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Variable neighborhood trust region search

vntrs.Rd

This function performs variable neighborhood trust region search.

Usage

vntrs(f, npar, minimize = TRUE, controls = NULL, quiet = TRUE, seed = NULL)

Arguments

f

A function that computes value, gradient, and Hessian of the function to be optimized and returns them as a named list with elements value, gradient, and hessian.

npar

The number of parameters of f.

minimize

If TRUE, f gets minimized. If FALSE, maximized.

controls

Either NULL or a named list with the following elements. Missing elements are set to the default values in parentheses.

  • init_runs (5): The number of initial searches.

  • init_min (-1): The minimum argument value for the random initialization.

  • init_max (1): The maximum argument value for the random initialization.

  • init_iterlim (20): The number of iterations for the initial searches.

  • neighborhoods (5): The number of nested neighborhoods.

  • neighbors (5): The number of neighbors in each neighborhood.

  • beta (0.05): A non-negative weight factor to account for the function's curvature in the selection of the neighbors. If beta = 0, the curvature is ignored. The higher the value, the higher the probability of selecting a neighbor in the direction of the highest function curvature.

  • iterlim (1000): The maximum number of iterations to be performed before the local search is terminated.

  • tolerance (1e-6): A positive scalar giving the tolerance for comparing different optimal arguments for equality.

  • time_limit (NULL): The time limit in seconds for the algorithm.

quiet

If TRUE, progress messages are suppressed.

seed

Set a seed for the sampling of the random starting points.

Value

A data frame. Each row contains information of an identified optimum. The first npar columns "p1",...,"p<npar>" store the argument values, the next column "value" has the optimal function values and the last column "global" contains TRUE for global optima and FALSE for local optima.

References

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

Examples

rosenbrock <- function(x) {
  stopifnot(is.numeric(x))
  stopifnot(length(x) == 2)
  f <- expression(100 * (x2 - x1^2)^2 + (1 - x1)^2)
  g1 <- D(f, "x1")
  g2 <- D(f, "x2")
  h11 <- D(g1, "x1")
  h12 <- D(g1, "x2")
  h22 <- D(g2, "x2")
  x1 <- x[1]
  x2 <- x[2]
  f <- eval(f)
  g <- c(eval(g1), eval(g2))
  h <- rbind(c(eval(h11), eval(h12)), c(eval(h12), eval(h22)))
  list(value = f, gradient = g, hessian = h)
}
vntrs(f = rosenbrock, npar = 2, seed = 1, controls = list(neighborhoods = 1))
#>   p1        p2        value global
#> 1  1 0.9999999 2.114623e-15   TRUE