Adaptative Hierarchical Recombination Evolutionary Strategy (AHR-ES) for derivative-free and black-box optimization

This function performs the optimization of a function using the Adaptative Hierarchical Recombination Evolutionary Strategy (AHR-ES, Oliveros & Shin, 2015).

ahres(
  par,
  fn,
  gr = NULL,
  ...,
  lower = -Inf,
  upper = +Inf,
  active = NULL,
  control = list(),
  hessian = FALSE,
  parallel = FALSE
)

Arguments

par

A numeric vector or list. The length of the par argument defines the number of parameters to be estimated (i.e. the dimension of the problem).

fn

The function to be minimized.

gr

A function computing the gradient of fn. If NULL, a numerical approximation of the gradient is used. It can be also a character specifying the method for the computation of the numerical gradient: 'central', 'forward' (the default), 'backward' or 'richardson'.

...

Additional parameters to be passed to fn.

lower

Lower threshold value(s) for parameters. One value or a vector of the same length as par. If one value is provided, it is used for all parameters. NA means -Inf. By default -Inf is used (unconstrained).

upper

Upper threshold value(s) for parameters. One value or a vector of the same length as par. If one value is provided, it is used for all parameters. NA means Inf. By default Inf is used (unconstrained).

active

Boolean vector of the same length as par, indicating if the parameter is used in the optimization (TRUE) or hold at a fixed value (FALSE).

control

Parameter for the control of the algorithm itself, see details.

hessian

Logical. Should a numerically differentiated Hessian matrix be returned? Currently not implemented.

parallel

Logical. Use parallel computation numerical of gradient?

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 and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.

convergence

An integer code. 0 indicates successful completion.

message

A character string giving any additional information returned by the optimizer, or NULL.

hessian

Only if argument hessian is true. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.

See also

Other optimisers: calibrate(), optim2(), optimh()

Author

Ricardo Oliveros-Ramos

Examples

if (FALSE) ahres(par=rep(1, 5), fn=sphereN)