Package 'mvTargetOpt' reference manual

Title:	Multivariate multi-target optimization
Description:	Multi-objective optimization algorithm. A new approach, using ideas from PCA dimension reduction and PLS regression.
Authors:	Andreas Maendle
Maintainer:	Andreas Maendler <[email protected]>
License:	GPL-3
Version:	0.2.0
Built:	2026-05-18 09:42:02 UTC
Source:	https://github.com/amaendle/mvTargetOpt

autosolve

Description

Applies the iterative optimization algorithm suggested in this package. To perform the simulations automatically, the true model has to be specified. When in practice the true model is unknown, use opt.onestep function instead to get a candidate for the unknown optimum in a single iteration.

Usage

autosolve(
  startx,
  tgmean,
  tgerr,
  reps = 25,
  maxit = 10,
  reality = foo,
  xeps = 0.01,
  pplot = FALSE,
  pcnr = c(1, 2),
  maxarea = NULL,
  useweights = TRUE,
  mknormweights = F,
  gr2retlimit = T,
  mindeg = 0,
  sequential = F,
  tgpcawg = 1,
  yweights = F,
  datlim = NULL,
  knearest = NULL,
  tgdim = 1,
  ylast = NULL,
  sto = T,
  mod.sd = NULL,
  ...
)
autosolve(
  startx,
  tgmean,
  tgerr,
  reps = 25,
  maxit = 10,
  reality = foo,
  xeps = 0.01,
  pplot = FALSE,
  pcnr = c(1, 2),
  maxarea = NULL,
  useweights = TRUE,
  mknormweights = F,
  gr2retlimit = T,
  mindeg = 0,
  sequential = F,
  tgpcawg = 1,
  yweights = F,
  datlim = NULL,
  knearest = NULL,
  tgdim = 1,
  ylast = NULL,
  sto = T,
  mod.sd = NULL,
  ...
)

Arguments

startx

numeric matrix, start values

tgmean

numeric v4ector, target value vector

tgerr

numeric vector, defines acceptable error range

reps

integer, number of repeated measurements

maxit

integer, maximum number of iterations

reality

function, real model

xeps

nunmeric, smallest (reasonably) distinguishable epsilon

pplot

boolean, diagnostic plots

pcnr

integer vector, defines which principal directions will be considered

maxarea

numeric matrix, area range, which will be explored

useweights

boolean

mknormweights

boolean

gr2retlimit

boolean

mindeg

integer, minimal degree of order of polynomial model

sequential

boolean

tgpcawg

numeric

yweights

boolean

datlim

NULL or integer

knearest

integer

tgdim

integer

ylast

integer

sto

boolean

mod.sd

numeric

...

Value

data.frame

Examples

# example 1: 2x2 MModell
tfoo <- function(x) {
  x1 <- x[,1]
  x2 <- x[,2]
  return( data.frame( y1=0.8*x1 - 1.2*x2,
                      y2=0.8*x1 - 1.2*abs(x2)^0.25
 ) ) }
dstgmean <- tfoo(cbind(1.35,1.4))
tgerr <- c(0.025,0.025)
xeps <- 0.01
startx <- expand.grid(x1=c(-1,3),x2=c(-1,3))
set.seed(123)
autosolve(startx,dstgmean,tgerr,reps=7,maxit=10,tfoo, xeps, F, pcnr=c(1,2), mod.sd=0.2)

# example 2, 3x3 model
set.seed(123)
startx <- data.frame(x1=runif(4,-4,4),x2=runif(4,-4,4),x3=runif(4,-4,4))
tfoo <- function(x) {
  x1 <- x[,1]
  x2 <- x[,2]
  x3 <- x[,3]
  return( data.frame( y1=0.8*x1 - 1.2*x2,
                      y2=0.8*x1 - 1.2*abs(x2)^0.25,
                      y3=0.8*x1 - 0.6*abs(x2)^0.25 + x3
 ) ) }
tgmean <- tfoo(cbind(1.35,1.4,1.5))#tfoo(cbind(0.35,0.4,0.5))
tgerr <- c(0.5,0.5,0.5)
tmp<-autosolve(startx,tgmean,tgerr*0.125,reps=4,maxit=6,tfoo, xeps=0.01, F, pcnr=c(1,2), mod.sd=0.2)

