Global multi-optimization function specification in R - r

Question

I would like to use ngsa2 of mco package to solve an optimization problem with 3 objectives. In short, I am lookink for optimal land uses to solve environmental problem.
Here is my experiment:
- 100 land uses are possible in total (all.options in the code below), each land use being characterized by three performances (main.goal1, main.goal2 and main.goal3).
- I have 50 fields, whose characteristics (soil in fields.Kq) subset the 100 land uses (i.e., all land uses are not possible for each field) => options.soil1 and options.soil2
My objective is to assign a land use to each of my 50 fields, in order to minimize alltogether main.goal1, main.goal2 and main.goal3. From what I read, Genetic Algorithms are very powerful for such type of problems.
So here are my virtual data.
set.seed(0)
all.options<-data.frame(num.option=1:100,main.goal1 = abs(rnorm(100)),
main.goal2 = abs(rnorm(100)),
main.goal3 = abs(rnorm(100))) # all possible combinations of the 3 goals
options.soil1<-subset(all.options, main.goal1>0.5) # possible combinations for soil1
options.soil2<-subset(all.options, main.goal3<0.5) # possible combinations for soil2
fields.Kq<-data.frame(num.field=1:50,soil=round(runif(50,0,1),0))
I guess that my objective function should look like
my.function<-function(x) {
x[1]<-sum(A[,1) # main.goal1 for selected options for each of fields.Kq
x[2]<-sum(A[,2) # main.goal2 for selected options for each of fields.Kq
x[3]<-sum(A[,3) # main.goal3 for selected options for each of fields.Kq
} # where A should be a matrix of 50 lines with one line per field, and #"choosen" land use option
nsga2(my.function)
Unfortunately I could not go further, as I am new in optimizing with R. How to build the matrix A, with choosen land use for each field?
And using, nga, how to return these land uses? (together with the optimized (minimized) values for main.goal1, main.goal2 and main.goal3?
Thanks in advance for all the help you could provide me, I am really looking forward advices/links/books... to advance on my optimization problem.
Best regards,
LH

Answer 1

Here is how I solved the problem:
library("mco")
set.seed(0)
all.options<-data.frame(num.option=1:100,main.goal1 = abs(rnorm(100)),
main.goal2 = abs(rnorm(100)),
main.goal3 = abs(rnorm(100)),soil=c(rep("soilType1",50),rep("soilType2",50))) # all possible combinations of the 3 goals
fields.Kq<-data.frame(num.field=1:50,soil=rep(c("soilType1","soilType2"),25))
main.goal1=function(x) # x - a vector
{
main.goal1=sum(all.options[x,1]) # compute main.goal1
return(main.goal1) }
main.goal2=function(x) # x - a vector
{
main.goal2=sum(all.options[x,2]) # compute main.goal2
return(main.goal2) }
main.goal3=function(x) # x - a vector
{
main.goal3=sum(all.options[x,3]) # compute main.goal3
return(main.goal3) }
eval=function(x) c(main.goal1(x),main.goal2(x),main.goal3(x)) #objectivefunction
D<-length(fields.Kq[,1]) # number of fields
D2<-length(fields.Kq[,1])/2 # number of fields per type (simplified)
D.soil1<-max(which(all.options$soil=="soilType1")) # get boundary for bound soil1
D.soil2<-min(which(all.options$soil=="soilType2")) # get boundary for bound soil2
G=nsga2(fn=eval,idim=D,odim=3,
lower.bounds=c(rep(1,D2),rep(D.soil2,D2)),upper.bounds=c(rep(D.soil1,D2),rep(100,D2)), # lower/upper bound: min/max num option
popsize=20,generations=1:1000, cprob = 0.7, cdist = 5,
mprob = 0.2, mdist = 10)
I defined it thanks to exemples found in the very helpful and informative book "Modern optimization in R" by Paulo Cortez.
LH