Collective Annealing by Switching Temperatures: a Boltzmann-type description

Abstract

The design of effective cooling strategies is a crucial component in simulated annealing algorithms based on the Metropolis method. Traditionally, this is achieved through inverse logarithmic decays of the temperature to ensure convergence to global minima. In this work, we propose Collective Annealing by Switching Temperatures ({CAST}), a novel collective simulated annealing dynamic in which agents interact to learn an adaptive cooling schedule. Inspired by the particle-swapping mechanism of parallel tempering, we introduce a Boltzmann-type framework in which particles exchange temperatures through stochastic binary interactions. Under suitable conditions on the interaction parameters, this process induces a monotone decrease of the expected average temperature in the system. Numerical results indicate that the proposed approach can improve convergence speed over classical simulated annealing on multimodal benchmark problems, especially in regimes where adaptive exploration is important.