Initialization of numerical optimization

The {ino} R package provides a framework for analyzing the role of initialization in numerical optimization. It allows for systematic comparisons of different initialization strategies and optimization algorithms using a unified R6 object called Nop. For detailed examples and usage guidance, please have a look at the package vignettes.

Installation

You can install the released version from CRAN with:

install.packages("ino")

Example

The Ackley function has multiple local minima and one global minimum at the origin. We define

1. the numerical optimization problem as a Nop object,
2. two optimization algorithms stats::nlm() and stats::optim(), and
3. 40 randomly drawn initial values:

library("ino")
set.seed(1)
Nop_ackley <- Nop$new(f = TestFunctions::TF_ackley, npar = 2)$
  set_optimizer(optimizeR::Optimizer$new("stats::nlm"))$
  set_optimizer(optimizeR::Optimizer$new("stats::optim"))$
  initialize_random(runs = 40)

We can visualize the function surface along with the initial values:

library("ggplot2")
Nop_ackley |> autoplot()

Next, we optimize the function via the previously defined initial values and optimizers:

Nop_ackley$optimize()

In this example, stats::nlm() appears to be both faster…

Nop_ackley$results |> 
  ggplot2::autoplot("seconds", group_by = "optimizer", relative = TRUE) +
  ggplot2::scale_x_continuous(labels = scales::percent_format()) +
  ggplot2::labs(
    "x" = "optimization time relative to overall median",
    "y" = "optimizer"
  )

… and more effective at locating the global minimum:

Nop_ackley$optima(digits = 2, group_by = "optimizer")
#> $`stats::nlm`
#> # A tibble: 5 × 2
#>   value     n
#>   <dbl> <int>
#> 1  0       13
#> 2  2.58    13
#> 3  3.57    10
#> 4  5.38     3
#> 5  4.88     1
#> 
#> $`stats::optim`
#> # A tibble: 5 × 2
#>   value     n
#>   <dbl> <int>
#> 1  2.58    17
#> 2  0       12
#> 3  3.57     5
#> 4  4.88     3
#> 5  5.38     3
#> 
#> attr(,"class")
#> [1] "Nop_optima" "group_by"   "list"

Overall, (only) 25% of of the initializations successfully converged to the global minimum.

Contact

Have a question, found a bug, request a feature, want to contribute? Please file an issue.

Related R packages

• The {trackopt} package tracks parameter value, gradient, and Hessian at each iteration of numerical optimizers in R. This can be useful for analyzing optimization progress, diagnosing issues, and studying convergence behavior.

• The {optimizeR} package provides a unified object-oriented framework for numerical optimizers in R. Allows for both minimization and maximization with any optimizer, optimization over more than one function argument, measuring of computation time, setting a time limit for long optimization tasks.

• The {ao} package implements an iterative process that optimizes a function by alternately performing restricted optimization over parameter subsets. Instead of joint optimization, it breaks the optimization problem down into simpler sub-problems. This approach can make optimization feasible when joint optimization is too difficult.

mirror server hosted at Truenetwork, Russian Federation.