# example 1: 2x2 MModell
tfoo <- function(x) {
  x1 <- x[,1]
  x2 <- x[,2]
  return( data.frame( y1=0.8*x1 - 1.2*x2,
                      y2=0.8*x1 - 1.2*abs(x2)^0.25
 ) ) }
dstgmean <- tfoo(cbind(1.35,1.4))
tgerr <- c(0.025,0.025)
xeps <- 0.01
startx <- expand.grid(x1=c(-1,3),x2=c(-1,3))
set.seed(123)
autosolve(startx,dstgmean,tgerr,reps=7,maxit=10,tfoo, xeps, F, pcnr=c(1,2), mod.sd=0.2)

# example 2, 3x3 model
set.seed(123)
startx <- data.frame(x1=runif(4,-4,4),x2=runif(4,-4,4),x3=runif(4,-4,4))
tfoo <- function(x) {
  x1 <- x[,1]
  x2 <- x[,2]
  x3 <- x[,3]
  return( data.frame( y1=0.8*x1 - 1.2*x2,
                      y2=0.8*x1 - 1.2*abs(x2)^0.25,
                      y3=0.8*x1 - 0.6*abs(x2)^0.25 + x3
 ) ) }
tgmean <- tfoo(cbind(1.35,1.4,1.5))#tfoo(cbind(0.35,0.4,0.5))
tgerr <- c(0.5,0.5,0.5)
tmp<-autosolve(startx,tgmean,tgerr*0.125,reps=4,maxit=6,tfoo, xeps=0.01, F, pcnr=c(1,2), mod.sd=0.2)

degByBIC

Description

internal function, determines the polynomial model order <=maxorder for the data dat which minimizes the BIC information criterion

Usage

degByBIC(dat, maxorder = 5, weights = NULL, mindeg = 0)
degByBIC(dat, maxorder = 5, weights = NULL, mindeg = 0)

Arguments

dat

list containing the data for predictors dat$x and descriptors dat$y

maxorder

integer, maximal order of polynomial model

weights

vector of weights for the data in dat

mindeg

integer, minimal order of polynomial model

Value

integer, recommended degree for polynomial model

euclw

Description

Takes a matrix/data.frame x with each coloumn having the scores corresponding to a principal component. Computes weights as needed in 1d regression models, i.e. returns for each of the 1d-projections on the PC the Euclidean distances from the n-dimensional point in the n-space.

Usage

euclw(x, normalize = T, sto = T)
euclw(x, normalize = T, sto = T)

Arguments

x

matrix, data.frame

normalize

boolean, TRUE for normalized weights.

sto

boolean, if TRUE ignore higher principal component coordinates.

Value

matrix

ftweights

Description

Internal function (for pred.patch, ored.solution). Replaces infinite numbers (weights) by large finite values. (clipping)

Usage

ftweights(w1)
ftweights(w1)

Arguments

w1

numeric vector

Value

numeric vector

getroots2

Description

getroots2

Usage

getroots2(dat, degree, target, limit = 40, weights = NULL, retlimit = FALSE)
getroots2(dat, degree, target, limit = 40, weights = NULL, retlimit = FALSE)

Arguments

dat

matrix

degree

integer

target

numeric vector

limit

integer

weights

numeric vector

retlimit

boolean

mimascores

Description

Internal function

Usage

mimascores(maxarea, mwgs)
mimascores(maxarea, mwgs)

Arguments

maxarea

matrix

mwgs

numeric

Value

matrix

mimascores2

Description

Internal function

Usage

mimascores2(maxarea, mwgs)
mimascores2(maxarea, mwgs)

Arguments

maxarea

matrix

mwgs

numeric

Value

matrix

mknorm

Description

internal function, standardizes a vector x by vector of means means and vector of standard deviations sds.

Usage

mknorm(x, means = NULL, sds = NULL)
mknorm(x, means = NULL, sds = NULL)

Arguments

x

input vector

means

vector of means

sds

vector of standard deviations

Value

standardized vector

mkreg

Description

internal function, inverse of mknorm. Back-transformation of a standardized vector.

