Particle initialisation

ConsensusBasedX.jl needs to initialise particles in order to perform function minimisation.

Default initialisation

If no options are provided, ConsensusBasedX.jl initialises its particles by sampling a standard normal distribution (a normal distribution with zero mean and unit variance).

Initial guess

If you have an initial guess for the global minimiser of the function f, you can pass the option initial_guess (or initial_mean). This can be a Real, if you want to use the same value for each coordinate of the initial guess, or an AbstractVector of size size(initial_guess) = (D,). The particles will be initialised by sampling a normal distribution with mean initial_guess/initial_mean and unit variance.

using ConsensusBasedX
f(x) = ConsensusBasedX.Ackley(x, shift = 1)
config = (; D = 2, N = 20, M = 1, initial_guess = [1.1, 0.9])
minimise(f, config) # should be close to [1, 1]

Specify a normal distribution

If you want to specify the variance of the normal distribution sampled around initial_guess/initial_mean, you can pass the option initial_variance (or initial_covariance). This can be a Real, if you want an isotropic distribution, an AbstractVector of size size(initial_variance) = (D,), if you want to specify the variance along each axis, or an AbstractMatrix of size size(initial_variance) = (D, D), if you want a general multivariate normal distribution.

using ConsensusBasedX

f(x) = ConsensusBasedX.Ackley(x, shift = 1)

config = (; D = 2, N = 20, initial_variance = 5)
minimise(f, config) # should be close to [1, 1]

Specify a uniform distribution

You can instead initialise the particles by sampling uniformly from a box around initial_guess/initial_mean. To do so, pass the option initialisation = :uniform.

using ConsensusBasedX
f(x) = ConsensusBasedX.Ackley(x, shift = 1)
config = (; D = 2, N = 20, initialisation = :uniform)
minimise(f, config) # should be close to [1, 1]

You can specify the radius of the box with the option initial_radius, or the diameter with initial_diameter. This can be a Real, if you want a hypercube, or an AbstractVector of size size(initial_guess) = (D,), if you want a hyperbox with different dimensions along each axis.

using ConsensusBasedX
f(x) = ConsensusBasedX.Ackley(x, shift = 1)
config = (; D = 2, N = 20, initial_radius = 3)
minimise(f, config) # should be close to [1, 1]

Custom initialisation

You can provide the initial position of the particles direcly by passing the option initial_particles. This must be an AbstractArray{<:Real,3} of size (D, N, M).

using ConsensusBasedX
f(x) = ConsensusBasedX.Ackley(x, shift = 1)
config = (; D = 2, N = 20, M = 1, initial_particles = rand(2, 20, 1))
minimise(f, config) # should be close to [1, 1]