(!*********************************************************************
Mosel NL examples
=================
file airport.mos
````````````````
Locate N airports each within a specified distance of a
city centre, and minimise the sum of square of the distances
between all the airports.
QCQP problem.
Based on AMPL model airport.mod by Hande Y. Benson
Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/cute/
Reference:
Rodrigo de Barros Nabholz & Maria Aparecida Diniz Ehrhardt
November 1994, DMA - IMECC- UNICAMP.
(c) 2008 Fair Issac Corporation
author: S. Heipcke, May 2008, rev. Mar. 2013
*********************************************************************!)
model "airport (QPQC)"
uses "mmxprs", "mmnl"
declarations
RN: range ! Set of airports
R: array(RN) of real ! Square of max. distance to given location
CX,CY: array(RN) of real ! Target location for each point
x,y: array(RN) of mpvar ! x-/y- coordinates
LimDist: array(RN) of nlctr
end-declarations
initialisations from "airport.dat"
CY CX R
end-initialisations
! Set bounds on variables
forall(i in RN) do
-10<=x(i); x(i)<=10
-10<=y(i); y(i)<=10
end-do
! Objective: minimise the total squared distance between all points
TotDist:= sum(i,j in RN | i<j) ((x(i)-x(j))^2+(y(i)-y(j))^2)
! Constraints: all points within given distance of their target location
forall(i in RN)
LimDist(i):= (x(i)-CX(i))^2+(y(i)-CY(i))^2 <= R(i)
(! For exporting the matrix file
setparam("XPRS_loadnames", true)
loadprob(TotDist)
writeprob("airport.mat","l")
!)
setparam("XPRS_verbose", true);
minimise(TotDist);
writeln("Solution: ", getobjval);
forall(i in RN) writeln(i, ": ", getsol(x(i)), ", ", getsol(y(i)))
end-model
|
(!*********************************************************************
Mosel NL examples
=================
file airport.mos
````````````````
Locate N airports each within a specified distance of a
city centre, and minimise the sum of square of the distances
between all the airports.
QCQP problem.
Based on AMPL model airport.mod by Hande Y. Benson
Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/cute/
Reference:
Rodrigo de Barros Nabholz & Maria Aparecida Diniz Ehrhardt
November 1994, DMA - IMECC- UNICAMP.
(c) 2008 Fair Issac Corporation
author: S. Heipcke, May 2008, rev. Sep. 2017
*********************************************************************!)
model "airport (QPQC)"
uses "mmxprs", "mmnl", "mmsvg"
declarations
RN: range ! Set of airports
R: array(RN) of real ! Square of max. distance to given location
CX,CY: array(RN) of real ! Target location for each point
x,y: array(RN) of mpvar ! x-/y-coordinates to determine
end-declarations
initialisations from "airport.dat"
CY CX R
end-initialisations
! Set bounds on variables
forall(i in RN) do
-10<=x(i); x(i)<=10
-10<=y(i); y(i)<=10
end-do
! Objective: minimise the total squared distance between all points
TotDist:= sum(i,j in RN | i<j) ((x(i)-x(j))^2+(y(i)-y(j))^2)
! Constraints: all points within given distance of their target location
forall(i in RN)
LimDist(i):= (x(i)-CX(i))^2+(y(i)-CY(i))^2 <= R(i)
setparam("XPRS_verbose", true);
minimise(TotDist);
writeln("Solution: ", getobjval);
forall(i in RN) writeln(i, ": ", getsol(x(i)), ", ", getsol(y(i)))
! **** Display the solution as user graph ****
! Scale the size of the displayed graph
svgsetgraphscale(50)
svgsetgraphpointsize(3)
svgsetgraphstyle(SVG_STROKEWIDTH,3)
! Draw the target locations
svgaddgroup("T", "Target area", SVG_SILVER)
svgsetstyle(SVG_FILL,SVG_CURRENT)
forall(i in RN) svgaddcircle(CX(i), CY(i), sqrt(R(i)))
! Draw the solution points
svgaddgroup("S", "Solution", SVG_BLUE)
forall(i in RN) svgaddpoint(x(i).sol, y(i).sol)
! Update the display
svgrefresh
svgsave("airport.svg")
svgwaitclose("Close browser window to terminate model execution.", 1)
end-model
|
(!******************************************************
Mosel User Guide Example Problems
=================================
file fin_nl.mos
```````````````
Financial application solved by SLP.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, June 2003, rev. Feb. 2013
*******************************************************!)
model "Recursion (NLP)"
uses "mmxnlp" ! Use Xpress NonLinear
declarations
NT=6 ! Time horizon
QUARTERS=1..NT ! Range of time periods
M,P,V: array(QUARTERS) of real ! Payments
interest: array(QUARTERS) of mpvar ! Interest
net: array(QUARTERS) of mpvar ! Net
balance: array(QUARTERS) of mpvar ! Balance
rate: mpvar ! Interest rate
end-declarations
M:: [-1000, 0, 0, 0, 0, 0]
P:: [206.6, 206.6, 206.6, 206.6, 206.6, 0]
V:: [-2.95, 0, 0, 0, 0, 0]
setinitval(rate, 0) ! Set initial values for variables
forall(t in QUARTERS) setinitval(balance(t), 1)
! net = payments - interest
forall(t in QUARTERS) net(t) = (M(t)+P(t)+V(t)) - interest(t)
! Money balance across periods
forall(t in QUARTERS) balance(t) = if(t>1, balance(t-1), 0) - net(t)
! Interest rate
forall(t in 2..NT) -(365/92)*interest(t) + balance(t-1) * rate = 0
interest(1) = 0 ! Initial interest is zero
forall (t in QUARTERS) net(t) is_free
forall (t in 1..NT-1) balance(t) is_free
balance(NT) = 0 ! Final balance is zero
! setparam("XNLP_VERBOSE",true) ! Uncomment to see detailed output
setparam("XNLP_SOLVER", 0) ! Use the SLP solver
minimize(0) ! Solve the problem (get feasible)
! Print the solution
writeln("\nThe interest rate is ", getsol(rate))
write(strfmt("t",5), strfmt(" ",4))
forall(t in QUARTERS) write(strfmt(t,5), strfmt(" ",3))
write("\nBalances ")
forall(t in QUARTERS) write(strfmt(getsol(balance(t)),8,2))
write("\nInterest ")
forall(t in QUARTERS) write(strfmt(getsol(interest(t)),8,2))
writeln
end-model
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