R/UTA.R
In paterijk/MCDA: Support for the Multicriteria Decision Aiding Process
Defines functions
UTA
Documented in
UTA
UTA <- function(performanceTable, criteriaMinMax, criteriaNumberOfBreakPoints, epsilon, alternativesRanks = NULL, alternativesPreferences = NULL, alternativesIndifferences = NULL, criteriaLBs=NULL, criteriaUBs=NULL, alternativesIDs = NULL, criteriaIDs = NULL, kPostOptimality = NULL){
## check the input data
if (!((is.matrix(performanceTable) || (is.data.frame(performanceTable)))))
stop("wrong performanceTable, should be a matrix or a data frame")
if (!(is.null(alternativesRanks) || is.vector(alternativesRanks)))
stop("alternativesRanks should be a vector")
if (!(is.null(alternativesPreferences) || is.matrix(alternativesPreferences)))
stop("alternativesPreferences should be a matrix")
if (!(is.null(alternativesIndifferences) || is.matrix(alternativesIndifferences)))
stop("alternativesIndifferences should be a matrix")
if (is.null(alternativesRanks) && is.null(alternativesPreferences) && is.null(alternativesIndifferences))
stop("at least one of alternativesRanks, alternativesPreferences or alternativesIndifferences should not be NULL")
if (!is.null(alternativesRanks) && (!is.null(alternativesPreferences) | !is.null(alternativesIndifferences)))
stop("alternativesRanks and one of alternativesPreferences or alternativesIndifferences cannot be simultaneously not NULL")
if (!(is.vector(criteriaMinMax)))
stop("criteriaMinMax should be a vector")
if (!(is.vector(criteriaNumberOfBreakPoints)))
stop("criteriaNumberOfBreakPoints should be a vector")
if (!(is.null(alternativesIDs) || is.vector(alternativesIDs)))
stop("alternativesIDs should be in a vector")
if (!(is.null(criteriaIDs) || is.vector(criteriaIDs)))
stop("criteriaIDs should be in a vector")
if (!(is.null(criteriaLBs) || is.vector(criteriaLBs)))
stop("criteriaLBs should be in a vector")
if (!(is.null(criteriaUBs) || is.vector(criteriaUBs)))
stop("criteriaUBs should be in a vector")
## filter the data according to the given alternatives and criteria
## in alternativesIDs and criteriaIDs
if (!is.null(alternativesIDs)){
performanceTable <- performanceTable[alternativesIDs,]
if (!is.null(alternativesRanks))
alternativesRanks <- alternativesRanks[alternativesIDs]
if (!is.null(alternativesPreferences)){
tmpIds <- intersect(alternativesPreferences, alternativesIDs)
tmpMatrix <- c()
for (i in 1:dim(alternativesPreferences)[1]){
if (all(alternativesPreferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesPreferences[i,])
}
alternativesPreferences <- tmpMatrix
}
if (!is.null(alternativesIndifferences)){
tmpIds <- intersect(alternativesIndifferences, alternativesIDs)
tmpMatrix <- c()
for (i in 1:dim(alternativesIndifferences)[1]){
if (all(alternativesIndifferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesIndifferences[i,])
}
alternativesIndifferences <- tmpMatrix
}
}
if (!is.null(criteriaIDs)){
criteriaMinMax <- criteriaMinMax[criteriaIDs]
performanceTable <- performanceTable[,criteriaIDs]
criteriaNumberOfBreakPoints <- criteriaNumberOfBreakPoints[criteriaIDs]
}
if (!is.null(criteriaIDs) && !is.null(criteriaUBs)){
criteriaUBs <- criteriaUBs[criteriaIDs]
}
if (!is.null(criteriaIDs) && !is.null(criteriaLBs)){
criteriaLBs <- criteriaLBs[criteriaIDs]
}
# only the alternatives which are in the ranking should be considered for the calculation
# we therefore take the intersection between the alternatives present in the performance
# table and those of the ranking
if (!is.null(alternativesRanks)){
reallyActiveAlternatives <- intersect(rownames(performanceTable),names(alternativesRanks))
if (length(reallyActiveAlternatives) != 0){
performanceTable <- performanceTable[reallyActiveAlternatives,]
alternativesRanks <- alternativesRanks[reallyActiveAlternatives]
} else {
stop("alternatives of alternativesRanks are not compatible with those of performanceTable")
}
}
if (!is.null(alternativesPreferences) || !is.null(alternativesIndifferences)){
reallyActiveAlternatives <- intersect(rownames(performanceTable),rbind(alternativesPreferences,alternativesIndifferences))
if (length(reallyActiveAlternatives) != 0){
performanceTable <- performanceTable[reallyActiveAlternatives,]
if (!is.null(alternativesPreferences)){
tmpIds <- intersect(alternativesPreferences, reallyActiveAlternatives)
tmpMatrix <- c()
for (i in 1:dim(alternativesPreferences)[1]){
if (all(alternativesPreferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesPreferences[i,])
}
alternativesPreferences <- tmpMatrix
}
if (!is.null(alternativesIndifferences)){
tmpIds <- intersect(alternativesIndifferences, reallyActiveAlternatives)
tmpMatrix <- c()
for (i in 1:dim(alternativesIndifferences)[1]){
if (all(alternativesIndifferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesIndifferences[i,])
}
alternativesIndifferences <- tmpMatrix
}
} else {
stop("alternatives of alternativesPreferences or alternativesIndifferences are not compatible with those of performanceTable")
