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Method parameters

You can change any of these parameters by passing them as keywords to the minimise routine.

Number of particles

ConsensusBasedX.jl uses N = 20 particles by default. At each iteration of the method, the function f is evaluated at the position of each particle.

Tip

Using more particles is likely to yield better results, but it will increase the computational cost of the minimisation.

Number of ensembles

ConsensusBasedX.jl uses M = 1 ensembles by default. Each ensemble will perform its own minimisation of f, and the final results will be averaged.

Tip

Using more ensembles is likely to yield better results, but it will increase the computational cost of the minimisation.

Time step

ConsensusBasedX.jl uses a time step of Δt = 0.1 by default. The evolution of the particles is given by a certain stochastic differential equation, which is solved using an Euler-Maruyama scheme with time step Δt.

Tip

Reducing Δt will require more iterations of the method to converge, but will provide additional stability. Reduce Δt only if your minimisation "blows up" (returns unusually large numbers, Inf, or NaN).

Consensus parameters

Consensus-based optimisation requires three parameters:

  • σ::Real = 1 is the noise strengh;
  • λ::Real = 1 is the drift strengh;
  • α::Real = 10 is the exponential weight parameter.
Tip

A low value of σ and a high value of λ make the particles converge towards the consensus point more directly; this is a good idea if you have a very good guess for the global minimiser (see Particle initialisation). A high value of σ and a low value of λ make the particles explore more of the landscape before converging, which is useful if your initial guess is bad. Similarly, a higher value of α biases the consensus point towards the current best particle, which is only desirable if your initial guess is good.

Full example
using ConsensusBasedX
f(x) = ConsensusBasedX.Ackley(x, shift = 1)
config = (; D = 2, N = 20, M = 1, Δt = 0.01, σ = 1, λ = 1, α = 10)
minimise(f, config) # should be close to [1, 1]