Function minimisation

The main functionality of ConsensusBasedX.jl is function minimisation via Consensus-Based Optimisation. It assumes you have defined a function f(x::AbstractVector) that takes a single vector argument x of length D = length(x).

For instance, if D = 2, you can minimise f by running:

minimise(f, D = 2)

By default, minimise returns a Vector{Float64} of length D which contains the candidate to the global minimiser of f.

Note

You must always provide D.

Full example
using ConsensusBasedX
f(x) = ConsensusBasedX.Ackley(x, shift = 1)
minimise(f, D = 2) # should be close to [1, 1]

Using a config object

For more advanced usage, you will select several options. You can pass these as extra keyword arguments to minimise, or you can create a NamedTuple called config and pass that:

config = (; D = 2)
minimise(f, config)
Note

If you pass a Dict instead, it will be converted to a NamedTuple automatically.

This is a version of the full-code example above, using config instead:

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

Receiving extended output

It is possible to receive extended output from minimise by passing the option extended_output = true:

config = (; D = 2, extended_output = true)
minimise(f, config)

For more details, see Extended output.

Maximisation

ConsensusBasedX.jl also defines maximise for convenience. If you call

maximise(f, D = 2)

or 

config = (; D = 2)
maximise(f, config)

maximise will attempt to define g(x) = -f(x) and call minimise(g, config).

These are full-code examples using keywords

Full example
using ConsensusBasedX
f(x) = -ConsensusBasedX.Ackley(x, shift = 1)
maximise(f, D = 2) # should be close to [1, 1]

or using config

Full example
using ConsensusBasedX
f(x) = -ConsensusBasedX.Ackley(x, shift = 1)
config = (; D = 2, N = 20)
maximise(f, config) # should be close to [1, 1]

Method reference

ConsensusBasedX.maximise — Function
maximise(f; keywords...)
maximise(f, config::NamedTuple)

Maximise the function f using Consensus-Based Optimisation.

Attempts to define x -> -f(x) and calls the minimise routine. This might be better handled directly by the user (see Maximisation).

See also minimise.

source
ConsensusBasedX.minimise — Function
minimise(f; keywords...)
minimise(f, config::NamedTuple)

Minimise the function f using Consensus-Based Optimisation (see Function minimisation).

You must specify the dimension D of the problem. Other parameters (e.g. the number of particles N or the number of ensembles M) can also be specified; see Summary of options.

Examples

minimise(f, D = 2)
config = (; D = 2);
minimise(f, config)
minimise(f, D = 2, N = 20)
config = (; D = 2, N = 20);
minimise(f, config)
source