Collective Annealing by Switching Temperatures: a Boltzmann-type description

TL;DR

This paper introduces Collective Annealing by Switching Temperatures (CAST), a new adaptive cooling strategy for simulated annealing that uses stochastic interactions among agents to improve convergence speed over traditional methods.

Contribution

The paper presents a novel Boltzmann-type framework for collective annealing, enabling agents to adaptively learn cooling schedules through temperature exchanges.

Findings

CAST outperforms classical simulated annealing in convergence speed

The approach effectively adapts cooling schedules via stochastic interactions

Numerical results validate the efficiency of the proposed method

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. This process leads to a gradual decrease of the average temperature in the system. Numerical results demonstrate that the proposed approach consistently outperforms classical simulated annealing with both logarithmic and geometric cooling schedules, particularly in terms of convergence speed.