A Consensus-Based Algorithm for Multi-Objective Optimization and Its Mean-Field Description

Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes, pp. 4131–4136

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.

Authors 3

1. Giacomo Borghi Aachen Institute of Geometry and Practical Mathematics

   RWTH Aachen University · University of Ferrara

   Affiliation as printed

   RWTH Aachen University,Institute of Geometry and Practical Mathematics,Aachen,Germany,52062

   Department of Mathematics and Computer Science, University of Ferrara, Italy

2. Michaël Herty Aachen Institute of Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Institute of Geometry and Practical Mathematics,Aachen,Germany,52062

3. Lorenzo Pareschi

   University of Ferrara

   Affiliation as printed

   University of Ferrara,Department of Mathematics and Computer Science,Italy,44121