Usage

mkreg(x, means, sds)
mkreg(x, means, sds)

Arguments

x

input vector (standardized)

means

vector of means

sds

vector of standard deviations

Value

back-transformed vector

mvdistance

Description

internal function, computes the Euclidean (euclid=T) or Manhattan distances (euclid=F) between vector y and the rows of matrix xs.

Usage

mvdistance(xs, y, euclid = F)
mvdistance(xs, y, euclid = F)

Arguments

xs

matrix, each row representing a vector

y

vector

euclid

TRUE for Euclidean distance, otherwise MAnhattan distance

Value

vector of the distances

nclose2mean

Description

Internal function. Returns a subset of size n of the points in datx which are closest to center.

Usage

nclose2mean(datx, center, n = 1)
nclose2mean(datx, center, n = 1)

Arguments

datx

matrix

center

numeric vector

n

integer

Value

matrix

newexp

Description

Creates new samples from model function. Used for simulations in the function autosolve as a helper function.

Usage

newexp(n = 25, xpos, foo, sd = 0.001)
newexp(n = 25, xpos, foo, sd = 0.001)

Arguments

n

integer, number of repeated measurements

xpos

numeric matrix, coordinates at which the measurement takes place

foo

function, model for the real relationship

sd

, standard deviation

Value

a matrix containing the samples

Examples

#not to be used
#not to be used

newexp2

Description

Creates new samples from model function. Used for simulations in the function autosolve as a helper function.

Usage

newexp2(n = 25, xpos, foo, sd = 0.001)
newexp2(n = 25, xpos, foo, sd = 0.001)

Arguments

n

integer, number of repeated measurements

xpos

numeric matrix, coordinates at which the measurement takes place

foo

function, model for the real relationship

sd

numeric, standard deviation

Value

a matrix containing the samples

Examples

#not to be used
#not to be used

opt.onestep

Description

Performs one iteration of the implemented optimization procedure. Suggest points for future measurements in order to find a solution that reaches the desired target value. One or more suggested points are returned.

Usage

opt.onestep(
  dat,
  tgmean,
  tgerr = NULL,
  xeps = 0.001,
  pcnr,
  maxarea = NULL,
  ptchoice = 1,
  useweights = TRUE,
  mknormweights = F,
  allpts = F,
  gr2retlimit = TRUE,
  bpcenter = F,
  mindeg = 0,
  wfun = function(x) {     (1/x)^2 },
  sequential = F,
  ptchng = F,
  nptc = 0,
  tgpcawg = 1,
  betterweights = F,
  yweights = F,
  datlim = NULL,
  knearest = NULL,
  tgdim = 1,
  ylast = NULL,
  sto = T,
  ...
)
opt.onestep(
  dat,
  tgmean,
  tgerr = NULL,
  xeps = 0.001,
  pcnr,
  maxarea = NULL,
  ptchoice = 1,
  useweights = TRUE,
  mknormweights = F,
  allpts = F,
  gr2retlimit = TRUE,
  bpcenter = F,
  mindeg = 0,
  wfun = function(x) {     (1/x)^2 },
  sequential = F,
  ptchng = F,
  nptc = 0,
  tgpcawg = 1,
  betterweights = F,
  yweights = F,
  datlim = NULL,
  knearest = NULL,
  tgdim = 1,
  ylast = NULL,
  sto = T,
  ...
)

Arguments

dat

data.frame, data set

tgmean

numerig vector, target mean

tgerr

NULL or numeric vector, maximally accepted deviation from target value

xeps

numeric, smallest delta

pcnr

integer vector, numbers the principal components that shall be considered

maxarea

matrix or NULL, maximal area that can/should be explored

ptchoice

integer

useweights

boolean

mknormweights

boolean

allpts

boolean

gr2retlimit

boolean

bpcenter

boolean

mindeg

integer, minimal degree for polynomial mdel

wfun

function, weight function

sequential

boolean

ptchng

boolean

nptc

integer

tgpcawg

numeric

betterweights

boolean

yweights

boolean

datlim

integer or NULL

knearest

integer, if specified only the knearest nearest observations to the target value are considered

tgdim

integer

ylast

integer, if a positive integer is defined, observations from the last ylast iterations are used only

sto

boolean

...