}
}
# data is filtered, check for some data consistency
# are the upper and lower bounds given in the function compatible with the data in the performance table ?
if (!(is.null(criteriaUBs))){
if (!all(apply(performanceTable,2,max)<=criteriaUBs))
stop("performanceTable contains higher values than criteriaUBs")
}
if (!(is.null(criteriaLBs))){
if (!all(apply(performanceTable,2,min)>=criteriaLBs))
stop("performanceTable contains lower values than criteriaLBs")
}
if (!all(criteriaNumberOfBreakPoints >= 2))
stop("in criteriaNumberOfBreakPoints there should at least be 2 breakpoints for each criterion")
# if there are less than 2 criteria or 2 alternatives, there is no MCDA problem
if (is.null(dim(performanceTable)))
stop("less than 2 criteria or 2 alternatives")
# if there are no alternatives left in the ranking or the pairwise preferences
# we stop here
if (is.null(alternativesRanks) && is.null(alternativesPreferences) && is.null(alternativesIndifferences))
stop("after filtering none of alternativesRanks, alternativesPreferences or alternativesIndifferences is not NULL")
# -------------------------------------------------------
numCrit <- dim(performanceTable)[2]
numAlt <- dim(performanceTable)[1]
# -------------------------------------------------------
criteriaBreakPoints <- list()
for (i in 1:numCrit){
tmp<-c()
if (!is.null(criteriaLBs))
mini <- criteriaLBs[i]
else{
mini <- min(performanceTable[,i])
}
if (!is.null(criteriaLBs))
maxi <- criteriaUBs[i]
else{
maxi <- max(performanceTable[,i])
}
if (mini == maxi){
# then there is only one value for that criterion, and the algorithm to build the linear interpolation
# will not work correctly
stop(paste("there is only one possible value left for criterion "),colnames(performanceTable)[i])
}
alphai <- criteriaNumberOfBreakPoints[i]
for (j in 1:alphai)
tmp<-c(tmp,mini + (j-1)/(alphai-1) * (maxi - mini))
# due to this formula, the minimum and maximum values might not be exactly the same than the real minimum and maximum values in the performance table
# to be sure there is no rounding problem, we recopy these values in tmp (important for the later comparisons to these values)
tmp[1] <- mini
tmp[alphai] <- maxi
# if the criterion has to be maximized, the worst value is in the first position
# else, we sort the vector the other way around to have the worst value in the first position
if (criteriaMinMax[i] == "min")
tmp<-sort(tmp,decreasing=TRUE)
criteriaBreakPoints <- c(criteriaBreakPoints,list(tmp))
}
names(criteriaBreakPoints) <- colnames(performanceTable)
# -------------------------------------------------------
# a is a matrix decomposing the alternatives in the break point space and adding the sigma columns
a<-matrix(0,nrow=numAlt, ncol=(sum(criteriaNumberOfBreakPoints)+numAlt))
for (n in 1:numAlt){
for (m in 1:numCrit){
if (length(which(performanceTable[n,m]==criteriaBreakPoints[[m]]))!=0){
# then we have a performance value which is on a breakpoint
j<-which(performanceTable[n,m]==criteriaBreakPoints[[m]])
if (m==1)
pos <- j
else
pos<-sum(criteriaNumberOfBreakPoints[1:(m-1)])+j
a[n,pos] <- 1
}
else{
# then we have value which needs to be approximated by a linear interpolation
# let us first search the lower and upper bounds of the interval of breakpoints around the value
if (criteriaMinMax[m] == "min"){
j<-which(performanceTable[n,m]>criteriaBreakPoints[[m]])[1]-1
}
else{
j<-which(performanceTable[n,m]<criteriaBreakPoints[[m]])[1]-1
}
if (m==1)
pos <- j
else
pos<-sum(criteriaNumberOfBreakPoints[1:(m-1)])+j
a[n,pos] <- 1-(performanceTable[n,m]-criteriaBreakPoints[[m]][j])/(criteriaBreakPoints[[m]][j+1] - criteriaBreakPoints[[m]][j])
a[n,pos+1] <- (performanceTable[n,m]-criteriaBreakPoints[[m]][j])/(criteriaBreakPoints[[m]][j+1] - criteriaBreakPoints[[m]][j])
}
# and now for sigma
a[n,dim(a)[2]-numAlt+n] <- 1
}
}
# -------------------------------------------------------
# the objective function : the first elements correspond to the ui's, the last one to the sigmas
obj<-rep(0,sum(criteriaNumberOfBreakPoints))
obj<-c(obj,rep(1,numAlt))
# -------------------------------------------------------
# we now build the part of the constraints matrix concerning the order / preferences / indifferences given by the decision maker
preferenceConstraints<-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
indifferenceConstraints <-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
if (!is.null(alternativesRanks)){
# determine now in which order the alternatives should be treated for the constraints
indexOrder <- c()
