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##
## h o o k e j e e v e s . R Hooke-Jeeves Minimization Algorithm
##
hjkb <- function(par, fn, lower = -Inf, upper = Inf, control = list(), ...) {
if (!is.numeric(par))
stop("Argument 'par' must be a numeric vector.", call. = FALSE)
n <- length(par)
if (n == 1)
stop("For univariate functions use some different method.", call. = FALSE)
if(!is.numeric(lower) || !is.numeric(upper))
stop("Lower and upper limits must be numeric.", call. = FALSE)
if (length(lower) == 1) lower <- rep(lower, n)
if (length(upper) == 1) upper <- rep(upper, n)
if (!all(lower <= upper))
stop("All lower limits must be smaller than upper limits.", call. = FALSE)
if (!all(lower <= par) || !all(par <= upper))
stop("Infeasible starting values -- check limits.", call. = FALSE)
#-- Control list handling ----------
cntrl <- list(tol = 1.e-06,
maxfeval = Inf, # set to Inf if no limit wanted
maximize = FALSE, # set to TRUE for maximization
target = Inf, # set to Inf for no restriction
info = FALSE) # for printing interim information
nmsCo <- match.arg(names(control), choices = names(cntrl), several.ok = TRUE)
if (!is.null(names(control))) cntrl[nmsCo] <- control
tol <- cntrl$tol;
maxfeval <- cntrl$maxfeval
maximize <- cntrl$maximize
target <- cntrl$target
info <- cntrl$info
scale <- if (maximize) -1 else 1
fun <- match.fun(fn)
f <- function(x) scale * fun(x, ...)
#-- Setting steps and stepsize -----
nsteps <- floor(log2(1/tol)) # number of steps
steps <- 2^c(-(0:(nsteps-1))) # decreasing step size
dir <- diag(1, n, n) # orthogonal directions
x <- par # start point
fx <- fbest <- f(x) # smallest value so far
fcount <- 1 # counts number of function calls
if (info) cat("step\tnofc\tfmin\txpar\n") # info header
#-- Start the main loop ------------
ns <- 0
while (ns < nsteps && fcount < maxfeval && abs(fx) < target) {
ns <- ns + 1
hjs <- .hjbsearch(x, f, lower, upper,
steps[ns], dir, fcount, maxfeval, target)
x <- hjs$x
fx <- hjs$fx
sf <- hjs$sf
fcount <- fcount + hjs$finc
if (info)
cat(ns, "\t", fcount, "\t", fx/scale, "\t", x[1], "...\n")
}
if (fcount > maxfeval) {
warning("Function evaluation limit exceeded -- may not converge.")
conv <- 1
} else if (abs(fx) > target) {
warning("Function exceeds min/max value -- may not converge.")
conv <- 1
} else {
conv <- 0
}
fx <- fx / scale # undo scaling
return(list(par = x, value = fx,
convergence = conv, feval = fcount, niter = ns))
}
## Search with a single scale -----------------------------
.hjbsearch <- function(xb, f, lo, up, h, dir, fcount, maxfeval, target) {
x <- xb
xc <- x
sf <- 0
finc <- 0
hje <- .hjbexplore(xb, xc, f, lo, up, h, dir)
x <- hje$x
fx <- hje$fx
sf <- hje$sf
finc <- finc + hje$numf
# Pattern move
while (sf == 1) {
d <- x-xb
xb <- x
xc <- x+d
xc <- pmax(pmin(xc, up), lo)
fb <- fx
hje <- .hjbexplore(xb, xc, f, lo, up, h, dir, fb)
x <- hje$x
fx <- hje$fx
sf <- hje$sf
finc <- finc + hje$numf
if (sf == 0) { # pattern move failed
hje <- .hjbexplore(xb, xb, f, lo, up, h, dir, fb)
x <- hje$x
fx <- hje$fx
sf <- hje$sf
finc <- finc + hje$numf
}
if (fcount + finc > maxfeval || abs(fx) > target) break
}
return(list(x = x, fx = fx, sf = sf, finc = finc))
}
## Exploratory move ---------------------------------------
.hjbexplore <- function(xb, xc, f, lo, up, h, dir, fbold) {
n <- length(xb)
x <- xb
if (missing(fbold)) {
fb <- f(x)
numf <- 1
} else {
fb <- fbold
numf <- 0
}
fx <- fb
xt <- xc
sf <- 0 # do we find a better point ?
dirh <- h * dir
fbold <- fx
for (k in sample.int(n, n)) { # resample orthogonal directions
p1 <- xt + dirh[, k]
if ( p1[k] <= up[k] ) {
ft1 <- f(p1)
numf <- numf + 1
} else {
ft1 <- fb
}
p2 <- xt - dirh[, k]
if ( lo[k] <= p2[k] ) {
ft2 <- f(p2)
numf <- numf + 1
} else {
ft2 <- fb
}
if (min(ft1, ft2) < fb) {
sf <- 1
if (ft1 < ft2) {
xt <- p1
fb <- ft1
} else {
xt <- p2
fb <- ft2
}
}
}
if (sf == 1) {
x <- xt
fx <- fb
}
return(list(x = x, fx = fx, sf = sf, numf = numf))
}
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