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Proceedings of ECCS 2014 pp 259–270Cite as

Multiobjective Optimization and Phase Transitions

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Part of the book series: Springer Proceedings in Complexity ((SPCOM))

Abstract

Many complex systems obey to optimality conditions that are usually not simple. Conflicting traits often interact making a Multi Objective Optimization (MOO) approach necessary. Recent MOO research on complex systems report about the Pareto front (optimal designs implementing the best trade-off) in a qualitative manner. Meanwhile, research on traditional Simple Objective Optimization (SOO) often finds phase transitions and critical points. We summarize a robust framework that accounts for phase transitions located through SOO techniques and indicates what MOO features resolutely lead to phase transitions. These appear determined by the shape of the Pareto front, which at the same time is deeply related to the thermodynamic Gibbs surface. Indeed, thermodynamics can be written as an MOO from where its phase transitions can be parsimoniously derived; suggesting that the similarities between transitions in MOO-SOO and Statistical Mechanics go beyond mere coincidence.

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Acknowledgments

This work has been supported by an ERC Advanced Grant, the Botín Foundation, by Banco Santander through its Santander Universities Global Division and by the Santa Fe Institute. We thank CSL members for insightful discussion.

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Authors and Affiliations

  1. ICREA-Complex Systems Lab, Universitat Pompeu Fabra-PRBB, Dr. Aiguader 88, 08003, Barcelona, Spain

    Luís F. Seoane & Ricard Solé

  2. Institut de Biologia Evolutiva, CSIC-UPF, Pg. Maritim de la Barceloneta 37, 08003, Barcelona, Spain

    Luís F. Seoane & Ricard Solé

  3. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

    Ricard Solé

Authors
  1. Luís F. Seoane
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  2. Ricard Solé
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Corresponding author

Correspondence to Luís F. Seoane .

Editor information

Editors and Affiliations

  1. RAF, University of Zürich, Zürich, Switzerland

    Stefano Battiston

  2. CREATE-NET, Trento, Italy

    Francesco De Pellegrini

  3. IMT Lucca, Lucca, Italy

    Guido Caldarelli

  4. School of Science and Technology, University of Camerino, Camerino, Italy

    Emanuela Merelli

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© 2016 Springer International Publishing Switzerland

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Seoane, L.F., Solé, R. (2016). Multiobjective Optimization and Phase Transitions. In: Battiston, S., De Pellegrini, F., Caldarelli, G., Merelli, E. (eds) Proceedings of ECCS 2014. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-29228-1_22

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