A Kinetic Approach to Swarm-Intelligence Optimizers and Their Statistical Applications

Music City Center 

Swarm intelligence (SI) techniques have become widespread in engineering applications, and more recently, as metaheuristic optimization algorithms. Despite their empirical success, a theoretical framework remains elusive due to their heuristic interactions. From the viewpoint of statistical physics, metaheuristics can be modeled as stochastic optimizers that sample and probe the solution space using principles from statistical mechanics. In this talk, we leverage tools from statistical physics to derive a mean-field approximation of SI dynamics in the large-population limit, thereby providing insight into their collective behavior. As a concrete example, we analyze the consensus-based optimization (CBO) method and illustrate its promise for challenging statistical tasks.