orderedAlternativesRanks <- sort(alternativesRanks)
tmpRanks1 <- alternativesRanks
tmpRanks2 <- alternativesRanks
while (length(orderedAlternativesRanks) != 0){
# search for the alternatives of lowest rank
tmpIndex <- which(alternativesRanks == orderedAlternativesRanks[1])
for (j in 1:length(tmpIndex))
indexOrder<-c(indexOrder,tmpIndex[j])
# remove the rank which has been dealt with now
orderedAlternativesRanks<-orderedAlternativesRanks[-which(orderedAlternativesRanks==orderedAlternativesRanks[1])]
}
for (i in 1:(length(alternativesRanks)-1)){
if (alternativesRanks[indexOrder[i]] == alternativesRanks[indexOrder[i+1]]){
# then the alternatives are indifferent and their overall values are equal
indifferenceConstraints <- rbind(indifferenceConstraints, a[indexOrder[i],] - a[indexOrder[i+1],])
}
else{
# then the first alternative i is ranked better than the second one i+1 and i has an overall value higher than i+1
preferenceConstraints <- rbind(preferenceConstraints, a[indexOrder[i],] - a[indexOrder[i+1],])
}
}
}
if (!is.null(alternativesPreferences)){
for (i in 1:dim(alternativesPreferences)[1]){
preferenceConstraints <- rbind(preferenceConstraints, a[which(rownames(performanceTable)==alternativesPreferences[i,1]),] - a[which(rownames(performanceTable)==alternativesPreferences[i,2]),])
}
}
if (!is.null(alternativesIndifferences)){
for (i in 1:dim(alternativesIndifferences)[1]){
indifferenceConstraints <- rbind(indifferenceConstraints, a[which(rownames(performanceTable)==alternativesIndifferences[i,1]),] - a[which(rownames(performanceTable)==alternativesIndifferences[i,2]),])
}
}
# add this to the constraints matrix mat
mat<-rbind(preferenceConstraints,indifferenceConstraints)
# right hand side of this part of mat
rhs <- c()
if (dim(preferenceConstraints)[1]!=0){
for (i in (1:dim(preferenceConstraints)[1]))
rhs<-c(rhs,epsilon)
}
if (dim(indifferenceConstraints)[1]!=0){
for (i in (1:dim(indifferenceConstraints)[1]))
rhs<-c(rhs,0)
}
# direction of the inequality for this part of mat
dir <- c()
if (dim(preferenceConstraints)[1]!=0){
for (i in (1:dim(preferenceConstraints)[1]))
dir<-c(dir,">=")
}
if (dim(indifferenceConstraints)[1]!=0){
for (i in (1:dim(indifferenceConstraints)[1]))
dir<-c(dir,"==")
}
# -------------------------------------------------------
# now the monotonicity constraints on the value functions
monotonicityConstraints<-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
for (i in 1:length(criteriaNumberOfBreakPoints)){
for (j in 1:(criteriaNumberOfBreakPoints[i]-1)){
tmp<-rep(0,sum(criteriaNumberOfBreakPoints)+numAlt)
if (i==1)
pos <- j
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+j
tmp[pos] <- -1
tmp[pos+1] <- 1
monotonicityConstraints <- rbind(monotonicityConstraints, tmp)
}
}
# add this to the constraints matrix mat
mat<-rbind(mat,monotonicityConstraints)
# the direction of the inequality
for (i in (1:dim(monotonicityConstraints)[1]))
dir<-c(dir,">=")
# the right hand side of this part of mat
for (i in (1:dim(monotonicityConstraints)[1]))
rhs<-c(rhs,0)
# -------------------------------------------------------
# normalization constraint for the upper values of the value functions (sum = 1)
tmp<-rep(0,sum(criteriaNumberOfBreakPoints)+numAlt)
for (i in 1:length(criteriaNumberOfBreakPoints)){
if (i==1)
pos <- criteriaNumberOfBreakPoints[i]
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+criteriaNumberOfBreakPoints[i]
tmp[pos] <- 1
}
# add this to the constraints matrix mat
mat<-rbind(mat,tmp)
# the direction of the inequality
dir<-c(dir,"==")
# the right hand side of this part of mat
rhs<-c(rhs,1)
# -------------------------------------------------------
# now the normalizaiton constraints for the lower values of the value functions (= 0)
minValueFunctionsConstraints<-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
for (i in 1:length(criteriaNumberOfBreakPoints)){
tmp<-rep(0,sum(criteriaNumberOfBreakPoints)+numAlt)
if (i==1)
pos <- i
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+1
tmp[pos] <- 1
minValueFunctionsConstraints <- rbind(minValueFunctionsConstraints,tmp)
}
# add this to the constraints matrix mat
mat<-rbind(mat,minValueFunctionsConstraints)
# the direction of the inequality
for (i in (1:dim(minValueFunctionsConstraints)[1]))
dir<-c(dir,"==")
# the right hand side of this part of mat
for (i in (1:dim(minValueFunctionsConstraints)[1]))
rhs<-c(rhs,0)
# -------------------------------------------------------
lpSolution <- Rglpk_solve_LP(obj, mat, dir, rhs)
