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MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm

Author

Listed:
  • Luis Martí

    (Universidade Federal Flumense)

  • Jesús García

    (Universidad Carlos III de Madrid)

  • Antonio Berlanga

    (Universidad Carlos III de Madrid)

  • José M. Molina

    (Universidad Carlos III de Madrid)

Abstract

The extension of estimation of distribution algorithms (EDAs) to the multi-objective domain has led to multi-objective optimization EDAs (MOEDAs). Most MOEDAs have limited themselves to porting single-objective EDAs to the multi-objective domain. Although MOEDAs have proved to be a valid approach, the last point is an obstacle to the achievement of a significant improvement regarding “standard” multi-objective optimization evolutionary algorithms. Adapting the model-building algorithm is one way to achieve a substantial advance. Most model-building schemes used so far by EDAs employ off-the-shelf machine learning methods. However, the model-building problem has particular requirements that those methods do not meet and even evade. The focus of this paper is on the model-building issue and how it has not been properly understood and addressed by most MOEDAs. We delve down into the roots of this matter and hypothesize about its causes. To gain a deeper understanding of the subject we propose a novel algorithm intended to overcome the drawbacks of current MOEDAs. This new algorithm is the multi-objective neural estimation of distribution algorithm (MONEDA). MONEDA uses a modified growing neural gas network for model-building (MB-GNG). MB-GNG is a custom-made clustering algorithm that meets the above demands. Thanks to its custom-made model-building algorithm, the preservation of elite individuals and its individual replacement scheme, MONEDA is capable of scalably solving continuous multi-objective optimization problems. It performs better than similar algorithms in terms of a set of quality indicators and computational resource requirements.

Suggested Citation

  • Luis Martí & Jesús García & Antonio Berlanga & José M. Molina, 2016. "MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm," Journal of Global Optimization, Springer, vol. 66(4), pages 729-768, December.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:4:d:10.1007_s10898-016-0415-7
    DOI: 10.1007/s10898-016-0415-7
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    References listed on IDEAS

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    1. Dimo Brockhoff & Eckart Zitzler, 2007. "Dimensionality Reduction in Multiobjective Optimization: The Minimum Objective Subset Problem," Operations Research Proceedings, in: Karl-Heinz Waldmann & Ulrike M. Stocker (ed.), Operations Research Proceedings 2006, pages 423-429, Springer.
    2. Johannes Bader & Kalyanmoy Deb & Eckart Zitzler, 2010. "Faster Hypervolume-Based Search Using Monte Carlo Sampling," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 313-326, Springer.
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