Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis
Provides a theoretical foundation for jump-based swarm optimization, but the contribution is incremental as it extends existing CBO dynamics.
The paper introduces a novel particle-based optimization algorithm using random velocity jumps, formalized via a kinetic BGK framework, and proves convergence to minimizers for Gaussian noise in bounded domains. Numerical benchmarks validate the approach.
Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle-based optimization methods, inspired by swarm intelligence principles, have shown effectiveness due to their ability to balance exploration and exploitation within the search space. In this work, we introduce a novel particle-based optimization algorithm where velocities are updated via random jumps, a strategy commonly used to enhance stochastic exploration. We formalize this approach by describing the dynamics through a kinetic modelling of BGK type, offering a unified framework that accommodates general noise distributions, including heavy-tailed ones like Cauchy. Under suitable parameter scaling, the model reduces to the Consensus-Based Optimization (CBO) dynamics. For non-degenerate Gaussian noise in bounded domains, we prove propagation of chaos and convergence towards minimizers. Numerical results on benchmark problems validate the approach and highlight its connection to CBO.