  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.
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. For the latter methods, convergence to the global
minimizer can be shown for a large class of functions. 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
applications to machine learning.
