Package {vntrs}

Title: Variable Neighborhood Trust Region Search
Version: 0.2.1
Description: Implements the variable neighborhood trust region search (VNTRS) algorithm for nonlinear global optimization, following Bierlaire et al. (2009) "A Heuristic for Nonlinear Global Optimization" <doi:10.1287/ijoc.1090.0343>. The method combines neighborhood exploration with a trust-region framework to search the solution space efficiently. It can terminate a local search early when the iterates converge toward a previously visited local optimum or when further improvement within the current region is unlikely. The algorithm can also be used to identify multiple local optima.
URL: https://loelschlaeger.de/vntrs/
BugReports: https://github.com/loelschlaeger/vntrs/issues
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.3.3
Imports: checkmate, oeli (≥ 0.7.5), Rcpp
LinkingTo: Rcpp, RcppArmadillo
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: yes
Packaged: 2026-05-07 15:43:18 UTC; Lennart Oelschläger
Author: Lennart Oelschläger ORCID iD [aut, cre]
Maintainer: Lennart Oelschläger <oelschlaeger.lennart@gmail.com>
Repository: CRAN
Date/Publication: 2026-05-07 17:50:34 UTC

vntrs: Variable Neighborhood Trust Region Search

Description

logo

Implements the variable neighborhood trust region search (VNTRS) algorithm for nonlinear global optimization, following Bierlaire et al. (2009) "A Heuristic for Nonlinear Global Optimization" doi:10.1287/ijoc.1090.0343. The method combines neighborhood exploration with a trust-region framework to search the solution space efficiently. It can terminate a local search early when the iterates converge toward a previously visited local optimum or when further improvement within the current region is unlikely. The algorithm can also be used to identify multiple local optima.

Author(s)

Maintainer: Lennart Oelschläger oelschlaeger.lennart@gmail.com (ORCID)

See Also

Useful links:

Examples

rosenbrock <- function(x) 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
vntrs(f = rosenbrock, npar = 2)

Variable neighborhood trust region search

Description

Run the variable neighborhood trust region search algorithm.

Usage

vntrs(
  f,
  npar,
  minimize = TRUE,
  init_runs = 5L,
  init_min = -1,
  init_max = 1,
  init_iterlim = 20L,
  neighborhoods = 5L,
  neighbors = 5L,
  beta = 0.05,
  iterlim = 100L,
  tolerance = 1e-06,
  inferior_tolerance = 1e-06,
  time_limit = NULL,
  cores = 1L,
  lower = NULL,
  upper = NULL,
  collect_all = FALSE,
  quiet = TRUE
)

Arguments

f

[function]
A function that accepts a numeric parameter vector and returns either

  • a numeric objective value, or

  • a list with value and optional gradient and hessian components.

Missing derivatives are approximated by finite differences.

npar

[integer(1)]
The number of parameters of f.

minimize

[logical(1)]
If TRUE, minimize f; otherwise, maximize it.

init_runs

[integer(1)]
Number of random starting points for the initialization stage.

init_min, init_max

[numeric(1)]
Lower and upper bounds for the uniform initialization range.

init_iterlim

[integer(1)]
Maximum trust-region iterations during initialization.

neighborhoods

[integer(1)]
Number of neighborhood expansions to try.

neighbors

[integer(1)]
Number of trial points sampled in each neighborhood.

beta

[numeric(1)]
Non-negative scaling factor for neighborhood expansion.

iterlim

[integer(1)]
Maximum trust-region iterations during the main search.

tolerance

[numeric(1)]
Minimum Euclidean distance for two optima to be treated as distinct.

inferior_tolerance

[numeric(1)]
Maximum objective-value gap from the best known solution before a local optimum is discarded early.

time_limit

[numeric(1) | NULL]
Optional time limit in seconds. If reached, the search stops early with a warning.

cores

[integer(1)]
Number of CPU cores used for parallel evaluation.

lower, upper

[numeric(npar) | NULL]
Optional lower and upper parameter bounds. Use NULL for unbounded dimensions.

collect_all

[logical(1)]
If TRUE, keep all converged local optima and disable early stopping for optima that are inferior to the best known solution.

quiet

[logical(1)]
If TRUE, suppress progress messages.

Value

A data.frame summarizing the identified optima or NULL if none could be determined.

References

Bierlaire et al. (2009) "A Heuristic for Nonlinear Global Optimization" doi:10.1287/ijoc.1090.0343.

Examples

rosenbrock <- function(x) 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
vntrs(f = rosenbrock, npar = 2)