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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.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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