A grid-based inverted generational distance for multi/many-objective optimization

Xinye Cai, Yushun Xiao, Miqing Li, Han Hu, Hisao Ishibuchi, Xiaoping Li

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Assessing the performance of Pareto front (PF) approximations is a key issue in the field of evolutionary multi/many-objective optimization. Inverted generational distance (IGD) has been widely accepted as a performance indicator for evaluating the comprehensive quality for a PF approximation. However, IGD usually becomes infeasible when facing a real-world optimization problem as it needs to know the true PF a priori. In addition, the time complexity of IGD grows quadratically with the size of the solution/reference set. To address the aforementioned issues, a grid-based IGD (Grid-IGD) is proposed to estimate both convergence and diversity of PF approximations for multi/many-objective optimization. In Grid-IGD, a set of reference points is generated by estimating PFs of the problem in question, based on the representative nondominated solutions of all the approximations in a grid environment. To reduce the time complexity, Grid-IGD only considers the closest solution within the grid neighborhood in the approximation for every reference point. Grid-IGD also possesses other desirable properties, such as Pareto compliance, immunity to dominated/duplicate solutions, and no need of normalization. In the experimental studies, Grid-IGD is verified on both the artificial and real PF approximations obtained by five many-objective optimizers. Effects of the grid specification on the behavior of Grid-IGD are also discussed in detail theoretically and experimentally.
Original languageEnglish
Article number9080110
Pages (from-to)21-34
Number of pages14
JournalIEEE Transactions on Evolutionary Computation
Issue number1
Early online date28 Apr 2020
Publication statusPublished - Feb 2021

Bibliographical note

Publisher Copyright:
© 1997-2012 IEEE.


  • Grid system
  • inverted generational distance (IGD)
  • many-objective optimization
  • performance indicator

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics


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