  Multi-objective optimization (MOO) aims to optimize multiple, possibly
conflicting objectives with widespread applications. We introduce a novel
interacting particle method for MOO inspired by molecular dynamics simulations.
Our approach combines overdamped Langevin and birth-death dynamics,
incorporating a "dominance potential" to steer particles toward global Pareto
optimality. In contrast to previous methods, our method is able to relocate
dominated particles, making it particularly adept at managing Pareto fronts of
complicated geometries. Our method is also theoretically grounded as a
Wasserstein-Fisher-Rao gradient flow with convergence guarantees. Extensive
experiments confirm that our approach outperforms state-of-the-art methods on
challenging synthetic and real-world datasets.
