Multiobjective Optimization and Phase Transitions
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.
KeywordsMulti Objective Optimization Pareto Front Order Transition Order Phase Transition Target Space
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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