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

TL;DR

This paper introduces a multi-agent consensus-based algorithm for multi-objective optimization that uses scalarization and is supported by a mean-field model for convergence analysis, with numerical validation.

Contribution

It extends consensus-based optimization to multi-objective problems using scalarization and provides a mean-field framework for theoretical analysis.

Findings

The algorithm effectively solves multi-objective problems.

The mean-field model accurately describes the algorithm dynamics.

Numerical results confirm the method's validity.

Abstract

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.