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).

Usage

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 par defines the number of parameters to be estimated (i.e., the dimension of the problem).

fn

The objective function to be minimised. It should accept a parameter vector (or list, depending on the wrapper) as first argument and return either a scalar value (single-objective) or a numeric vector (multi-objective).

gr

A function computing the gradient of fn. If NULL, a numerical approximation is used. Alternatively, a character string can specify the numerical gradient scheme: "central", "forward" (default), "backward", or "richardson".

...

Additional arguments passed to fn and gr.

lower

Lower bounds for parameters. One value or a vector of the same length as par. NA is treated as -Inf. Default is unconstrained.

upper

Upper bounds for parameters. One value or a vector of the same length as par. NA is treated as Inf. Default is unconstrained.

active

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

control

A list of control options. Common options include ncores, run, master, verbose, REPORT, restart.file, gradient, and gr.method. Additional solver-specific options may be passed through to the underlying optimiser.

hessian

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

parallel

Logical. Enable parallel computation (e.g., for replicated evaluations and/or numerical gradients) using up to control$ncores cores.

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) # \dontrun{}