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opt_functions.R
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ackley <- function(xx, a=20, b=0.2, c=2*pi)
{
##########################################################################
#
# ACKLEY FUNCTION
#
# Authors: Sonja Surjanovic, Simon Fraser University
# Derek Bingham, Simon Fraser University
# Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
#
# Copyright 2013. Derek Bingham, Simon Fraser University.
#
# THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
# FOR THE USE OF THIS SOFTWARE. If software is modified to produce
# derivative works, such modified software should be clearly marked.
# Additionally, this program is free software; you can redistribute it
# and/or modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; version 2.0 of the License.
# Accordingly, this program is distributed in the hope that it will be
# useful, but WITHOUT ANY WARRANTY; without even the implied warranty
# of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# For function details and reference information, see:
# http://www.sfu.ca/~ssurjano/
#
##########################################################################
#
# INPUTS:
#
# xx = c(x1, x2, ..., xd)
# a = constant (optional), with default value 20
# b = constant (optional), with default value 0.2
# c = constant (optional), with default value 2*pi
#
##########################################################################
d <- length(xx)
sum1 <- sum(xx^2)
sum2 <- sum(cos(c*xx))
term1 <- -a * exp(-b*sqrt(sum1/d))
term2 <- -exp(sum2/d)
y <- term1 + term2 + a + exp(1)
return(y)
}
grlee12 <- function(x)
{
##########################################################################
#
# GRAMACY & LEE (2012) FUNCTION
#
# Authors: Sonja Surjanovic, Simon Fraser University
# Derek Bingham, Simon Fraser University
# Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
#
# Copyright 2013. Derek Bingham, Simon Fraser University.
#
# THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
# FOR THE USE OF THIS SOFTWARE. If software is modified to produce
# derivative works, such modified software should be clearly marked.
# Additionally, this program is free software; you can redistribute it
# and/or modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; version 2.0 of the License.
# Accordingly, this program is distributed in the hope that it will be
# useful, but WITHOUT ANY WARRANTY; without even the implied warranty
# of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# For function details and reference information, see:
# http://www.sfu.ca/~ssurjano/
#
##########################################################################
term1 <- sin(10*pi*x) / (2*x)
term2 <- (x-1)^4
y <- term1 + term2
return(y)
}
# http://www.sfu.ca/~ssurjano/forretal08.html
forretal08 <- function(x)
{
##########################################################################
#
# FORRESTER ET AL. (2008) FUNCTION
#
# Authors: Sonja Surjanovic, Simon Fraser University
# Derek Bingham, Simon Fraser University
# Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
#
# Copyright 2013. Derek Bingham, Simon Fraser University.
#
# THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
# FOR THE USE OF THIS SOFTWARE. If software is modified to produce
# derivative works, such modified software should be clearly marked.
# Additionally, this program is free software; you can redistribute it
# and/or modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; version 2.0 of the License.
# Accordingly, this program is distributed in the hope that it will be
# useful, but WITHOUT ANY WARRANTY; without even the implied warranty
# of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# For function details and reference information, see:
# http://www.sfu.ca/~ssurjano/
#
##########################################################################
fact1 <- (6*x - 2)^2
fact2 <- sin(12*x - 4)
y <- fact1 * fact2
return(y)
}
forretal08lc <- function(x, A=0.5, B=10, C=-5)
{
##########################################################################
#
# FORRESTER ET AL. (2008) FUNCTION, LOWER FIDELITY CODE
# Calls: forretal08.r
# This function is used as the "low-accuracy code" version of the function
# forretal08.r.
#
# Authors: Sonja Surjanovic, Simon Fraser University
# Derek Bingham, Simon Fraser University
# Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
#
# Copyright 2013. Derek Bingham, Simon Fraser University.
#
# THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
# FOR THE USE OF THIS SOFTWARE. If software is modified to produce
# derivative works, such modified software should be clearly marked.
# Additionally, this program is free software; you can redistribute it
# and/or modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; version 2.0 of the License.
# Accordingly, this program is distributed in the hope that it will be
# useful, but WITHOUT ANY WARRANTY; without even the implied warranty
# of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# For function details and reference information, see:
# http://www.sfu.ca/~ssurjano/
#
##########################################################################
#
# INPUTS:
#
# x = scalar
# A = constant (optional), with default value 0.5
# B = constant (optional), with default value 10
# C = constant (optional), with default value -5
#
##########################################################################
# source('forretal08.r')
yh <- forretal08(x)
term1 <- A * yh
term2 <- B * (x-0.5)
y <- term1 + term2 - C
return(y)
}
permdb <- function(xx, b=0.5)
{
##########################################################################
#
# PERM FUNCTION d, beta
#
# Authors: Sonja Surjanovic, Simon Fraser University
# Derek Bingham, Simon Fraser University
# Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
#
# Copyright 2013. Derek Bingham, Simon Fraser University.
#
# THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
# FOR THE USE OF THIS SOFTWARE. If software is modified to produce
# derivative works, such modified software should be clearly marked.
# Additionally, this program is free software; you can redistribute it
# and/or modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; version 2.0 of the License.
# Accordingly, this program is distributed in the hope that it will be
# useful, but WITHOUT ANY WARRANTY; without even the implied warranty
# of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# For function details and reference information, see:
# http://www.sfu.ca/~ssurjano/
#
##########################################################################
#
# INPUTS:
#
# xx = c(x1, x2)
# b = constant (optional), with default value 0.5
#
##########################################################################
d <- length(xx)
ii <- c(1:d)
jj <- matrix(rep(ii,times=d), d, d, byrow=TRUE)
xxmat <- matrix(rep(xx,times=d), d, d, byrow=TRUE)
inner <- rowSums((jj^ii+b)*((xxmat/jj)^ii-1))
outer <- sum(inner^2)
y <- outer
return(y)
}
################
# borehole_model
################
borehole_model_HF <- function(Rw=0.05, L=1120, Kw=9855){
# high-fidelity
# Rw in (0.05, 0.15)
# L in (1120, 1680)
# Kw in (9855, 12045)
R = 25050
Tu = 89335
Hu = 1050
Tl = 89.55
Hl = 760
numerator = 2*pi*Tu*(Hu-Hl)
denominator = log(R/Rw) * ( 1+(2*L*Tu)/(log(R/Rw)*Rw^2*Kw) + Tu/Tl )
return(numerator/denominator)
}
borehole_model_LF <- function(Rw=0.05, L=1120, Kw=9855){
# low-fidelity
# Rw in (0.05, 0.15)
# L in (1120, 1680)
# Kw in (9855, 12045)
R = 25050
Tu = 89335
Hu = 1050
Tl = 89.55
Hl = 760
numerator = 5*pi*Tu*(Hu-Hl)
denominator = log(R/Rw) * ( 1.5+(2*L*Tu)/(log(R/Rw)*Rw^2*Kw) + Tu/Tl )
return(numerator/denominator)
}