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On Timing the Nadir-Point Estimation and/or Termination of Reference-Based Multi- and Many-objective Evolutionary Algorithms

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Evolutionary Multi-Criterion Optimization (EMO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11411))

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Abstract

There is considerable evidence that the Multi- and Many-objective Evolutionary Algorithms (jointly referred as MâOEAs, here) are mostly run for arbitrarily fixed number of generations. The absence of any justification for the same raises more questions than answers, and it is plausible to infer that the choices made for different problems coincide with the best-observed results. Reference-based MâOEAs (RMâOEAs) are a prominently emerging class of MâOEAs, where the diversity maintenance is assisted by externally provided reference vectors or points. However, the performance of most existing RMâOEAs is impacted by the efficacy with which the population is normalized along the search. This paper presents a novel and computationally efficient Termination Algorithm which under different parameter settings (strong and mild) not only determines the appropriate timing for RMâOEAs’ termination but also the intermittent timings at which the population ought to be normalized. The proposed Algorithm can be tuned to integrate with different RMâOEAs. An instance of it is demonstrated here, with respect to NSGA-III. Experimental Results on the call for final termination of NSGA-III have been validated through Hypervolume measures. The results also establish that the performance of NSGA-III could be improved just by changing the frequency of Nadir-point estimates (used for population normalization). While several efforts have been made on how to estimate the Nadir-point, this to the best of the authors’ knowledge is one of the rarest studies that explores when to estimate the Nadir-point.

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Notes

  1. 1.

    The source code used can be found at: https://esa.github.io/pagmo2/.

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Authors and Affiliations

  1. Indian Institute of Technology Roorkee, Roorkee, 247667, Uttarakhand, India

    Dhish Kumar Saxena & Sarang Kapoor

Authors
  1. Dhish Kumar Saxena
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  2. Sarang Kapoor
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Corresponding author

Correspondence to Dhish Kumar Saxena .

Editor information

Editors and Affiliations

  1. Michigan State University, East Lansing, MI, USA

    Kalyanmoy Deb

  2. Michigan State University, East Lansing, MI, USA

    Erik Goodman

  3. CINVESTAV-IPN, Mexico, Mexico

    Carlos A. Coello Coello

  4. University of Wuppertal, Wuppertal, Germany

    Kathrin Klamroth

  5. University of Jyvaskyla, Jyväskylä, Finland

    Kaisa Miettinen

  6. Otto von Guericke University Magdeburg, Magdeburg, Germany

    Sanaz Mostaghim

  7. Cornell University, Ithaca, NY, USA

    Patrick Reed

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Saxena, D.K., Kapoor, S. (2019). On Timing the Nadir-Point Estimation and/or Termination of Reference-Based Multi- and Many-objective Evolutionary Algorithms. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_16

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  • DOI: https://doi.org/10.1007/978-3-030-12598-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12597-4

  • Online ISBN: 978-3-030-12598-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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