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International Conference on Parallel Problem Solving from Nature

PPSN 2022: Parallel Problem Solving from Nature – PPSN XVII pp 96–109Cite as

An Exact Inverted Generational Distance for Continuous Pareto Front

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13399))

Abstract

So far, many performance indicators have been proposed to compare different evolutionary multiobjective optimization algorithms (MOEAs). Among them, the inverted generational distance (IGD) is one of the most commonly used, mainly because it can measure a population’s convergence, diversity, and evenness. However, the effectiveness of IGD highly depends on the quality of the reference set. That is to say, all the reference points should be as close to the Pareto front (PF) as possible and evenly distributed to become ready for a fair performance evaluation. Currently, it is still challenging to generate well-configured reference sets, even if the PF can be given analytically. Therefore, biased reference sets might be a significant source of systematic error. However, in most MOEA literature, biased reference sets are utilized in experiments without an error estimation, which may make the experimental results unconvincing. In this paper, we propose an exact IGD (eIGD) for continuous PF, which is derived from the original IGD under an additional assumption that the reference set is perfect, i.e., the PF itself is directly utilized as an infinite-sized reference set. Therefore, the IGD values produced by biased reference sets can be compared with eIGD so that systematic error can be quantitatively evaluated and analyzed.

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Notes

  1. 1.

    In Sect. 3 and below, the variable x is not related to the x mentioned in Eq. (1), i.e., the solutions in the decision space. Here, since we are discussing performance evaluation, all the points or coordinates are in the objective space.

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Acknowledgements

This work is supported by the Scientific and Technological Innovation 2030 Major Projects under Grant No. 2018AAA0100902, the Science and Technology Commission of Shanghai Municipality under Grant No. 19511120601, the National Natural Science Foundation of China under Grant No. 61731009 and 61907015, and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Shanghai Institute of AI for Education, School of Computer Science and Technology, East China Normal University, Shanghai, 200062, China

    Zihan Wang, Chunyun Xiao & Aimin Zhou

Authors
  1. Zihan Wang
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  2. Chunyun Xiao
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  3. Aimin Zhou
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Corresponding authors

Correspondence to Chunyun Xiao or Aimin Zhou .

Editor information

Editors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Günter Rudolph

  2. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  3. Shinshu University, Nagano, Japan

    Hernán Aguirre

  4. Technische Universität Dresden, Dresden, Germany

    Pascal Kerschke

  5. University of Stirling, Stirling, UK

    Gabriela Ochoa

  6. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

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Wang, Z., Xiao, C., Zhou, A. (2022). An Exact Inverted Generational Distance for Continuous Pareto Front. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13399. Springer, Cham. https://doi.org/10.1007/978-3-031-14721-0_7

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  • DOI: https://doi.org/10.1007/978-3-031-14721-0_7

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  • Online ISBN: 978-3-031-14721-0

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