Wednesday, March 30, 2022

A consensus-based algorithm for multi-objective optimization and its mean-field description

Giacomo Borghi, Michael Herty, Lorenzo Pareschi (to appear in Proceedings of the 61st IEEE Conference on Decision and Control. Preprint arXiv:2203.16384)

We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting agents exploring the search space and attempting to solve all scalar sub-problems simultaneously. We show that those dynamics are described by a mean-field model, which is suitable for a theoretical analysis of the algorithm convergence. Numerical results show the validity of the proposed method.