# -------------------------------------------------------
# create a structure containing the value functions
valueFunctions <- list()
for (i in 1:length(criteriaNumberOfBreakPoints)){
tmp <- c()
if (i==1)
pos <- 0
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])
for (j in 1:criteriaNumberOfBreakPoints[i]){
tmp <- c(tmp,lpSolution$solution[pos+j])
}
tmp<-rbind(criteriaBreakPoints[[i]],tmp)
colnames(tmp)<- NULL
rownames(tmp) <- c("x","y")
valueFunctions <- c(valueFunctions,list(tmp))
}
names(valueFunctions) <- colnames(performanceTable)
# it might happen on certain computers that these value functions
# do NOT respect the monotonicity constraints (especially because of too small differences and computer arithmetics)
# therefore we check if they do, and if not, we "correct" them
for (i in 1:numCrit){
for (j in 1:(criteriaNumberOfBreakPoints[i]-1)){
if (valueFunctions[[i]][2,j] > valueFunctions[[i]][2,j+1]){
valueFunctions[[i]][2,j+1] <- valueFunctions[[i]][2,j]
}
}
}
# -------------------------------------------------------
overallValues <- as.vector(t(a[,1:sum(criteriaNumberOfBreakPoints)]%*%lpSolution$solution[1:sum(criteriaNumberOfBreakPoints)]))
names(overallValues) <- rownames(performanceTable)
# -------------------------------------------------------
# the error values for each alternative (sigma)
errorValues <- as.vector(lpSolution$solution[(sum(criteriaNumberOfBreakPoints)+1):length(lpSolution$solution)])
names(errorValues) <- rownames(performanceTable)
# -------------------------------------------------------
# the ranks of the alternatives
outRanks <- rank(-overallValues, ties.method="min")
# -------------------------------------------------------
if ((numAlt >= 3) && !is.null(alternativesRanks))
tau = cor(alternativesRanks,outRanks,method="kendall")
else
tau = NULL
# prepare the output
out <- list(optimum = round(lpSolution$optimum, digits=5), valueFunctions = valueFunctions, overallValues = round(overallValues, digits=5), ranks = outRanks, errors = round(errorValues, digits=5), Kendall = tau)
# -------------------------------------------------------
# post-optimality analysis if the optimum is found and if kPostOptimality is not NULL, i.e. the solution space is not empty
minWeights <- NULL
maxWeights <- NULL
averageValueFunctions <- NULL
if (!is.null(kPostOptimality) && (lpSolution$optimum == 0)){
# add F \leq F* + k(F*) to the constraints, where F* is the optimum and k(F*) is a positive threshold, which is a small proportion of F*
mat <- rbind(mat,obj)
dir <- c(dir,"<=")
rhs <- c(rhs,kPostOptimality)
minWeights <- c()
maxWeights <- c()
combinedSolutions <- c()
for (i in 1:numCrit){
# first maximize the best ui for each criterion, then minimize it
# this gives the interval of variation for each weight
# the objective function : the first elements correspond to the ui's, the last one to the sigmas
obj<-rep(0,sum(criteriaNumberOfBreakPoints))
obj<-c(obj,rep(0,numAlt))
if (i==1)
pos <- criteriaNumberOfBreakPoints[i]
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+criteriaNumberOfBreakPoints[i]
obj[pos] <- 1
lpSolutionMin <- Rglpk_solve_LP(obj, mat, dir, rhs)
lpSolutionMax <- Rglpk_solve_LP(obj, mat, dir, rhs, max=TRUE)
minWeights <- c(minWeights,lpSolutionMin$optimum)
maxWeights <- c(maxWeights,lpSolutionMax$optimum)
combinedSolutions <- rbind(combinedSolutions,lpSolutionMin$solution)
combinedSolutions <- rbind(combinedSolutions,lpSolutionMax$solution)
}
names(minWeights) <- colnames(performanceTable)
names(maxWeights) <- colnames(performanceTable)
# calculate the average value function, for which each component is the average value obtained for each of the programs above
averageSolution <- apply(combinedSolutions,2,mean)
# create a structure containing the average value functions
averageValueFunctions <- list()
for (i in 1:length(criteriaNumberOfBreakPoints)){
tmp <- c()
if (i==1)
pos <- 0
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])
for (j in 1:criteriaNumberOfBreakPoints[i]){
tmp <- c(tmp,averageSolution[pos+j])
}
tmp<-rbind(criteriaBreakPoints[[i]],tmp)
colnames(tmp)<- NULL
rownames(tmp) <- c("x","y")
averageValueFunctions <- c(averageValueFunctions,list(tmp))
}
names(averageValueFunctions) <- colnames(performanceTable)
}
out <- c(out, list(minimumWeightsPO = minWeights, maximumWeightsPO = maxWeights, averageValueFunctionsPO = averageValueFunctions))
return(out)
}
paterijk/MCDA documentation built on April 7, 2023, 8:31 p.m.
