If you’re looking for a way to standardize the inputs and outputs of numerical optimizers in R, you might find the {optimizeR} package useful. This package provides a unified framework for representing the inputs and outputs of different optimizers. It does not actually implement any optimizer functions itself.
When working with popular R optimizers such as stats::nlm()
and stats::optim(),
it can be challenging to compare their results due to inconsistencies in
function arguments and output labels. For instance,
stats::nlm() uses f as its function argument
and p as the argument for initial values, while
stats::optim() uses fn for its function
argument and par for initial values. Additionally, the
optimal parameters and function values are labeled differently, with
estimate and minimum used in
stats::nlm() and par and value in
stats::optim(). And all is different again with, for
example, pracma::nelder_mead().
This inconsistency is frustrating, especially if one wants to apply and
compare different optimizers.
To standardize the inputs and outputs of different R optimizers and
make them easier to apply and compare, you can define them using the
define_optimizer() function and then apply them using
apply_optimizer(). This way, the inputs and outputs will
always be in a consistent format across different optimizers.
For demonstration, say we want to minimize the Ackley function …
f_ackley <- function(x) {
stopifnot(is.numeric(x), length(x) == 2)
-20 * exp(-0.2 * sqrt(0.5 * (x[1]^2 + x[2]^2))) -
exp(0.5 * (cos(2 * pi * x[1]) + cos(2 * pi * x[2]))) + exp(1) + 20
}… and compare the performance of three optimizers:
stats::nlm(), stats::optim(), and
pracma::nelder_mead(). The first two are already
pre-specified …
optimizer_nlm()
#> <optimizer 'stats::nlm'>
optimizer_optim()
#> <optimizer 'stats::optim'>… and for the latter (as for any other optimizer you like) we can use the general constructor:
optimizer_nelder_mead <- define_optimizer(
optimizer = pracma::nelder_mead,
objective = "fn",
initial = "x0",
value = "fmin",
parameter = "xmin"
)Now we optimize (with initial parameter vector
initial = c(-1, 1)):
results <- lapply(
list(optimizer_nlm(), optimizer_optim(), optimizer_nelder_mead),
apply_optimizer,
objective = f_ackley,
initial = c(-1, 1)
)
names(results) <- c("stats::nlm", "stats::optim", "pracma::nelder_mead")In the optimization output, value and
parameter consistently denote the optimal function values
and the optimal parameters, while additional optimizer-specific outputs
are preserved. The optimization time in seconds, seconds,
and the initial parameter vector, initial, are added:
str(results)
#> List of 3
#> $ stats::nlm :List of 7
#> ..$ value : num 1.66e-06
#> ..$ parameter : num [1:2] -2.91e-07 5.08e-07
#> ..$ seconds : num 0.0305
#> ..$ initial : num [1:2] -1 1
#> ..$ gradient : num [1:2] -0.00824 0.0144
#> ..$ code : int 2
#> ..$ iterations: int 33
#> $ stats::optim :List of 7
#> ..$ value : num 3.57
#> ..$ parameter : num [1:2] -0.969 0.969
#> ..$ seconds : num 0.000356
#> ..$ initial : num [1:2] -1 1
#> ..$ counts : Named int [1:2] 45 NA
#> .. ..- attr(*, "names")= chr [1:2] "function" "gradient"
#> ..$ convergence: int 0
#> ..$ message : NULL
#> $ pracma::nelder_mead:List of 7
#> ..$ value : num 0
#> ..$ parameter : num [1:2] 0 0
#> ..$ seconds : num 0.00217
#> ..$ initial : num [1:2] -1 1
#> ..$ count : num 111
#> ..$ convergence: num 0
#> ..$ info :List of 2
#> .. ..$ solver : chr "Nelder-Mead"
#> .. ..$ restarts: num 0By the way, are you surprised to see that value for
stats::optim() is different from the other optimizers? It
seems that this optimizer has become trapped in a local minimum. If you
are interested in exploring the initialization problem in numerical
optimization, you may find the {ino} R package to be
useful.
You can install the released version of {optimizeR} from CRAN with:
install.packages("optimizeR")… and the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("loelschlaeger/optimizeR")Have a question, found a bug, request a feature, want to contribute? Please file an issue on GitHub.