| Title: | Covariance Matrix Adapting Evolutionary Strategy |
|---|---|
| Description: | Single objective optimization using a CMA-ES. |
| Authors: | Heike Trautmann <[email protected]> and Olaf Mersmann <[email protected]> and David Arnu <[email protected]> |
| Maintainer: | Olaf Mersmann <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0-12 |
| Built: | 2024-12-23 06:39:21 UTC |
| Source: | CRAN |
Create a biased test function
bias_function(f, bias)bias_function(f, bias)
f |
test function |
bias |
bias value. |
Returns a new biased test function defined as
The biased test function.
Olaf Mersmann [email protected]
Global optimization procedure using a covariance matrix adapting evolutionary strategy.
cma_es(par, fn, ..., lower, upper, control=list()) cmaES(...)cma_es(par, fn, ..., lower, upper, control=list()) cmaES(...)
par |
Initial values for the parameters to be optimized over. |
fn |
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 |
Lower bounds on the variables. |
upper |
Upper bounds on the variables. |
control |
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
maximize if 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 maxit appropriately.
If you set vectorize==TRUE, 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.
The control argument is a list that can supply any of the
following components:
fnscaleAn overall scaling to be applied to the value
of fn during optimization. If negative,
turns the problem into a maximization problem. Optimization is
performed on fn(par)/fnscale.
maxitThe maximum number of iterations. Defaults to
, where is the dimension of the parameter space.
stopfitnessStop if function value is smaller than or
equal to stopfitness. This is the only way for the CMA-ES
to “converge”.
return the best overall solution and not the best solution in the last population. Defaults to true.
sigmaInitial variance estimates. Can be a single
number or a vector of length , where is the dimension
of the parameter space.
muPopulation size.
lambdaNumber of offspring. Must be greater than or
equal to mu.
weightsRecombination weights
dampsDamping for step-size
csCumulation constant for step-size
ccumCumulation constant for covariance matrix
vectorizedIs the function fn vectorized?
ccov.1Learning rate for rank-one update
ccov.muLearning rate for rank-mu update
diag.sigmaSave current step size
in each iteration.
diag.eigenSave current principle components
of the covariance matrix in each iteration.
diag.popSave current population in each iteration.
diag.valueSave 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 par.
A two-element integer vector giving the number of calls
to fn. The second element is always zero for call
compatibility with optim.
An integer code. 0 indicates successful
convergence. Possible error codes are
1indicates that the iteration limit maxit
had been reached.
Always set to NULL, provided for call
compatibility with optim.
List containing diagnostic information. Possible elements are:
Vector containing the step size
for each iteration.
matrix containing the
principle components of the covariance matrix .
An array
containing all populations. The last dimension is the iteration
and the second dimension the individual.
A 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
set to TRUE.
Olaf Mersmann [email protected] and David Arnu [email protected]
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
Extract the iter-th population
extract_population(res, iter)extract_population(res, iter)
res |
A |
iter |
Which population to return. |
Return the population of the iter-th iteration of the
CMA-ES algorithm. For this to work, the populations must be saved
in the result object. This is achieved by setting
diag.pop=TRUE in the control list. Function values
are included in the result if present in the result object.
A list containing the population as the par element
and possibly the function values in value if they are
present in the result object.
Random function
f_rand(x)f_rand(x)
x |
parameter vector. |
Olaf Mersmann [email protected]
Rastrigin function
f_rastrigin(x)f_rastrigin(x)
x |
parameter vector. |
David Arnu [email protected]
Rosenbrock function
f_rosenbrock(x)f_rosenbrock(x)
x |
parameter vector. |
David Arnu [email protected]
Sphere function
f_sphere(x)f_sphere(x)
x |
parameter vector. |
Create a rotated test function
rotate_function(f, M)rotate_function(f, M)
f |
test function. |
M |
orthogonal square matrix defining the rotation. |
Returns a new rotated test function defined as
The rotated test function.
Olaf Mersmann [email protected]
Returns a new function
shift_function(f, offset)shift_function(f, offset)
f |
test function |
offset |
offset. |
The shifted test function.
Olaf Mersmann [email protected]