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


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.


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



The authors would like to thank Prof. Raino A.E. Mäkinen and Dr. Timo Aittokoski for fruitful discussions.


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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

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