Advances in Differential Evolution for Solving Multiobjective Optimization Problems

  • Hongtao Ye
  • Meifang Zhou
  • Yan Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7331)


Differential evolution (DE) is a powerful evolutionary optimization algorithm with many successful scientific and engineering applications. This paper presents a survey of DE for solving multiobjective optimization problems (MOPs). It provides several prominent variants of the DE for solving MOPs. Then it presents an overview of the most significant engineering applications of DE. Finally, it points out the potential future research directions.


Differential evolution Multiobjective optimization problems Evolutionary algorithms 


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  1. 1.
    Stron, R., Price, K.: Differential evolution – A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359 (1997)CrossRefGoogle Scholar
  2. 2.
    Robič, T., Filipič, B.: DEMO: Differential Evolution for Multiobjective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Tizhoosh, H.R.: Opposition-based learning: A new scheme for machine intelligence. In: Processing of Computational Intelligence for Modelling, Control and Automation, Vienna, Austria, pp. 695–701 (2005)Google Scholar
  4. 4.
    Dong, N., Wang, Y.P.: Multiobjective differential evolution based on opposite operation. In: International Conference on Computational Intelligence and Security, Beijing, China, pp. 123–127 (2009)Google Scholar
  5. 5.
    Qian, W.Y., Li, A.J.: Adaptive differential evolution algorithm for multiobjective optimization problems. Applied Mathematics and Computation 201, 431–440 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Abbass, H.A., Sarker, R., Newton, C.: PDE: A pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the Congress on Evolutionary Computation, pp. 831–836. IEEE Service Center Piscataway, New Jersey (2002)Google Scholar
  7. 7.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3, 257–271 (1999)CrossRefGoogle Scholar
  8. 8.
    Xue, F., Sanderson, A.C., Graves, R.J.: Pareto-based multi-objective differential evolution. In: Proceedings of the 2003 Congress on Evolutionary Computation, pp. 862–869. IEEE Press, Canberra (2003)Google Scholar
  9. 9.
    Yao, F., Yang, W.D., Zhang, M.: Multi-objective differential evolution used for load distribution of hot strip mills. Control Theory & Application 27, 897–902 (2010)Google Scholar
  10. 10.
    Deb, K., Pratap, A., Agarwal, S., et al.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)CrossRefGoogle Scholar
  11. 11.
    Li, K., Zheng, J.H.: Improved multi-objective evolutionary algorithm based on differential evolution. Computer Engineering and Applications 44, 51–56 (2008)Google Scholar
  12. 12.
    Li, H., Zhang, Q.F.: Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Transactions on Evolutionary Computation 13, 284–302 (2009)CrossRefGoogle Scholar
  13. 13.
    Li, H., Zhang, Q.: A Multiobjective Differential Evolution Based on Decomposition for Multiobjective Optimization with Variable Linkages. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 583–592. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Qu, B.Y., Suganthan, P.N.: Multiobjective evolutionary algorithms based on the summation of normalized objectives and diversified selection. Information Science 80, 3170–3181 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Eiben, A.E., Smith, J.E.: Introduction to evolutionary computing (natural computing series). Springer, Berlin (2003)Google Scholar
  16. 16.
    Zhang, J.Q., Sanderson, A.C.: JADE: Adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation 13, 945–958 (2009)CrossRefGoogle Scholar
  17. 17.
    Zaharie, D., Petcu, D.: Adaptive pareto differential evolution algorithm and its parallelization. In: Proc. 5th. Conf. Parallel Process. Appl. Math., Czestochowa, Poland, pp. 261–268 (2003)Google Scholar
  18. 18.
    Abbass, H.A.: The self-adaptive pareto differential evolution algorithm. In: Proc. IEEE Congr. Evol. Comput., Honolulu, HI, pp. 831–836 (2002)Google Scholar
  19. 19.
    Wu, L.H., Wang, Y.N., Yuan, X.F., et al.: Multiobjective Optimization of HEV Fuel Economy and Emissions Using the Self-Adaptive Differential Evolution Algorithm. IEEE Transactions on Vehicular Technology 60, 2458–2470 (2011)CrossRefGoogle Scholar
  20. 20.
    Huang, V.L., Qin, A.K., Suganthan, P.N., et al.: Multi-objective optimization based on self-adaptive differential evolution algorithm. In: Proceedings of the Evolutionary Computation, pp. 3601–3608 (2007)Google Scholar
  21. 21.
    Huang, V.L., Zhao, S.Z., Mallipeddi, R., et al.: Multi-objective optimization using self-adaptive differential evolution algorithm. In: Proceedings of the Eleventh Conference on Congress on Evolutionary Computation, pp. 190–194. IEEE Press (2009)Google Scholar
