Global optimization procedure using a covariance matrix adapting evolutionary strategy.
Initial values for the parameters to be optimized over.
A function to be minimized (or maximized), with first argument the vector of parameters over which minimization is to take place. It should return a scalar result.
Further arguments to be passed to
Lower bounds on the variables.
Upper bounds on the variables.
A list of control parameters. See ‘Details’.
cma_es: Note that arguments after
... must be matched exactly.
By default this function performs minimization, but it will
control$fnscale is negative. It can usually be
used as a drop in replacement for
optim, but do note, that
no sophisticated convergence detection is included. Therefore you
need to choose
If you set
fn will be passed matrix
arguments during optimization. The columns correspond to the
lambda new individuals created in each iteration of the
ES. In this case
fn must return a numeric vector of
lambda corresponding function values. This enables you to
do up to
lambda function evaluations in parallel.
control argument is a list that can supply any of the
An overall scaling to be applied to the value
fn during optimization. If negative,
turns the problem into a maximization problem. Optimization is
The maximum number of iterations. Defaults to 100*D^2, where D is the dimension of the parameter space.
Stop if function value is smaller than or
stopfitness. This is the only way for the CMA-ES
return the best overall solution and not the best solution in the last population. Defaults to true.
Inital variance estimates. Can be a single number or a vector of length D, where D is the dimension of the parameter space.
Number of offspring. Must be greater than or
Damping for step-size
Cumulation constant for step-size
Cumulation constant for covariance matrix
Is the function
Learning rate for rank-one update
Learning rate for rank-mu update
Save current step size sigma in each iteration.
Save current principle components of the covariance matrix C in each iteration.
Save current population in each iteration.
Save function values of the current population in each iteration.
cma_es: A list with components:
The best set of parameters found.
The value of
fn corresponding to
A two-element integer vector giving the number of calls
fn. The second element is always zero for call
An integer code.
0 indicates successful
convergence. Possible error codes are
indicates that the iteration limit
had been reached.
Always set to
NULL, provided for call
List containing diagnostic information. Possible elements are:
Vector containing the step size sigma for each iteration.
d * niter matrix containing the principle components of the covariance matrix C.
An d * mu * niter array containing all populations. The last dimension is the iteration and the second dimension the individual.
A niter x mu matrix containing the function values of each population. The first dimension is the iteration, the second one the individual.
These are only present if the respective diagnostic control variable is
Hansen, N. (2006). The CMA Evolution Strategy: A Comparing Review. In J.A. Lozano, P. Larranga, I. Inza and E. Bengoetxea (eds.). Towards a new evolutionary computation. Advances in estimation of distribution algorithms. pp. 75-102, Springer
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