Binary Interaction Methods for High Dimensional Global Optimization and Machine Learning

Alessandro Benfenati, Giacomo Borghi, Lorenzo Pareschi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction the particles act taking into account both the best microscopic binary position and the best macroscopic collective position. For the resulting kinetic optimization methods, convergence to the global minimizer is guaranteed for a large class of functions under appropriate parameter constraints that do not depend on the dimension of the problem. In the mean-field limit we show that the resulting Fokker-Planck partial differential equations generalize the current class of consensus based optimization (CBO) methods. Algorithmic implementations inspired by the well-known direct simulation Monte Carlo methods in kinetic theory are derived and discussed. Several examples on prototype test functions for global optimization are reported including an application to machine learning.

Original languageEnglish
Article number9
JournalApplied Mathematics & Optimization
Issue number1
StatePublished - Aug 2022
Externally publishedYes


  • Boltzmann equation
  • Consensus-based optimization
  • Global optimization
  • Gradient-free methods
  • Machine learning
  • Mean-field limit


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