R/select_neighbors.R

In loelschlaeger/locglob: Variable Neighborhood Trust Region Search

#' Select neighbors
#'
#' @description
#' Function that selects neighbors around a given point \code{x}.
#'
#' @inheritParams vntrs
#' @param x
#' A point in the domain of \code{f}.
#' @param neighborhood_expansion
#' A scaling factor, specifying the expansion of the neighborhood.
#'
#' @return
#' A list points in the domain of \code{f} which neighbors of \code{x}.
#'
#' @keywords
#' internal
#'
#' @importFrom stats runif

select_neighbors <- function(f, x, neighborhood_expansion, controls) {
  ### list of neighbors
  z <- list()

  ### compute eigenvectors and eigenvalues of the Hessian of 'f'
  H_f <- f(x)$hessian
  H_f_eig <- eigen(H_f)
  v <- H_f_eig$vectors
  lambda <- H_f_eig$values

  ### set selection probabilities
  p_v <- exp(controls$beta * lambda / neighborhood_expansion)
  p_v <- p_v / sum(p_v)

  ### select neighbors
  for (j in 1:controls$neighbors) {
    alpha <- stats::runif(1, 0.75, 1)
    dir <- sample(c(-1, 1), 1)

    ### select eigenvector
    v_i <- v[, sample(1:length(lambda), size = 1, prob = p_v)]

    ### compute neighbor value
    z[[j]] <- x + alpha * neighborhood_expansion * dir * v_i
  }

  return(z)
}