 FICO Xpress Optimization Examples Repository
 FICO Optimization Community FICO Xpress Optimization Home   Facility location

Description
Euclidean facility location problem.

Further explanation of this example:

Source Files

emfl.mos

```(!*********************************************************************
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
*********************************************************************!)

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)
setparam("XNLP_solver", 0)
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

```   