Value

matrix with recommended points (process parameters for future measurements) in each line

Examples

library(mvTargetOpt)
# Let there be the following true model tfoo:
tfoo <- function(x) {
  x1 <- x[,1]
  x2 <- x[,2]
  return( data.frame(y1=0.8*x1 - 1.2*x2,
                     y2=0.8*x1 - 1.2*abs(x2)^0.25) )
}
# assume we have measurements dat taken at startx:
startx <- expand.grid(x1=c(0,6,7,8,9,10,11,12),x2=c(-1,3,4,5,6,7))
dat <- cbind(startx,tfoo(startx))
# assume we want to find process parameters close to tgmean
tgmean <- tfoo(cbind(0.35,0.4))
# make a guess for a solution based on the specified parameters:
opt.onestep(dat, tgmean=tgmean,tgerr=c(0.2,0.2), pcnr=1:2)
library(mvTargetOpt)
# Let there be the following true model tfoo:
tfoo <- function(x) {
  x1 <- x[,1]
  x2 <- x[,2]
  return( data.frame(y1=0.8*x1 - 1.2*x2,
                     y2=0.8*x1 - 1.2*abs(x2)^0.25) )
}
# assume we have measurements dat taken at startx:
startx <- expand.grid(x1=c(0,6,7,8,9,10,11,12),x2=c(-1,3,4,5,6,7))
dat <- cbind(startx,tfoo(startx))
# assume we want to find process parameters close to tgmean
tgmean <- tfoo(cbind(0.35,0.4))
# make a guess for a solution based on the specified parameters:
opt.onestep(dat, tgmean=tgmean,tgerr=c(0.2,0.2), pcnr=1:2)

PIhcheck

Description

internal function, determinas a prediction interval for given linear model model with confidence level alpha. currently unused.

Usage

PIhcheck(model, alph = 0.05)
PIhcheck(model, alph = 0.05)

Arguments

model

linear model

alph

numeric, confidence level

Value

vector, upper and lower prediction intervall

plotexp

Description

Function which plots...

Usage

plotexp(
  dat,
  target,
  tgerr,
  prediction = NULL,
  model = NULL,
  limit0 = FALSE,
  reality = NULL,
  xlab = "Process parameter (p)",
  ylab = "Descriptor (d)"
)
plotexp(
  dat,
  target,
  tgerr,
  prediction = NULL,
  model = NULL,
  limit0 = FALSE,
  reality = NULL,
  xlab = "Process parameter (p)",
  ylab = "Descriptor (d)"
)

Arguments

dat

data.frame, with dat$x matrix of proces parameter data

target

numeric vector

tgerr

numeric vector

prediction

numeric

model

function

limit0

boolean

reality

function

Value

plot

polymodel

Description

internal function, returns polynomial regression model of degree degree for the predictor and descriptor data given in dat. If weights are provided, the weighted regression model is returned.

Usage

polymodel(dat, degree = 1, weights = NULL)
polymodel(dat, degree = 1, weights = NULL)

Arguments

dat

list containing the data for predictors dat$x and descriptors dat$y

degree

integer, degree of polynomial regression

weights

vector of weights for the data provided in dat

Value

linear model

polymodel

Description

internal function, returns polynomial regression model of degree degree for the predictor and descriptor data given in dat. If weights are provided, the weighted regression model is returned.

Usage

polymodel2(dat, degree, weights = NULL)
polymodel2(dat, degree, weights = NULL)

Arguments

dat

list containing the data for predictors dat$x and descriptors dat$y

degree

integer, degree of polynomial regression

weights

vector of weights for the data provided in dat

Details

like polymodel, but here degree has no default

Value

linear model

pred.ptch

Description

Internal function. Extends the function opt.onestep.

Usage

pred.ptch(
  shift,
  pcnr,
  pls1,
  mknormweights,
  dat1d.PC12,
  mindeg,
  tgmean_norm,
  gr2retlimit,
  wfun,
  sto
)
pred.ptch(
  shift,
  pcnr,
  pls1,
  mknormweights,
  dat1d.PC12,
  mindeg,
  tgmean_norm,
  gr2retlimit,
  wfun,
  sto
)

Arguments

shift

numeric vector

pcnr

integer vector

pls1

result of PLS1-function

mknormweights

boolean

dat1d.PC12

matrix

mindeg

integer

tgmean_norm

numeric vector

gr2retlimit

boolean

wfun

function

sto

boolean

ptchoose

Description

Internal function. Continues search in unexplored space, when no solution can be found.