  22. 22.
    Zamuda, A., Brest, J., Boškovic, B., et al.: Differential Evolution for Multiobjective Optimization with Self Adaptation. In: IEEE Congress on Evolutionary Computation, pp. 3617–3624 (2007)Google Scholar
  23. 23.
    Xue, F., Sanderson, A.C., Bonissone, P.P., et al.: Fuzzy logic controlled multiobjective differential evolution. In: Proc. IEEE Int. Conf. Fuzzy Syst., Reno, NV, pp. 720–725 (2005)Google Scholar
  24. 24.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multi-objective evolutionary algorithms: empirical results. Evolutionary Computation 8, 173–195 (2000)CrossRefGoogle Scholar
  25. 25.
    Das, S., Suganthan, P.N.: Differential evolution: A survey of the state-of-the-art. IEEE Transactions on Evolutionary Computation 15, 4–31 (2011)CrossRefGoogle Scholar
  26. 26.
    Deb, K., Miettinen, K., Chaudhuri, S.: Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. IEEE Transactions on Evolutionary Computation 14, 821–841 (2010)CrossRefGoogle Scholar
  27. 27.
    Niu, D.P., Wang, F.L., He, D.K., et al.: Chaotic differential evolution for multiobjective optimization. Control and Decision 24, 361–364 (2009)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Wang, X.Z., Li, P., Yu, G.Y.: Multi-objective chaotic differential evolution algorithm with grading second mutation. Control and Decision 26, 457–463 (2011)MathSciNetGoogle Scholar
  29. 29.
    Chang, Y.P., Wu, C.J.: Optimal multiobjective planning of large-scale passive harmonic filters using hybrid differential evolution method considering parameter and loading uncertainty. IEEE Transactions on Power Delivery 20, 408–416 (2005)CrossRefGoogle Scholar
  30. 30.
    Gujarathi, A.M., Babu, B.V.: Optimization of adiabatic styrene reactor: a hybrid multiobjective differential evolution (H-MODE) approach. Ind. Eng. Chem. Res. 48, 11115–11132 (2009)CrossRefGoogle Scholar
  31. 31.
    Santana-Quintero, L.V., Coello Coello, C.A.: An algorithm based on differential evolution for multiobjective problems. International Journal of Computational Intelligence Research 1, 151–169 (2005)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Meng, H.Y., Zhang, X.H., Liu, S.Y.: A differential evolution based on double populations for constrained multi-objective optimization problem. Chinese Journal of Computer 31, 228–235 (2008)CrossRefGoogle Scholar
  33. 33.
    Wu, L.H., Wang, Y.N., Zhou, S.W., et al.: Research and application of pseudo parallel differential evolution algorithm with dual subpopulations. Control Theory & Applications 24, 453–458 (2007)Google Scholar
  34. 34.
    Goudos, S.K., Sahalos, J.N.: Pareto Optimal Microwave Filter Design Using Multiobjective Differential Evolution. IEEE Transactions on Antennas and Propagation 58, 132–144 (2010)CrossRefGoogle Scholar
  35. 35.
    Suresh, K., Kundu, D., Ghosh, S., et al.: Multi-Objective Differential Evolution for Automatic Clustering with Application to Micro-Array Data Analysis. Sensors 9, 3981–4004 (2009)CrossRefGoogle Scholar
  36. 36.
    Niu, D.P., Wang, F.L., He, D.K., et al.: Optimization of nosiheptide fermentation process based on the improved differential evolution algorithm for multi-objective optimization. Control Theory & Applications 27, 505–508 (2010)Google Scholar
  37. 37.
    Chen, Y., Bo, Y.M., Zou, W.J., et al.: Satisfactory Optimization for PID Regulator with Constraints on Exceeding Tolerance Characteristic Indices. Information and Control 39, 581–587 (2010)Google Scholar
  38. 38.
    Zhao, S.Z., Qu, B.Y., Suganthan, P.N., et al.: Multi-objective robust PID controller tuning using multi-objective differential evolution. In: International Conference on Control, Automation, Robotics and Vision, pp. 2398–2403 (2011)Google Scholar
  39. 39.
    Qiu, W., Zhang, J.H., Liu, N.: A Self-Adaptive Multi-0bjective Differential Evolution Algorithm for Reactive Power Optimization Considering Voltage Stability. Power System Technology 35, 81–87 (2011)Google Scholar
  40. 40.
    Basu, M.: Economic environmental dispatch using multi-objective differential evolution. Applied Soft Computing 11, 2845–2853 (2011)CrossRefGoogle Scholar
  41. 41.
    Krink, T., Paterlini, S.: Multiobjective optimization using differential evolution for real-world portfolio optimization. Computational Management Science 8, 157–179 (2011)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. Springer, Berlin (2007)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hongtao Ye
    • 1
  • Meifang Zhou
    • 2
  • Yan Wu
    • 1
  1. 1.Department of Electronic Information and Control EngineeringGuangxi University of TechnologyLiuzhouChina
  2. 2.Office of the PresidentGuangxi University of TechnologyLiuzhouChina

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