Consensus based optimization with memory effects: Random selection and applications

Giacomo Borghi*, Sara Grassi, Lorenzo Pareschi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system. We discuss some implementation aspects which lead to increased efficiency while preserving the success rate in the optimization process. In particular, we show how employing a random selection strategy to discard particles during the computation improves the overall performance. Several benchmark problems and applications to image segmentation and Neural Networks training are used to validate and test the proposed method. A theoretical analysis allows to recover convergence guarantees under mild assumptions on the objective function. This is done by first approximating the evolution of the particles with a continuous-in-time dynamics, and then by taking the mean-field limit of such dynamics. Convergence to a global minimizer is finally proved at the mean-field level.

Original languageEnglish
Article number113859
JournalChaos, Solitons and Fractals
Early online date1 Aug 2023
Publication statusPublished - Sept 2023


  • Consensus-based optimization
  • Machine learning
  • Mean-field limit
  • Memory effects
  • Random selection
  • Stochastic particle methods

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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