(!*********************************************************************
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
|
(!*********************************************************************
Mosel NL examples
=================
file emfl_graph.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/
- Graphical representation of results -
*** 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", "mmsvg"
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
!**************** Graphical representation of results ****************
! Draw links between facilities
svgaddgroup("GrXSArc", "Arcs w<0.15", svgcolor(255,200,50))
svgsetstyle(SVG_STROKEWIDTH, 0.5)
forall(j in RN, jj in RN | j < jj and WEIGHTNN(j,jj)<0.15 and WEIGHTNN(j,jj)>0)
svgaddline(x(j,1).sol, x(j,2).sol, x(jj,1).sol, x(jj,2).sol)
forall(i in RM, j in RN | WEIGHTON(i,j)<0.15 and WEIGHTON(i,j)>0)
svgaddline(POS(i,1), POS(i,2), x(j,1).sol, x(j,2).sol)
svgaddgroup("GrSArc", "Arcs w<0.5", svgcolor(240,175,35))
svgsetstyle(SVG_STROKEWIDTH, 1)
forall(j in RN, jj in RN | j < jj and WEIGHTNN(j,jj)<0.5 and WEIGHTNN(j,jj)>=0.15)
svgaddline(x(j,1).sol, x(j,2).sol, x(jj,1).sol, x(jj,2).sol)
forall(i in RM, j in RN | WEIGHTON(i,j)<0.5 and WEIGHTON(i,j)>=0.15)
svgaddline(POS(i,1), POS(i,2), x(j,1).sol, x(j,2).sol)
svgaddgroup("GrMArc", "Arcs w>=0.5", svgcolor(225,150,20))
svgsetstyle(SVG_STROKEWIDTH, 3)
forall(j in RN, jj in RN | j < jj and WEIGHTNN(j,jj)>=0.5)
svgaddline(x(j,1).sol, x(j,2).sol, x(jj,1).sol, x(jj,2).sol)
forall(i in RM, j in RN | WEIGHTON(i,j)>=0.5)
svgaddline(POS(i,1), POS(i,2), x(j,1).sol, x(j,2).sol)
! Draw facility nodes
svgaddgroup("OldFac", "Existing facilities", svgcolor(135,135,135))
forall(i in RM) svgaddpoint(POS(i,1), POS(i,2))
svgaddgroup("NewFac", "New facilities", svgcolor(163,18,14))
forall(j in RN) svgaddpoint(x(j,1).sol, x(j,2).sol)
! Scale the size of the displayed graph
svgsetgraphscale(500)
svgsetgraphpointsize(2)
svgsetgraphstyle(SVG_STROKEWIDTH,2)
svgsave("emfl.svg")
svgrefresh
svgwaitclose("Close browser window to terminate model execution.", 1)
end-model
|
