(!*********************************************************************
   Mosel NL examples
   =================
   file emfl.mos
   `````````````
   Euclidean facility location problem
   Convex NLP problem

   Based on AMPL model emfl_eps.mod
   Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/facloc/ 

   *** This model cannot be run with a Community Licence 
       for the provided data instance ***

   (c) 2008 Fair Issac Corporation
       author: S. Heipcke, Sep. 2008, rev. Jun. 2023
*********************************************************************!)

model "emfl"
 uses "mmxnlp"

 parameters
  EPS = 1.0E-8
  M = 200                         ! Number of existing facilities
  N1 = 5
  N2 = 5
 end-parameters 

 declarations
  N = N1*N2                       ! Number of new facilities
  RM = 1..M                       ! Set of existing facilities
  R2 = 1..2
  RN = 1..N                       ! Set of new facilities
  POS: array(RM,R2) of real       ! Coordinates of existing facility
  WEIGHTON: array(RM,RN) of real  ! Weights associated with old-new connections
  WEIGHTNN: array(RN,RN) of real  ! Weights associated with new-new connections
  IVAL: array(RN,R2) of real      ! Start values for x

  x: array(RN,R2) of mpvar        ! Coordinates of new facilities
 end-declarations

 forall(i in RN,j in R2) x(i,j) is_free

 setrandseed(3)
 forall(i in RM, k in 1..2) POS(i,k):= random
 forall(j in RN, jj in RN | j < jj) WEIGHTNN(j,jj):= 0.2

 forall(j1 in 1..N1, j2 in 1..N2) do
  IVAL(j1+N1*(j2-1),1):= (j1-0.5)/N1
  IVAL(j1+N1*(j2-1),2):= (j2-0.5)/N2
  setinitval(x(j1+N1*(j2-1),1), IVAL(j1+N1*(j2-1),1))
  setinitval(x(j1+N1*(j2-1),2), IVAL(j1+N1*(j2-1),2))
 end-do

 forall(i in RM, j in RN)          
   WEIGHTON(i,j):= if(abs(POS(i,1)-IVAL(j,1)) <= 1/(2*N1) and
                      abs(POS(i,2)-IVAL(j,2)) <= 1/(2*N2),
                      0.95, 
                      if(abs(POS(i,1)-IVAL(j,1)) <= 2/(2*N1) and
                         abs(POS(i,2)-IVAL(j,2)) <= 2/(2*N2),
                         0.05, 0) )

! Objective function: distances
! A small positive constant 'EPS' is added to make sure 'sqrt' is differentiable
 SumEucl:= sum(i in RM,j in RN) WEIGHTON(i,j)*sqrt(EPS + sum(k in R2) (x(j,k)-POS(i,k))^2) +
        sum(j,jj in RN | j<jj) WEIGHTNN(j,jj)*sqrt(EPS + sum(k in R2) (x(j,k)-x(jj,k))^2)

 setparam("XNLP_verbose", true)
! Since this is a convex problem, it is sufficient to call a local solver
 setparam("xprs_nlpsolver", 1)    
 setparam("XNLP_solver", 0)       ! Solver choice: Xpress NonLinear (SLP)
 minimise(SumEucl)
 
 writeln("Solution: ", SumEucl.sol, " (eps), ",
   getsol(sum(i in RM,j in RN) WEIGHTON(i,j)*sqrt(sum(k in R2) (x(j,k)-POS(i,k))^2) +
     sum(j,jj in RN | j<jj) WEIGHTNN(j,jj)*sqrt(sum(k in R2) (x(j,k)-x(jj,k))^2)) )
 
 forall(i in RN) do
  write(i, ": ")
  forall(j in R2) write(x(i,j).sol, ", ")
  writeln
 end-do

end-model