CMAEvolutionStrategy.NoiseHandling — Type
NoiseHandling(ασ = 1.1, callback = s -> s > 0,
              r = .3, ϵ = 0., θ = .5, c = .3)

The standard settings may work well for noisy objective functions. To avoid premature convergence due to too fast decrease of sigma, there is the option noise_handling = CMAEvolutionStrategy.NoiseHandling(ασ = 1.1, callback = s -> s > 0). Choose ασ such that sigma decreases slowly (and does not diverge). The callback function can be used to change the objective function, e.g. increase the measurement duration, if this leads to smaller noise. The variable s indicates whether CMA-ES can handle the current level of noise: s > 0 indicates that the noise level is too high. Whenever the callback returns true, sigma gets multiplied by ασ, which is the case when s > 0, with the default callback.

For details on noise handling see Hansen 2009.

CMAEvolutionStrategy.minimize — Method
minimize(f, x0, s0;
         lower = nothing,
         upper = nothing,
         constraints = _constraints(lower, upper),
         noise_handling = nothing,
         popsize = 4 + floor(Int, 3*log(length(x0))),
         callback = (o, y, fvals, perm) -> nothing,
         parallel_evaluation = false,
         multi_threading = false,
         verbosity = 1,
         seed = rand(UInt),
         logger = BasicLogger(x0, verbosity = verbosity, callback = callback),
         maxtime = nothing,
         maxiter = nothing,
         maxfevals = nothing,
         stagnation = 100 + 100 * length(x0)^1.5/popsize,
         ftarget = nothing,
         xtol = nothing,
         ftol = 1e-11)

Minimize function f starting around x0 with initial covariance s0 * I under box constraints lower .<= x0 .<= upper, where x0, lower and upper are vectors of the same length or nothing.

The result is an Optimizer object from which e.g. xbest, fbest or population_mean can be extracted.

If parallel_evaluation = true, the objective function f receives matrices of n rows (n = length(x0)) and popsize columns and should return a vector of length popsize. To use multi-threaded parallel evaluation of the objective function, set multi_threading = true and start julia with multiple threads (c.f. julia manual for the multi-threading setup).

Example 1

using CMAEvolutionStrategy

function rosenbrock(x)
   n = length(x)
   sum(100 * (x[2i-1]^2 - x[2i])^2 + (x[2i-1] - 1)^2 for i in 1:div(n, 2))
end

result = minimize(rosenbrock, zeros(6), 1.)

xbest(result) # show best input x

fbest(result) # show best function value

population_mean(result) # show mean of final population

Example 2

# continuation of Example 1 with parallel evaluation

rosenbrock_parallel(x) = [rosenbrock(xi) for xi in eachcol(x)]

result = minimize(rosenbrock_parallel, zeros(6), 1., parallel_evaluation = true)