YIC2025

Follower-leader dynamics in optimization: a Genetic KBO approach.

  • Albi, Giacomo (University of Verona)
  • Ferrarese, Federica (University of Ferrara)
  • Totzeck, Claudia (University of Wuppertal)

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The study of numerical methods for global optimization of non-convex, high-dimensional functions has gained significant attention in recent years. Many traditional approaches rely on gradient-based methods, such as Newton’s method, which can be computationally expensive and struggle in cases where the gradient is difficult to compute, discontinuous, or highly nonlinear. These challenges become even more pronounced in the presence of multiple local minima, making the design of efficient gradient-free methods a crucial area of research. This talk introduces Genetic KBO, a novel and efficient gradient-free numerical method for global optimization, inspired by consensus-based and genetic algorithms. The idea is to have a group of agents divided into two sub-populations, namely followers and leaders. Followers explore the space while leaders are attracted toward the estimated position of the global minimizer at time t, which is computed according to Laplace Principle. A key feature of Genetic KBO is its adaptive population dynamics, where agents transition between follower and leader status. This label-switching process is governed by a stochastic model with transition rates that are in general non-linear functions of the state. A theoretical convergence analysis of the method will be presented, offering insights into its efficiency and reliability. Additionally, numerical experiments will be shown to compare Genetic KBO with other particle based optimization schemes, highlighting its advantages. Finally, the method will be extended to multi-modal optimization, demonstrating its capability to handle problems with multiple minima and complex objective landscapes.