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Defines functions UTA
Documented in UTA
UTA <- function(performanceTable, criteriaMinMax, criteriaNumberOfBreakPoints, epsilon, alternativesRanks = NULL, alternativesPreferences = NULL, alternativesIndifferences = NULL, criteriaLBs=NULL, criteriaUBs=NULL, alternativesIDs = NULL, criteriaIDs = NULL, kPostOptimality = NULL){
## check the input data
if (!((is.matrix(performanceTable) || (is.data.frame(performanceTable)))))
stop("wrong performanceTable, should be a matrix or a data frame")
if (!(is.null(alternativesRanks) || is.vector(alternativesRanks)))
stop("alternativesRanks should be a vector")
if (!(is.null(alternativesPreferences) || is.matrix(alternativesPreferences)))
stop("alternativesPreferences should be a matrix")
if (!(is.null(alternativesIndifferences) || is.matrix(alternativesIndifferences)))
stop("alternativesIndifferences should be a matrix")
if (is.null(alternativesRanks) && is.null(alternativesPreferences) && is.null(alternativesIndifferences))
stop("at least one of alternativesRanks, alternativesPreferences or alternativesIndifferences should not be NULL")
if (!is.null(alternativesRanks) && (!is.null(alternativesPreferences) | !is.null(alternativesIndifferences)))
stop("alternativesRanks and one of alternativesPreferences or alternativesIndifferences cannot be simultaneously not NULL")
if (!(is.vector(criteriaMinMax)))
stop("criteriaMinMax should be a vector")
if (!(is.vector(criteriaNumberOfBreakPoints)))
stop("criteriaNumberOfBreakPoints should be a vector")
if (!(is.null(alternativesIDs) || is.vector(alternativesIDs)))
stop("alternativesIDs should be in a vector")
if (!(is.null(criteriaIDs) || is.vector(criteriaIDs)))
stop("criteriaIDs should be in a vector")
if (!(is.null(criteriaLBs) || is.vector(criteriaLBs)))
stop("criteriaLBs should be in a vector")
if (!(is.null(criteriaUBs) || is.vector(criteriaUBs)))
stop("criteriaUBs should be in a vector")
## filter the data according to the given alternatives and criteria
## in alternativesIDs and criteriaIDs
if (!is.null(alternativesIDs)){
performanceTable <- performanceTable[alternativesIDs,]
if (!is.null(alternativesRanks))
alternativesRanks <- alternativesRanks[alternativesIDs]
if (!is.null(alternativesPreferences)){
tmpIds <- intersect(alternativesPreferences, alternativesIDs)
tmpMatrix <- c()
for (i in 1:dim(alternativesPreferences)[1]){
if (all(alternativesPreferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesPreferences[i,])
}
alternativesPreferences <- tmpMatrix
}
if (!is.null(alternativesIndifferences)){
tmpIds <- intersect(alternativesIndifferences, alternativesIDs)
tmpMatrix <- c()
for (i in 1:dim(alternativesIndifferences)[1]){
if (all(alternativesIndifferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesIndifferences[i,])
}
alternativesIndifferences <- tmpMatrix
}
}
if (!is.null(criteriaIDs)){
criteriaMinMax <- criteriaMinMax[criteriaIDs]
performanceTable <- performanceTable[,criteriaIDs]
criteriaNumberOfBreakPoints <- criteriaNumberOfBreakPoints[criteriaIDs]
}
if (!is.null(criteriaIDs) && !is.null(criteriaUBs)){
criteriaUBs <- criteriaUBs[criteriaIDs]
}
if (!is.null(criteriaIDs) && !is.null(criteriaLBs)){
criteriaLBs <- criteriaLBs[criteriaIDs]
}
# only the alternatives which are in the ranking should be considered for the calculation
# we therefore take the intersection between the alternatives present in the performance
# table and those of the ranking
if (!is.null(alternativesRanks)){
reallyActiveAlternatives <- intersect(rownames(performanceTable),names(alternativesRanks))
if (length(reallyActiveAlternatives) != 0){
performanceTable <- performanceTable[reallyActiveAlternatives,]
alternativesRanks <- alternativesRanks[reallyActiveAlternatives]
} else {
stop("alternatives of alternativesRanks are not compatible with those of performanceTable")
}
}
if (!is.null(alternativesPreferences) || !is.null(alternativesIndifferences)){
reallyActiveAlternatives <- intersect(rownames(performanceTable),rbind(alternativesPreferences,alternativesIndifferences))
if (length(reallyActiveAlternatives) != 0){
performanceTable <- performanceTable[reallyActiveAlternatives,]
if (!is.null(alternativesPreferences)){
tmpIds <- intersect(alternativesPreferences, reallyActiveAlternatives)
tmpMatrix <- c()
for (i in 1:dim(alternativesPreferences)[1]){
if (all(alternativesPreferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesPreferences[i,])
}
alternativesPreferences <- tmpMatrix
}
if (!is.null(alternativesIndifferences)){
tmpIds <- intersect(alternativesIndifferences, reallyActiveAlternatives)
tmpMatrix <- c()
for (i in 1:dim(alternativesIndifferences)[1]){
if (all(alternativesIndifferences[i,] %in% tmpIds))
tmpMatrix <- rbind(tmpMatrix,alternativesIndifferences[i,])
}
alternativesIndifferences <- tmpMatrix
}
} else {
stop("alternatives of alternativesPreferences or alternativesIndifferences are not compatible with those of performanceTable")
