Multiobjective Optimization and Phase Transitions

  • Luís F. SeoaneEmail author
  • Ricard Solé
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


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.


Multi Objective Optimization Pareto Front Order Transition Order Phase Transition Target Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.ICREA-Complex Systems LabUniversitat Pompeu Fabra-PRBBBarcelonaSpain
  2. 2.Institut de Biologia Evolutiva, CSIC-UPFBarcelonaSpain
  3. 3.Santa Fe InstituteSanta FeUSA

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