# cma_es

0th

Percentile

##### Covariance matrix adapting evolutionary strategy

Global optimization procedure using a covariance matrix adapting evolutionary strategy.

Keywords
optimize
##### Usage
cma_es(par, fn, ..., lower, upper, control=list())
cmaES(...)
##### Arguments
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 fn.
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: 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 Inital 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 : 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$d * niter$matrix containing the principle components of the covariance matrix$C$. pop An$d * mu * niter$array containing all populations. The last dimension is the iteration and the second dimension the individual. value 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 set to TRUE.

##### 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

extract_population