}
}
# data is filtered, check for some data consistency
# are the upper and lower bounds given in the function compatible with the data in the performance table ?
if (!(is.null(criteriaUBs))){
if (!all(apply(performanceTable,2,max)<=criteriaUBs))
stop("performanceTable contains higher values than criteriaUBs")
}
if (!(is.null(criteriaLBs))){
if (!all(apply(performanceTable,2,min)>=criteriaLBs))
stop("performanceTable contains lower values than criteriaLBs")
}
if (!all(criteriaNumberOfBreakPoints >= 2))
stop("in criteriaNumberOfBreakPoints there should at least be 2 breakpoints for each criterion")
# if there are less than 2 criteria or 2 alternatives, there is no MCDA problem
if (is.null(dim(performanceTable)))
stop("less than 2 criteria or 2 alternatives")
# if there are no alternatives left in the ranking or the pairwise preferences
# we stop here
if (is.null(alternativesRanks) && is.null(alternativesPreferences) && is.null(alternativesIndifferences))
stop("after filtering none of alternativesRanks, alternativesPreferences or alternativesIndifferences is not NULL")
# -------------------------------------------------------
numCrit <- dim(performanceTable)[2]
numAlt <- dim(performanceTable)[1]
# -------------------------------------------------------
criteriaBreakPoints <- list()
for (i in 1:numCrit){
tmp<-c()
if (!is.null(criteriaLBs))
mini <- criteriaLBs[i]
else{
mini <- min(performanceTable[,i])
}
if (!is.null(criteriaLBs))
maxi <- criteriaUBs[i]
else{
maxi <- max(performanceTable[,i])
}
if (mini == maxi){
# then there is only one value for that criterion, and the algorithm to build the linear interpolation
# will not work correctly
stop(paste("there is only one possible value left for criterion "),colnames(performanceTable)[i])
}
alphai <- criteriaNumberOfBreakPoints[i]
for (j in 1:alphai)
tmp<-c(tmp,mini + (j-1)/(alphai-1) * (maxi - mini))
# due to this formula, the minimum and maximum values might not be exactly the same than the real minimum and maximum values in the performance table
# to be sure there is no rounding problem, we recopy these values in tmp (important for the later comparisons to these values)
tmp[1] <- mini
tmp[alphai] <- maxi
# if the criterion has to be maximized, the worst value is in the first position
# else, we sort the vector the other way around to have the worst value in the first position
if (criteriaMinMax[i] == "min")
tmp<-sort(tmp,decreasing=TRUE)
criteriaBreakPoints <- c(criteriaBreakPoints,list(tmp))
}
names(criteriaBreakPoints) <- colnames(performanceTable)
# -------------------------------------------------------
# a is a matrix decomposing the alternatives in the break point space and adding the sigma columns
a<-matrix(0,nrow=numAlt, ncol=(sum(criteriaNumberOfBreakPoints)+numAlt))
for (n in 1:numAlt){
for (m in 1:numCrit){
if (length(which(performanceTable[n,m]==criteriaBreakPoints[[m]]))!=0){
# then we have a performance value which is on a breakpoint
j<-which(performanceTable[n,m]==criteriaBreakPoints[[m]])
if (m==1)
pos <- j
else
pos<-sum(criteriaNumberOfBreakPoints[1:(m-1)])+j
a[n,pos] <- 1
}
else{
# then we have value which needs to be approximated by a linear interpolation
# let us first search the lower and upper bounds of the interval of breakpoints around the value
if (criteriaMinMax[m] == "min"){
j<-which(performanceTable[n,m]>criteriaBreakPoints[[m]])[1]-1
}
else{
j<-which(performanceTable[n,m]<criteriaBreakPoints[[m]])[1]-1
}
if (m==1)
pos <- j
else
pos<-sum(criteriaNumberOfBreakPoints[1:(m-1)])+j
a[n,pos] <- 1-(performanceTable[n,m]-criteriaBreakPoints[[m]][j])/(criteriaBreakPoints[[m]][j+1] - criteriaBreakPoints[[m]][j])
a[n,pos+1] <- (performanceTable[n,m]-criteriaBreakPoints[[m]][j])/(criteriaBreakPoints[[m]][j+1] - criteriaBreakPoints[[m]][j])
}
# and now for sigma
a[n,dim(a)[2]-numAlt+n] <- 1
}
}
# -------------------------------------------------------
# the objective function : the first elements correspond to the ui's, the last one to the sigmas
obj<-rep(0,sum(criteriaNumberOfBreakPoints))
obj<-c(obj,rep(1,numAlt))
# -------------------------------------------------------
# we now build the part of the constraints matrix concerning the order / preferences / indifferences given by the decision maker
preferenceConstraints<-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
indifferenceConstraints <-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
if (!is.null(alternativesRanks)){
# determine now in which order the alternatives should be treated for the constraints
indexOrder <- c()
