polarcbo.dynamic.CCBS

class polarcbo.dynamic.CCBS(x, V, beta=1.0, tau=0.1, mode='sampling', kernel=<polarcbo.functional.Gaussian_kernel object>, num_means=1, repulsion_scale=0.0)

Bases: ParticleDynamic

Cluster CBO class

This class implements the cluster CBO algorithm as described in [1]. The algorithm is based on the consensus-based dynamics (CBO) algorithm [2].

Parameters:

• x (array_like) – The initial positions of the particles. The shape of the array should be (num_particles, num_dimensions).

• V (obejective) – The objective function \(V(x)\) of the system.

• beta (float, optional) – The heat parameter \(\beta\) of the system. The default is 1.0.

• tau (float, optional) – The time constant \(\tau\) of the noise model. The default is 0.1.

• mode (str, optional) – The mode of the algorithm. The default is sampling.

• kernel (object, optional) – The kernel function \(K(x_i, x_j)\) that is used to compute the mean \(\mathsf{m}(x_i)\). The default is Gaussian_kernel().

• num_means (int, optional) – The number of means \(\mathsf{m}(x_i)\) that are used to compute the polarized mean \(\mathsf{m}_\beta(x_i)\). The default is 1.

• repulsion_scale (float, optional) – The repulsion scale \(\lambda\) of the repulsion term. The default is 0.0.

References

[1]

Bungert, L., Wacker, P., & Roith, T. (2022). Polarized consensus-based dynamics for optimization and sampling. arXiv preprint arXiv:2211.05238.

[2]

Pinnau, R., Totzeck, C., Tse, O., & Martin, S. (2017). A consensus-based model for global optimization and its mean-field limit. Mathematical Models and Methods in Applied Sciences, 27(01), 183-204.

See also

CBO

Consensus-based dynamics

PolarCBS

Polarized CBS

CCBO

Cluster CBO