A Study of Convergence Speed in Multi-objective Metaheuristics

  • Antonio Jesús Nebro
  • Juan José Durillo
  • Carlos A. Coello Coello
  • Francisco Luna
  • Enrique Alba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


An open issue in multi-objective optimization is designing metaheuristics that reach the Pareto front using a low number of function evaluations. In this paper, we adopt a benchmark composed of three well-known problem families (ZDT, DTLZ, and WFG) and analyze the behavior of six state-of-the-art multi-objective metaheuristics, namely, NSGA-II, SPEA2, PAES, OMOPSO, AbYSS, and MOCell, according to their convergence speed, i.e., the number of evaluations required to obtain an accurate Pareto front. By using the hypervolume as a quality indicator, we measure the algorithms converging faster, as well as their hit rate over 100 independent runs. Our study reveals that modern multi-objective metaheuristics such as MOCell, OMOPSO, and AbYSS provide the best overall performance, while NSGA-II and MOCell achieve the best hit rates.


Pareto Front Multiobjective Optimization Convergence Speed Multiobjective Optimization Problem Nondominated Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Antonio Jesús Nebro
    • 1
  • Juan José Durillo
    • 1
  • Carlos A. Coello Coello
    • 2
  • Francisco Luna
    • 1
  • Enrique Alba
    • 1
  1. 1.Department of Computer ScienceUniversity of MálagaSpain
  2. 2.Department of Computer ScienceCINVESTAV-IPNMexico

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