orderedAlternativesRanks <- sort(alternativesRanks)
tmpRanks1 <- alternativesRanks
tmpRanks2 <- alternativesRanks
while (length(orderedAlternativesRanks) != 0){
# search for the alternatives of lowest rank
tmpIndex <- which(alternativesRanks == orderedAlternativesRanks[1])
for (j in 1:length(tmpIndex))
indexOrder<-c(indexOrder,tmpIndex[j])
# remove the rank which has been dealt with now
orderedAlternativesRanks<-orderedAlternativesRanks[-which(orderedAlternativesRanks==orderedAlternativesRanks[1])]
}
for (i in 1:(length(alternativesRanks)-1)){
if (alternativesRanks[indexOrder[i]] == alternativesRanks[indexOrder[i+1]]){
# then the alternatives are indifferent and their overall values are equal
indifferenceConstraints <- rbind(indifferenceConstraints, a[indexOrder[i],] - a[indexOrder[i+1],])
}
else{
# then the first alternative i is ranked better than the second one i+1 and i has an overall value higher than i+1
preferenceConstraints <- rbind(preferenceConstraints, a[indexOrder[i],] - a[indexOrder[i+1],])
}
}
}
if (!is.null(alternativesPreferences)){
for (i in 1:dim(alternativesPreferences)[1]){
preferenceConstraints <- rbind(preferenceConstraints, a[which(rownames(performanceTable)==alternativesPreferences[i,1]),] - a[which(rownames(performanceTable)==alternativesPreferences[i,2]),])
}
}
if (!is.null(alternativesIndifferences)){
for (i in 1:dim(alternativesIndifferences)[1]){
indifferenceConstraints <- rbind(indifferenceConstraints, a[which(rownames(performanceTable)==alternativesIndifferences[i,1]),] - a[which(rownames(performanceTable)==alternativesIndifferences[i,2]),])
}
}
# add this to the constraints matrix mat
mat<-rbind(preferenceConstraints,indifferenceConstraints)
# right hand side of this part of mat
rhs <- c()
if (dim(preferenceConstraints)[1]!=0){
for (i in (1:dim(preferenceConstraints)[1]))
rhs<-c(rhs,epsilon)
}
if (dim(indifferenceConstraints)[1]!=0){
for (i in (1:dim(indifferenceConstraints)[1]))
rhs<-c(rhs,0)
}
# direction of the inequality for this part of mat
dir <- c()
if (dim(preferenceConstraints)[1]!=0){
for (i in (1:dim(preferenceConstraints)[1]))
dir<-c(dir,">=")
}
if (dim(indifferenceConstraints)[1]!=0){
for (i in (1:dim(indifferenceConstraints)[1]))
dir<-c(dir,"==")
}
# -------------------------------------------------------
# now the monotonicity constraints on the value functions
monotonicityConstraints<-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
for (i in 1:length(criteriaNumberOfBreakPoints)){
for (j in 1:(criteriaNumberOfBreakPoints[i]-1)){
tmp<-rep(0,sum(criteriaNumberOfBreakPoints)+numAlt)
if (i==1)
pos <- j
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+j
tmp[pos] <- -1
tmp[pos+1] <- 1
monotonicityConstraints <- rbind(monotonicityConstraints, tmp)
}
}
# add this to the constraints matrix mat
mat<-rbind(mat,monotonicityConstraints)
# the direction of the inequality
for (i in (1:dim(monotonicityConstraints)[1]))
dir<-c(dir,">=")
# the right hand side of this part of mat
for (i in (1:dim(monotonicityConstraints)[1]))
rhs<-c(rhs,0)
# -------------------------------------------------------
# normalization constraint for the upper values of the value functions (sum = 1)
tmp<-rep(0,sum(criteriaNumberOfBreakPoints)+numAlt)
for (i in 1:length(criteriaNumberOfBreakPoints)){
if (i==1)
pos <- criteriaNumberOfBreakPoints[i]
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+criteriaNumberOfBreakPoints[i]
tmp[pos] <- 1
}
# add this to the constraints matrix mat
mat<-rbind(mat,tmp)
# the direction of the inequality
dir<-c(dir,"==")
# the right hand side of this part of mat
rhs<-c(rhs,1)
# -------------------------------------------------------
# now the normalizaiton constraints for the lower values of the value functions (= 0)
minValueFunctionsConstraints<-matrix(nrow=0, ncol=sum(criteriaNumberOfBreakPoints)+numAlt)
for (i in 1:length(criteriaNumberOfBreakPoints)){
tmp<-rep(0,sum(criteriaNumberOfBreakPoints)+numAlt)
if (i==1)
pos <- i
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+1
tmp[pos] <- 1
minValueFunctionsConstraints <- rbind(minValueFunctionsConstraints,tmp)
}
# add this to the constraints matrix mat
mat<-rbind(mat,minValueFunctionsConstraints)
# the direction of the inequality
for (i in (1:dim(minValueFunctionsConstraints)[1]))
dir<-c(dir,"==")
# the right hand side of this part of mat
for (i in (1:dim(minValueFunctionsConstraints)[1]))
rhs<-c(rhs,0)
