies and control parameters. Trans. Evol. Comput. 15(1), 55–66 (2011)

    Google Scholar 

  15. Zhang, J., Sanderson, A.: JADE: Adaptive differential evolution with optional external archive. Trans. Evol. Comput. 13(5), 945–958 (2009)

    Google Scholar 

  16. Zielinski, K., Wang, X., Laur, R.: Comparison of adaptive approaches for differential evolution. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds) Parallel Problem Solving from Nature (PPSN X). Lecture Notes in Computer Science, vol. 5199, pp. 641–650. Springer, Berlin Heidelberg (2008)

  17. Zielinski, K., Weitkemper, P., Laur, R., Kammeyer, K.D.: Parameter study for differential evolution using a power allocation problem including interference cancellation. In: IEEE Congress on Evolutionary Computation 2006 (CEC’06), pp. 1857–1864 (2006)

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Acknowledgments

The second author is also affiliated with the UMI LAFMIA 3175 CNRS at CINVESTAV-IPN. He also acknowledges the financial support from CONACyT project no. 103570. This work was also funded in part by the ec (FEDER) and the Spanish Ministry of Science and Innovation as part of the ‘Plan Nacional de i+d+i’, with contract number tin2011-25448. The work of Eduardo Segredo was funded by grant fpu-ap2009-0457.

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Authors and Affiliations

  1. Departamento de Computación, CINVESTAV-IPN, UMI LAFMIA 3175 CNRS, Av. IPN No. 2508, Col. San Pedro Zacatenco, 07300 , México, DF, México

    Carlos Segura

  2. Departamento de Computación (Evolutionary Computation Group), CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, 07300 , México, DF, México

    Carlos A. Coello Coello

  3. Dpto. Estadística, I.O. y Computación, Astrofísico Fco. Sánchez, Edif. Matemáticas, Universidad de La Laguna, 38271 , Santa Cruz de Tenerife, Spain

    Eduardo Segredo & Coromoto León

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  1. Carlos Segura
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  2. Carlos A. Coello Coello
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  3. Eduardo Segredo
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  4. Coromoto León
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Correspondence to Carlos Segura.

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Segura, C., Coello Coello, C.A., Segredo, E. et al. On the adaptation of the mutation scale factor in differential evolution. Optim Lett 9, 189–198 (2015). https://doi.org/10.1007/s11590-014-0723-0

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