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Handling Priority Levels in Mixed Pareto-Lexicographic Many-Objective Optimization Problems

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Evolutionary Multi-Criterion Optimization (EMO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12654))

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Abstract

This paper studies a class of mixed Pareto-Lexicographic multi-objective optimization problems where the preference among the objectives is available in different priority levels (PLs) before the start of the optimization process – akin to many practical problems involving domain experts. Each priority level (PL) is a group of objectives having an identical importance in terms of optimization, so that they must be optimized in the standard Pareto sense. However, between two PLs, a lexicographic preference structure exists. Clearly, finding the entire set of Pareto optimal solutions first and then choosing the lexicographic solutions using the given PL structure is not computationally efficient. A new efficient algorithm is presented here using a recent mathematical breakthrough in handling infinite and infinitesimal quantities: the Grossone methodology. The proposal has been implemented within a popular multi-objective optimization algorithm (NSGA-II), thereby obtaining its generalized version named PL-NSGA-II, although other EMO or EMaO algorithms could have also been used instead. A quantitative comparison of PL-NSGA-II performance against existing algorithms is made. Results clearly show the advantage of the proposed Grossone-based methodology in solving such priority-level many-objective problems.

Work partially supported by the Italian MIUR – CrossLab project (Departments of Excellence) and partially by the University of Pisa funded project PRA_2018_81 “Wearable sensor systems: personalized analysis and data security in healthcare”.

COIN Report Number 2020025.

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Authors and Affiliations

  1. Pisa University, Largo Lucio Lazzarino 1, 56122, Pisa, Italy

    Leonardo Lai, Lorenzo Fiaschi & Marco Cococcioni

  2. Michigan State University, East Lansing, MI, 48824, USA

    Kalyanmoy Deb

Authors
  1. Leonardo Lai
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  2. Lorenzo Fiaschi
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  3. Marco Cococcioni
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  4. Kalyanmoy Deb
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Corresponding author

Correspondence to Marco Cococcioni .

Editor information

Editors and Affiliations

  1. Southern University of Science and Technology, Shenzhen, China

    Hisao Ishibuchi

  2. City University of Hong Kong, Kowloon Tong, China

    Qingfu Zhang

  3. Southern University of Science and Technology, Shenzhen, China

    Ran Cheng

  4. University of Exeter, Exeter, UK

    Ke Li

  5. Xi'an Jiaotong University, Xi'an, China

    Hui Li

  6. Xidian University, Xi'an, China

    Handing Wang

  7. East China Normal University, Shanghai, China

    Aimin Zhou

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Lai, L., Fiaschi, L., Cococcioni, M., Deb, K. (2021). Handling Priority Levels in Mixed Pareto-Lexicographic Many-Objective Optimization Problems. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_29

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  • DOI: https://doi.org/10.1007/978-3-030-72062-9_29

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  • Online ISBN: 978-3-030-72062-9

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