A consensus-based model for global optimization and its mean-field limit

R. Pinnau, C. Totzeck, O. Tse, S. Martin

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39 Citations (Scopus)
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We introduce a novel first-order stochastic swarm intelligence (SI) model in the spirit of consensus formation models, namely a consensus-based optimization (CBO) algorithm, which may be used for the global optimization of a function in multiple dimensions. The CBO algorithm allows for passage to the mean-field limit, which results in a nonstandard, nonlocal, degenerate parabolic partial differential equation (PDE). Exploiting tools from PDE analysis we provide convergence results that help to understand the asymptotic behavior of the SI model. We further present numerical investigations underlining the feasibility of our approach.

Original languageEnglish
Pages (from-to)183-204
Number of pages22
JournalMathematical Models & Methods in Applied Sciences
Issue number1
Publication statusPublished - 2017


  • Consensus formation
  • global optimization
  • interacting system
  • mean-field limit
  • stochastic differential equations


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