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## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are
## met:
##
## Redistributions of source code must retain the above copyright
## notice, this list of conditions and the following disclaimer.
##
## Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in
## the documentation and/or other materials provided with the
## distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
## "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
## LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
## A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
## HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
## DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
## THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#' @title Simulated annealing
#'
#' @name sa
#' @rdname sa
#'
#' @description
#' Use simulated annealing to find the global minimum
#'
#' @param f function representing \code{f}
#' @param x an initial estimate of the minimum
#' @param temp the initial temperature
#' @param rate the cooling rate
#'
#' @details
#'
#' Simulated annealing finds a global minimum by mimicing the
#' metallurgical process of annealing.
#'
#' @return the \code{x} value of the minimum found
#'
#' @family optimz
#'
#' @examples
#' f <- function(x) { x^6 - 4 * x^5 - 7 * x^4 + 22 * x^3 + 24 * x^2 + 2}
#' sa(f, 0)
#'
#' f <- function(x) { (x[1] - 1)^2 + (x[2] - 1)^2 }
#' sa(f, c(0, 0), 0.05)
#'
#' @importFrom stats runif
#' @importFrom stats rnorm
#'
#' @rdname sa
#' @export
sa <- function(f, x, temp = 1e4, rate = 1e-4) {
step = 1 - rate
n <- length(x)
xbest <- xcurr <- xnext <- x
ybest <- ycurr <- ynext <- f(x)
while(temp > 1) {
temp <- temp * step
i <- ceiling(runif(1, 0, n))
xnext[i] <- rnorm(1, xcurr[i], temp)
ynext <- f(xnext)
accept <- exp(-(ynext - ycurr) / temp)
if(ynext < ycurr || runif(1) < accept) {
xcurr <- xnext
ycurr <- ynext
}
if(ynext < ybest) {
xbest <- xcurr
ybest <- ycurr
}
}
return(xbest)
}
#' @rdname sa
#' @export
tspsa <- function(x, temp = 1e2, rate = 1e-4) {
step = 1 - rate
n <- nrow(x)
xbest <- xcurr <- xnext <- c(1:n)
ynext <- 0
for(i in 2:n) {
a <- xnext[i - 1]
b <- xnext[i]
ynext <- ynext + vecnorm(x[a,] - x[b,])
}
a <- xnext[1]
b <- xnext[n]
ynext <- ynext + vecnorm(x[a,] - x[b,])
ybest <- ycurr <- ynext
while(temp > 1) {
temp <- temp * step
i <- ceiling(runif(1, 1, n))
xnext <- xcurr
temporary <- xnext[i]
xnext[i] <- xnext[i - 1]
xnext[i - 1] <- temporary
ynext <- 0
for(i in 2:n) {
a <- xnext[i - 1]
b <- xnext[i]
ynext <- ynext + vecnorm(x[a,] - x[b,])
}
a <- xnext[1]
b <- xnext[n]
ynext <- ynext + vecnorm(x[a,] - x[b,])
accept <- exp(-(ynext - ycurr) / temp)
if(ynext < ycurr || runif(1) < accept) {
xcurr <- xnext
ycurr <- ynext
}
if(ynext < ybest) {
xbest <- xcurr
ybest <- ycurr
}
}
return(list(order = xbest, distance = ybest))
}
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