Application of an Improved Generalized Differential Evolution Algorithm to Multi-objective Optimization Problems

  • Subramanian Ramesh
  • Subramanian Kannan
  • Subramanian Baskar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7076)

Abstract

An Improved Multiobjective Generalized Differential Evolution (I- GDE3) approach is proposed in this paper. For maintaining good diversity, the concepts of Simulated Binary Crossover (SBX) based recombination and Dynamic Crowding Distance (DCD) are implemented in GDE3 algorithm. The proposed approach is applied to different sets of classical test problems suggested in the MOEA literature to validate the performance of the I-GDE3. Later, the proposed approach is implemented to Reactive Power Planning (RPP) problem. The objective functions are minimization of combined operating and VAR allocation cost and bus voltage profile improvement. The performance of the proposed approach is tested in standard IEEE 30-bus test systems. The performance of I-GDE3 is compared with respect to multi- objective performance measures namely gamma, spread, minimum spacing and Inverted Generational Distance (IGD). The results show the effectiveness of I-GDE3 and confirm its potential to solve the multi-objective problems.

Keywords

Differential Evolution Multiobjective Optimization Multiobjective Evolutionary Algorithm Thyristor Control Series Compensator Invert Generational Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abbass, H.A., Sarker, R., Newton, C.: PDE: A Pareto-frontier Differential Evolution Approach for Multi-objective Optimization Problems. In: Proc. of IEEE Cong. on Evol. Comp., pp. 971–978 (2001) Google Scholar
  2. 2.
    Abbass, H.A.: The Self-Adaptive Pareto Differential Evolution Algorithm. In: Proc.of IEEE Cong. on Evol. Comp., vol. 1, pp. 831–836 (2002)Google Scholar
  3. 3.
    Abido, M.A., Bakhashwain J.M.: A Novel Multi-objective Evolutionary Algorithm for Reactive Power Dispatch Problem. In: ICECS 2003, pp. 1054–1057 (2003)Google Scholar
  4. 4.
    Chang, C.S., Xu, D.Y., Quek, H.B.: Pareto-optimal set based multi-objective tuning of fuzzy automatic train operation for mass transit system. IEE Proceedings on Electric Power Applications 146(5), 577–583 (1999)CrossRefGoogle Scholar
  5. 5.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms, 1st edn. John Wiley & Sons, Ltd., Singapore (2001)MATHGoogle Scholar
  6. 6.
    Gujarathi, A.M., Babu, B.V.: Improved Multi-Objective Differential Evolution (MODE) Approach for Purified Terephthalic Acid (PTA) Oxidation Process. Materials and Manufacturing Processes 24(3), 303–319 (2009)CrossRefGoogle Scholar
  7. 7.
    Gujarathi, A.M., Babu, B.V.: Multi-objective Optimization of Industrial Styrene Reactor: Adiabatic and Pseudo-isothermal Operation. Chem. Engg. Science 65(6), 2009–2026 (2010)CrossRefGoogle Scholar
  8. 8.
    Gujarathi, A.M., Babu, B.V.: Optimization of Adiabatic Styrene Reactor: A Hybrid Multi-Objective Differential Evolution (H–MODE) Approach. Industrial & Engineering Chemistry Research 48(24), 11115–11132 (2009)CrossRefGoogle Scholar
  9. 9.
    Gujarathi, A.M., Babu, B.V.: Hybrid Multi-objective Differential Evolution (HMODE) for optimization of Polyethylene Terephthalate (PET) reactor. Int. J. of Bio. Insp. Comp. 2(3/4), 213–221 (2010)CrossRefGoogle Scholar
  10. 10.
    Hsaio, Y.T., Chaing, H.D., Liu, C.C., Chen, Y.L.: A Computer Package for Optimal Multi-objective VAR Planning in Large Scale Power Systems. IEEE Trans. on Power Syst. 9(2), 668–676 (1994)Google Scholar
  11. 11.
    Kannan, S., Baskar, S., McCalley, J.D., Murugan, P.: Application of NSGA-II Algorithm to Generation Expansion Planning. IEEE Trans. on Power Syst. 24(1), 454–461 (2009)CrossRefGoogle Scholar
  12. 12.
