polarcbo.dynamic.CBO

class polarcbo.dynamic.CBO(x, V, noise, beta=1.0, noise_decay=0.0, diff_exp=1.0, tau=0.1, sigma=1.0, lamda=1.0, M=None, overshoot_correction=False, heavi_correction=False)

Bases: ParticleDynamic

Consensus-based optimization (CBO) class

This class implements the CBO algorithm as described in [1]. The algorithm is a particle dynamic algorithm that is used to minimize the objective function \(V(x)\).

Parameters:

• x (array_like, shape (J, d)) – The initial positions of the particles. For a system of \(J\) particles, the i-th row of this array x[i,:] represents the position \(x_i\) of the i-th particle.

• 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.

• noise (noise_model, optional) – The noise model that is used to compute the noise vector. The default is normal_noise(tau=0.1).

• noise_decay (float, optional) – The decay parameter \(\lambda\) of the noise model. The default is 0.0.

• diff_exp (float, optional) – The exponent \(\alpha\) of the difference vector \(x_i - \mathsf{m}(x_i)\). The default is 1.0.

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

• sigma (float, optional) – The parameter \(\sigma\) of the noise model. The default is 1.0.

• lamda (float, optional) – The decay parameter \(\lambda\) of the noise model. The default is 1.0.

• M (int, optional) – The number of particles that are used to compute the batch mean \(\mathsf{m}(x_i)\) as described in [2]. The default is None. If None, then \(M = J\).

• overshoot_correction (bool, optional) – If True, then the overshoot correction is used as described in [3]. The default is False.

• heavi_correction (bool, optional) – If True, then the Heaviside correction is used as described in [4]. The default is False.

References

[1]

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.

[2]

Carrillo, J. A., Jin, S., Li, L., & Zhu, Y. (2021). A consensus-based global optimization method for high dimensional machine learning problems. ESAIM: Control, Optimisation and Calculus of Variations, 27, S5.

[3]

ref missing

[4]

ref missing

step(time=0.0)

Performs one step of the CBO algorithm.

Parameters:

time (float, optional) – The current time of the algorithm. The default is 0.0.

compute_mean(ind=None)

Computes the mean of the particles.

Parameters:

ind (array_like, optional) – The indices of the particles that are used to compute the mean. The default is None. If None, then all particles are used.

Returns:

m_beta – The mean of the particles.

Return type:

numpy.ndarray