Soft Computing

, Volume 15, Issue 10, pp 2041–2055 | Cite as

A new hybrid mutation operator for multiobjective optimization with differential evolution

  • Karthik Sindhya
  • Sauli Ruuska
  • Tomi Haanpää
  • Kaisa Miettinen
Original Paper

Abstract

Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this paper, we propose a new hybrid mutation operator consisting of a polynomial-based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, for the efficient handling of various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evolutionary algorithms. Particularly, it can be used as a replacement in all algorithms utilizing the original mutation operator of differential evolution. We demonstrate how the new hybrid operator can be used by incorporating it into MOEA/D, a winning evolutionary multiobjective algorithm in a recent competition. The usefulness of the hybrid operator is demonstrated with extensive numerical experiments showing improvements in performance compared with the previous state of the art.

Keywords

Evolutionary algorithms DE Nonlinear Multi-criteria optimization Polynomial Pareto optimality MOEA/D 

References

  1. Abbass HA (2002) The self-adaptive pareto differential evolution algorithm. In: Proceedings of the congress on evolutionary computation (CEC ’02). IEEE Press, pp 831–836Google Scholar
  2. Ali M, Pant M (2010) Improving the performance of differential evolution algorithm using cauchy mutation. Soft Comput. doi:10.1007/s00500-010-0655-2
  3. Ali MM, Törn A, Viitanen S (1997) A numerical comparison of some modified controlled random search algorithms. J Glob Optim 11(4):377–385MATHCrossRefGoogle Scholar
  4. Babu BV, Jehan MML (2003) Differential evolution for multi-objective optimization. In: Proceedings of the congress on evolutionary computation (CEC ’03). IEEE Press, pp 2696–2073Google Scholar
  5. Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming: theory and algorithms. Wiley, HobokenMATHCrossRefGoogle Scholar
  6. Coello CAC, Lamont GB, Veldhuizen DAV (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, New YorkMATHGoogle Scholar
  7. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, ChichesterMATHGoogle Scholar
  8. Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129MathSciNetMATHCrossRefGoogle Scholar
  9. Gibbons JD, Chakraborti S (2003) Nonparametric statistical inference. Marcel Dekker, New YorkMATHGoogle Scholar
  10. Huang VL, Qin AQ, Deb K, Zitzler E, Suganthan PN, Liang JJ, Preuss M, Huband S (2007) Problem definitions for performance assessment of multi-objective optimization algorithms. Technical report, Nanyang Technological UniversityGoogle Scholar
  11. Jin Y, Sendhoff B (2003) Connectedness, regularity and the success of local search in evolutionary multi-objective optimization. In: Proceedings of the congress on evolutionary computation (CEC ’03). IEEE Press, pp 1910–1917Google Scholar
  12. Kaelo P, Ali MM (2007) Differential evolution algorithms using hybrid mutation. Comput Optim Appl 5(2):231–246MathSciNetCrossRefGoogle Scholar
  13. Kincaid D, Cheney W (2002) Numerical analysis: mathematics of scientific computing. Brooks/Cole Publishing CoGoogle Scholar
  14. Kukkonen S, Lampinen J (2005) GDE3: The third evolution step of generalized differential evolution. In: Proceedings of the congress on evolutionary computation (CEC ’05). IEEE Press, pp 443–450Google Scholar
  15. Kukkonen S, Lampinen J (2006) Constrained real-parameter optimization with generalized differential evolution. In: Proceedings of the congress on evolutionary computation (CEC ’06). IEEE Press, pp 207–214Google Scholar
  16. Lara A, Sanchez G, Coello CAC, Schütze O (2010) HCS: A new local search strategy for memetic multiobjective evolutionary algorithms. IEEE Trans Evol Comput 14(1):112–132CrossRefGoogle Scholar
  17. Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9:448–462MATHCrossRefGoogle Scholar
  18. Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer, BostonMATHGoogle Scholar
  19. Nocedal J, Wright SJ (1999) Numerical optimization. Springer, New YorkMATHCrossRefGoogle Scholar
  20. Okabe T, Jin Y, Olhofer M, Sendhoff B (2004) On test functions for evolutionary multi-objective optimization. In: Yao X et al (eds) Proceedings of the parallel problem solving from nature (PPSN VIII 2004), Springer, Berlin, pp 792–802Google Scholar
  21. Price KV, Storn RM, Lampinen JA (2005) Differential evolution—a practical approach to global optimization. Springer, BerlinMATHGoogle Scholar
  22. Robic T, Filipic B (2005) DEMO: Differential evolution for multiobjective optimization. In: Coello CAC, et al (eds) Proceedings of the evolutionary multi-criterion optimization (EMO 2005). Springer, Berlin, pp 520–533Google Scholar
  23. Ruuska S, Aittokoski T (2008) The effect of trial point generation schemes on the efficiency of population-based global optimization algorithms. In: Proceedings of the international conference on engineering optimization (EngOpt ’08)Google Scholar
  24. Santana-Quintero LV, Coello CAC (2005) An algorithm based on Differential Evolution for multi-objective problems. Int J Comput Intell Res 1(2):151–169MathSciNetGoogle Scholar
  25. Schütze O, Talbi E, Coello CC, Santana-Quintero LV, Pulido GT (2007) A memetic PSO algorithm for scalar optimization problems. In: Proceedings of the symposium on swarm intelligence (SIS ’07). IEEE Press, pp 128–134Google Scholar
  26. Storn R, Price K (1996) Minimizing the real functions of the ICEC’96 contest by differential evolution. In: Proceedings of the conference on evolutionary computation (ICEC ’96). IEEE Press, pp 842–844Google Scholar
  27. Wang X, Hao M, Cheng Y, Lei R (2009) PDE-PEDA: A new pareto-based multi-objective optimization algorithm. J Univ Comput Sci 15(4):722–741MathSciNetMATHGoogle Scholar
  28. Zhang Q, Li H (2007) MOEA/D: A multi-objective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  29. Zhang Q, Zhou A, Jin Y (2008) RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm. IEEE Trans Evol Comput 12(1):41–63CrossRefGoogle Scholar
  30. Zhang Q, Liu W, Li H (2009a) The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: Proceedings of the conference on evolutionary computation (CEC ’09). IEEE Press, pp 203–208Google Scholar
  31. Zhang Q, Zhou A, Zhao SZ, Suganthan PN, Liu W, Tiwari S (2009b) Multiobjective optimization test instances for the CEC09 special session and competition. Technical report, CES-487, University of Essex and Nanyang Technological UniversityGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Karthik Sindhya
    • 1
  • Sauli Ruuska
    • 1
  • Tomi Haanpää
    • 1
  • Kaisa Miettinen
    • 1
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläFinland

Personalised recommendations