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In this work we introduce a new class of gradient-free global optimizationmethods based on a binary interaction dynamics governed by a Boltzmann typeequation. In each interaction the particles act taking into account both thebest microscopic binary position and the best macroscopic collective position.In the mean-field limit we show that the resulting Fokker-Planck partialdifferential equations generalize the current class of consensus basedoptimization (CBO) methods. For the latter methods, convergence to the globalminimizer can be shown for a large class of functions. Algorithmicimplementations inspired by the well-known direct simulation Monte Carlomethods in kinetic theory are derived and discussed. Several examples onprototype test functions for global optimization are reported includingapplications to machine learning.

Binary interaction methods for high dimensional global optimization and machine learning