Create a biased test function...

Description

Create a biased test function

Usage

bias_function(f, bias)

Arguments

Details

Returns a new biased test function defined as

g(x) = f(x) + bias.

Value

The biased test function.

Author(s)

Olaf Mersmann olafm@statistik.tu-dortmund.de

Covariance matrix adapting evolutionary strategy

Description

Global optimization procedure using a covariance matrix adapting evolutionary strategy.

Usage

cma_es(par, fn, ..., lower, upper, control=list())
cmaES(...)

Arguments

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:

fnscale

An 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.

maxit

The maximum number of iterations. Defaults to 100*D^2, where D is the dimension of the parameter space.

stopfitness

Stop if function value is smaller than or equal to stopfitness. This is the only way for the CMA-ES to “converge”.

keep.best

return the best overall solution and not the best solution in the last population. Defaults to true.

sigma

Initial variance estimates. Can be a single number or a vector of length D, where D is the dimension of the parameter space.

mu

Population size.

lambda

Number of offspring. Must be greater than or equal to mu.

weights

Recombination weights

damps

Damping for step-size

cs

Cumulation constant for step-size

ccum

Cumulation constant for covariance matrix

vectorized

Is the function fn vectorized?

ccov.1

Learning rate for rank-one update

ccov.mu

Learning rate for rank-mu update

diag.sigma

Save current step size \sigma in each iteration.

diag.eigen

Save current principle components of the covariance matrix C in each iteration.

diag.pop

Save current population in each iteration.

diag.value

Save function values of the current population in each iteration.

Value

cma_es: A list with components:

par

The best set of parameters found.

value

The value of fn corresponding to par.

counts

A two-element integer vector giving the number of calls to fn. The second element is always zero for call compatibility with optim.

convergence

An integer code. 0 indicates successful convergence. Possible error codes are

1

indicates that the iteration limit maxit had been reached.

message

Always set to NULL, provided for call compatibility with optim.

diagnostic

List containing diagnostic information. Possible elements are:

sigma

Vector containing the step size \sigma for each iteration.

eigen

d \times niter matrix containing the principle components of the covariance matrix C.

pop

An d\times\mu\times niter array containing all populations. The last dimension is the iteration and the second dimension the individual.

value

A niter \times \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 set to TRUE.

Author(s)

Olaf Mersmann olafm@statistik.tu-dortmund.de and David Arnu david.arnu@tu-dortmun.de

References

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

See Also

extract_population

Extract the iter-th population...

Description

Extract the iter-th population

Usage

extract_population(res, iter)

Arguments

Details

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.

Value

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...

Description

Random function

Usage

f_rand(x)

Arguments

Details

f(x) = runif(1)

Author(s)

Olaf Mersmann olafm@statistik.tu-dortmund.de

Rastrigin function...

Description

Rastrigin function

Usage

f_rastrigin(x)

Arguments

Author(s)

David Arnu david.arnu@tu-dortmund.de

Rosenbrock function...

Description

Rosenbrock function

Usage

f_rosenbrock(x)

Arguments

Author(s)

David Arnu david.arnu@tu-dortmund.de

Sphere function...

Description

Sphere function

Usage

f_sphere(x)

Arguments

Details

f(x) = x'x

Create a rotated test function...

Description

Create a rotated test function

Usage

rotate_function(f, M)

Arguments

Details

Returns a new rotated test function defined as

g(x) = f(Mx).

Value

The rotated test function.

Author(s)

Olaf Mersmann olafm@statistik.tu-dortmund.de

shift_function

Description

Returns a new function

g(x) = f(x - offset).

Usage

shift_function(f, offset)

Arguments

Value

The shifted test function.

Author(s)

Olaf Mersmann olafm@statistik.tu-dortmund.de