Differential Evolution with Modified Mutation Strategy for Solving Global Optimization Problems

  • Pravesh Kumar
  • Millie Pant
  • V. P. Singh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7076)


In the present work we propose a modified variant of Differential Evolution (DE) algorithm named MDE. MDE differs from the basic DE in the manner in which the base vector is generated. While in simple/basic DE, base vector is usually randomly selected from the population of individuals, in MDE base vector is generated as convex linear combination (clc) of three randomly selected vectors out of which one is the one having best fitness value. This mutation scheme is used stochastically with mutation scheme in which the base generated using a clc of three randomly generated vectors. MDE is validated on a set of benchmark problems and is compared with basic DE and other DE variants. Numerical and statistical analysis shows the competence of proposed MDE.


differential evolution mutation strategy global optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Storn, R., Price, K.: Differential Evolution—A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Berkeley, CA, Tech. Rep. TR-95-012 (1995)Google Scholar
  2. 2.
    Storn, R., Price, K.: Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization 11(4), 341–359 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Alatas, B., Akin, E., Karci, A.: Modenar: Multi-Objective Differential Evolution Algorithm for Mining Numeric Association Rules. Applied Soft Computing 8(1), 646–656 (2008)CrossRefGoogle Scholar
  4. 4.
    Das, S., Abraham, A., Konar, A.: Automatic Clustering Using an Improved Differential Evolution Algorithm. IEEE Transaction on Systems Man and Cybernetics: Part A 38(1), 218–237 (2008)CrossRefGoogle Scholar
  5. 5.
    Price, K., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Berlin (2005)zbMATHGoogle Scholar
  6. 6.
    Vesterstrom, J., Thomsen, R.: A Comparative Study of Differential Evolution, Particle Swarm Optimization and Evolutionary Algorithms on Numerical Benchmark Problems. In: Congress on Evolutionary Computation, pp. 980–987 (2004)Google Scholar
  7. 7.
    Montes, E.M., Reyes, J.V.: A Comperative Study of Differential Evolution Variants for Global Optimization. In: GECCO, Seattle Washington USA, pp. 485–492 (2006)Google Scholar
  8. 8.
    Pant, M., Ali, M., Abraham, A.: Mixed Mutation Strategy Embedded Differential Evolution. In: IEEE Congress on Evolutionary Computation, pp. 1240–1246 (2009)Google Scholar
  9. 9.
    Noman, N., Iba, H.: Accelerating Differential Evolution Using an Adaptive Local Search. IEEE Transactions on Evolutionary Computation 12, 107–125 (2008)CrossRefGoogle Scholar
  10. 10.
    Fan, H.Y., Lampinen J., Dulikravich, G.S.: Improvements to Mutation Donor Formulation of Differential Evolution. In: International Congress on Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems Eurogen (2003)Google Scholar
  11. 11.
    Ali, M.M.: Differential Evolution with Preferential Crossover. European Journal of Operational Research 181, 1137–1147 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Fan, H., Lampinen, J.: A Trigonometric Mutation Operation to Differentia Evolution. Journal of Global Optimization 27, 105–112 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Brest, J., Greiner, S., Bošković, B., Mernik, M., Žumer, V.: Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems. IEEE Transactions on Evolutionary Computation 10(6), 646–657 (2006)CrossRefGoogle Scholar
  14. 14.
    Jia, L., Gong, W., Wu, H.: An Improved Self-adaptive Control Parameter of Differential Evolution for Global Optimization. In: Cai, Z., Li, Z., Kang, Z., Liu, Y. (eds.) ISICA 2009. CCIS, vol. 51, pp. 215–224. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Suganthan, P., Hansen, N., Liang, J.: Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization (2005)Google Scholar
  16. 16.
    Rahnamayan, S., Tizhoosh, H., Salama, M.: Opposition-Based Differential Evolution. IEEE Transactions on Evolutionary Computation 12(1), 64–79 (2008)CrossRefGoogle Scholar
  17. 17.
    Zhu, R.: Statistical Analysis Methods. China Forestry Publishing House, Beijing (1989)Google Scholar
  18. 18.
    Zhang, M., Luo, W., Wang, X.: Differential Evolution with Dynamic Stochastic Selection for Constrained Optimization. Information Science: An International Journal 178, 3043–3074 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pravesh Kumar
    • 1
  • Millie Pant
    • 1
  • V. P. Singh
    • 2
  1. 1.Indian Insitute of TechnologyRoorkeeIndia
  2. 2.Millenium Insitute of Engineering and TechnolgyIndia

Personalised recommendations