A multiscale consensus-based algorithm for multilevel optimization
File(s)
Accepted version
OA Location
Author(s)
Herty, Michael
Huang, Yuyang
Kalise, Dante
Kouhkouh, Hicham
Type
Journal Article
Abstract
In this paper, a novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting populations of particles, each of which is used to optimize one level of the problem. These particle populations are evolved through multiscale-in-time dynamics, which are formulated as a singularly perturbed system of stochastic differential equations. Theoretical convergence analysis for the multiscale CBO model to an averaged effective dynamics as the time-scale separation parameter approaches zero is provided. The resulting algorithm is presented for both bi-level and tri-level optimization problems. The effectiveness of the approach in tackling complex multilevel optimization tasks is demonstrated through numerical experiments on various benchmark functions. Additionally, it is shown that the proposed method performs well on min–max optimization problems, comparing favorably with existing CBO algorithms for saddle point problems.
Date Issued
2025-09-01
Date Acceptance
2025-05-05
Citation
Mathematical Models and Methods in Applied Sciences, 2025, 35 (10), pp.2207-2243
ISSN
0218-2025
Publisher
World Scientific Pub Co Pte Ltd
Start Page
2207
End Page
2243
Journal / Book Title
Mathematical Models and Methods in Applied Sciences
Volume
35
Issue
10
Copyright Statement
© 2025 World Scientific Publishing Co Pte Ltd. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2025-06-17