    King, R.T.F.A., Rughooputh, H.C.S.: Elitist multiobjective evolutionary algorithm for environmental/economic dispatch. In: The 2003 Congress on Evolutionary Computation, vol. 2, pp. 1108–1114 (2003)Google Scholar
  13. 13.
    Knowles, J., Corne, D.: The Pareto archived evolution strategy: A new baseline algorithm for multi-objective optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, pp. 98–105 (1999)Google Scholar
  14. 14.
    Kukkonen, S., Lampinen, J.: GDE3: The third evolution step of Generalized Differential Evolution. In: Proceedings of the 2005 Congress on Evolutionary Computation (CEC 2005), pp. 443–450 (2005)Google Scholar
  15. 15.
    Lai, L.L., Ma, J.T.: Application of Evolutionary Programming to Reactive Power Planning – Comparison with Nonlinear Programming Approach. IEEE Trans. on Power Syst. 12(1), 198–206 (1997)CrossRefGoogle Scholar
  16. 16.
    Luo, B., Zheng, J., Xie, J., Wu, J.: Dynamic Crowding Distance - A New Diversity Maintenance Strategy for MOEAs. In: ICNC 2008, 4th International Conference Natural Computation, vol. 1, pp. 580–585 (2008)Google Scholar
  17. 17.
    Madavan, N.K.: Multiobjective Optimization Using a Pareto Differential Evolution Approach. In: Proceedings of Congress on Evolutionary Computation (CEC 2002), vol. 2, pp. 1145–1150 (2002)Google Scholar
  18. 18.
    Manoharan, P.S., Kannan, P.S., Baskar, S., Willjuice Iruthayarajan, M., Dhananjeyan, V.: Covariance matrix adapted evolution strategy algorithm-based solution to dynamic economic dispatch problems. Engg. Optimization 41(7), 635–657 (2009)CrossRefGoogle Scholar
  19. 19.
    Ramesh, S., Kannan, S., Baskar, S.: An improved generalized differential evolution algorithm for multi-objective reactive power dispatch. Engineering Optimization (2011), doi:10.1080/0305215X.2011.576761 Google Scholar
  20. 20.
    Ramesh, S., Kannan, S., Baskar, S.: Multi-objective Evolutionary Algorithm based Reactive Power Dispatch with Thyristor Controlled Series Compensators. In: IEEE PEDES 2010 and Power India, pp. 1–5 (2010)Google Scholar
  21. 21.
    Storn, R., Price, K.: Differential evolution-A simple and Efficient Heuristic for Global Optimization over Continuous Spaces. J. Glob. Optim. 11, 341–359 (1997)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    University of Washington, Power Systems Test Case Archive, http://www.ee.washington.edu/research/pstca/
  23. 23.
    Wang, Y., Wu, L., Yuan, X.: Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure. Soft Computing 14(3), 193–209 (2010)CrossRefGoogle Scholar
  24. 24.
    Xue, F., Sanderson, A.C., Graves, R.J.: Modeling and convergence analysis of a continuous multi-objective differential evolution algorithm. In: 2005 IEEE Congress on Evolutionary Computation (CEC 2005), vol. 1, pp. 228–235 (2005)Google Scholar
  25. 25.
    Zhao, S.Z., Suganthan, P.N.: Two-lbests Based Multi-objective Particle Swarm Optimizer. Engineering Optimization 43(1), 1–17 (2011)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Zhao, S.Z., Suganthan, P.N., Zhang, Q.: Decomposition Based Multiobjective Evolutionary Algorithm with an Ensemble of Neighborhood Sizes. IEEE Trans. on Evolutionary Computation (accepted)Google Scholar
  27. 27.
    Zhihuan, L., Yinhong, L., Xianzhong, D.: Non-dominated sorting genetic algorithm-II for robust multi-objective optimal reactive power dispatch. IET Gen., Trans. and Dist. 4(9), 1000–1008 (2010)CrossRefGoogle Scholar
  28. 28.
    Zhou, A., Qu, B.Y., Li, H., Zhao, S.Z., Suganthan, P.N., Zhang, Q.: Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation 1, 32–49 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Subramanian Ramesh
    • 1
  • Subramanian Kannan
    • 2
  • Subramanian Baskar
    • 3
  1. 1.Arulmigu Kalasalingam College of EngineeringIndia
  2. 2.Kalasalingam UniversityIndia
  3. 3.Thiagarajar College of EngineeringMaduraiIndia

Personalised recommendations