# -------------------------------------------------------
lpSolution <- Rglpk_solve_LP(obj, mat, dir, rhs)
# -------------------------------------------------------
# create a structure containing the value functions
valueFunctions <- list()
for (i in 1:length(criteriaNumberOfBreakPoints)){
tmp <- c()
if (i==1)
pos <- 0
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])
for (j in 1:criteriaNumberOfBreakPoints[i]){
tmp <- c(tmp,lpSolution$solution[pos+j])
}
tmp<-rbind(criteriaBreakPoints[[i]],tmp)
colnames(tmp)<- NULL
rownames(tmp) <- c("x","y")
valueFunctions <- c(valueFunctions,list(tmp))
}
names(valueFunctions) <- colnames(performanceTable)
# it might happen on certain computers that these value functions
# do NOT respect the monotonicity constraints (especially because of too small differences and computer arithmetics)
# therefore we check if they do, and if not, we "correct" them
for (i in 1:numCrit){
for (j in 1:(criteriaNumberOfBreakPoints[i]-1)){
if (valueFunctions[[i]][2,j] > valueFunctions[[i]][2,j+1]){
valueFunctions[[i]][2,j+1] <- valueFunctions[[i]][2,j]
}
}
}
# -------------------------------------------------------
overallValues <- as.vector(t(a[,1:sum(criteriaNumberOfBreakPoints)]%*%lpSolution$solution[1:sum(criteriaNumberOfBreakPoints)]))
names(overallValues) <- rownames(performanceTable)
# -------------------------------------------------------
# the error values for each alternative (sigma)
errorValues <- as.vector(lpSolution$solution[(sum(criteriaNumberOfBreakPoints)+1):length(lpSolution$solution)])
names(errorValues) <- rownames(performanceTable)
# -------------------------------------------------------
# the ranks of the alternatives
outRanks <- rank(-overallValues, ties.method="min")
# -------------------------------------------------------
if ((numAlt >= 3) && !is.null(alternativesRanks))
tau = cor(alternativesRanks,outRanks,method="kendall")
else
tau = NULL
# prepare the output
out <- list(optimum = round(lpSolution$optimum, digits=5), valueFunctions = valueFunctions, overallValues = round(overallValues, digits=5), ranks = outRanks, errors = round(errorValues, digits=5), Kendall = tau)
# -------------------------------------------------------
# post-optimality analysis if the optimum is found and if kPostOptimality is not NULL, i.e. the solution space is not empty
minWeights <- NULL
maxWeights <- NULL
averageValueFunctions <- NULL
if (!is.null(kPostOptimality) && (lpSolution$optimum == 0)){
# add F \leq F* + k(F*) to the constraints, where F* is the optimum and k(F*) is a positive threshold, which is a small proportion of F*
mat <- rbind(mat,obj)
dir <- c(dir,"<=")
rhs <- c(rhs,kPostOptimality)
minWeights <- c()
maxWeights <- c()
combinedSolutions <- c()
for (i in 1:numCrit){
# first maximize the best ui for each criterion, then minimize it
# this gives the interval of variation for each weight
# the objective function : the first elements correspond to the ui's, the last one to the sigmas
obj<-rep(0,sum(criteriaNumberOfBreakPoints))
obj<-c(obj,rep(0,numAlt))
if (i==1)
pos <- criteriaNumberOfBreakPoints[i]
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])+criteriaNumberOfBreakPoints[i]
obj[pos] <- 1
lpSolutionMin <- Rglpk_solve_LP(obj, mat, dir, rhs)
lpSolutionMax <- Rglpk_solve_LP(obj, mat, dir, rhs, max=TRUE)
minWeights <- c(minWeights,lpSolutionMin$optimum)
maxWeights <- c(maxWeights,lpSolutionMax$optimum)
combinedSolutions <- rbind(combinedSolutions,lpSolutionMin$solution)
combinedSolutions <- rbind(combinedSolutions,lpSolutionMax$solution)
}
names(minWeights) <- colnames(performanceTable)
names(maxWeights) <- colnames(performanceTable)
# calculate the average value function, for which each component is the average value obtained for each of the programs above
averageSolution <- apply(combinedSolutions,2,mean)
# create a structure containing the average value functions
averageValueFunctions <- list()
for (i in 1:length(criteriaNumberOfBreakPoints)){
tmp <- c()
if (i==1)
pos <- 0
else
pos<-sum(criteriaNumberOfBreakPoints[1:(i-1)])
for (j in 1:criteriaNumberOfBreakPoints[i]){
tmp <- c(tmp,averageSolution[pos+j])
}
tmp<-rbind(criteriaBreakPoints[[i]],tmp)
colnames(tmp)<- NULL
rownames(tmp) <- c("x","y")
averageValueFunctions <- c(averageValueFunctions,list(tmp))
}
names(averageValueFunctions) <- colnames(performanceTable)
}
out <- c(out, list(minimumWeightsPO = minWeights, maximumWeightsPO = maxWeights, averageValueFunctionsPO = averageValueFunctions))
return(out)
}
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