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.

翻译：多目标优化旨在优化多个可能相互冲突的目标函数，具有广泛的应用场景。受分子动力学模拟启发，我们提出了一种新颖的交互式粒子方法。该方法融合过阻尼朗之万动力学与生灭过程，通过引入"支配势"引导粒子向全局帕累托最优演化。与现有方法相比，我们的方法能够重新定位被支配粒子，尤其擅长处理具有复杂几何结构的帕累托前沿。该方法在理论上可被视作具有收敛保证的Wasserstein-Fisher-Rao梯度流。大量实验表明，在具有挑战性的合成数据集与真实数据集上，本方法均优于现有最先进技术。