Usage

ptchoose(
  ptchoice = ptchoice,
  dat1d,
  tgmean_norm,
  maxarea,
  xmeans,
  xsds,
  pls1,
  jjj
)
ptchoose(
  ptchoice = ptchoice,
  dat1d,
  tgmean_norm,
  maxarea,
  xmeans,
  xsds,
  pls1,
  jjj
)

Arguments

ptchoice

numeric, 1 to continue search outside the explored parameters

dat1d

data.frame, predictor data must be in dat1d$x

tgmean_norm

numeric vector

maxarea

NULL or matrix

xmeans

numeric vector

xsds

numeric vector

pls1

result of the PLS1 function

jjj

integer, counts how often this function has been called

Value

matrix

repna

Description

Internal function. Replaces NAs in a vector x by 0.

Usage

repna(x)
repna(x)

Arguments

x

numeric vector

Value

numeric vector

sumthelowers

Description

internal helper function which is used by euclw .

Usage

sumthelowers(x)
sumthelowers(x)

Arguments

x

numeric vector

Value

numeric vector

sumtheothers

Description

internal helper function which is used by euclw .

Usage

sumtheothers(x)
sumtheothers(x)

Arguments

x

vector

Value

vector

tgpca

Description

Function which performs a principal component analysis (PCA) on the descriptor variable data (in the target space) given by dat, In order to choose a certain direction through the target point for the projections, wg has to be set to 1 – then the target point is chosen as center for the PCA. If wg lies between 0 and 1, pseudo observations at the target point are created such that a ratio of wg of the observations are pseudo observations. Then prcomp is applied to the standardized data and pseudo data.

Usage

tgpca(
  dat,
  tgmean = NULL,
  tgerr = NULL,
  wg = 1,
  wfun,
  mknormweights,
  yweights = F,
  ylast = NULL
)
tgpca(
  dat,
  tgmean = NULL,
  tgerr = NULL,
  wg = 1,
  wfun,
  mknormweights,
  yweights = F,
  ylast = NULL
)

Arguments

dat

matrix, data.frame

tgmean

numeric vector, optional

tgerr

numeric vector, optional

wg

numeric, weight for the target value. If wg equals 1 or 2 then the pca is performed with the target value as center

wfun

function, weight function

mknormweights

unused

yweights

boolean, use weights?

ylast

integer or NULL, if integer, ignore observations older than the last ylast evaluation points.

Value

returns the results of the pca and some extra stuff

Examples

tgpca(matrix(rnorm(20),ncol=2), tgmean=c(0,0))
tgpca(matrix(rnorm(20),ncol=2), tgmean=c(0,0))

uniqP

Description

Internal function. Returns a subset of the unique points of newx whgich are not (up to an epsilon xeps) identical to the points in datx.

Usage

uniqP(newx, xeps, datx)
uniqP(newx, xeps, datx)

Arguments

newx

matrix

xeps

numeric

datx

matrix

Value

matrix

Package 'mvTargetOpt'

Help Index

autosolve

Description

Usage

Arguments

Value

Examples

degByBIC

Description

Usage

Arguments

Value

euclw

Description

Usage

Arguments

Value

ftweights

Description

Usage

Arguments

Value

getroots2

Description

Usage

Arguments

mimascores

Description

Usage

Arguments

Value

mimascores2

Description

Usage

Arguments

Value

mknorm

Description

Usage

Arguments

Value

mkreg

Description

Usage

Arguments

Value

mvdistance

Description

Usage

Arguments

Value

nclose2mean

Description

Usage

Arguments

Value

newexp

Description

Usage

Arguments

Value

Examples

newexp2

Description

Usage

Arguments

Value

Examples

opt.onestep

Description

Usage

Arguments

Value

Examples

PIhcheck

Description

Usage

Arguments

Value