Hyper-spherical inversion transformations in multi-objective evolutionary optimization

J. W. Large*, D. F. Jones, M. Tamiz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Multi-objective evolutionary algorithms (MOEAs) are widely considered to have two goals: convergence towards the true Pareto front and maintaining a diverse set of solutions. The primary concern here is with the first goal of convergence, in particular when one or more variables must converge to a constant value. Using a number of well known test problems, the difficulties that are currently impeding convergence are discussed and then a new method is proposed that transforms the decision space using the geometric properties of hyper-spherical inversions to converge towards/onto the true Pareto front. Future extensions of this work and its application to multi-objective optimisation is discussed.

Original languageEnglish
Pages (from-to)1678-1702
Number of pages25
JournalEuropean Journal of Operational Research
Issue number3
Publication statusPublished - 16 Mar 2007


  • Convergence
  • Crossover
  • Inversion transformation
  • Multi-objective evolutionary algorithms


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