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Locate airport while minimizing average distance

Description
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.

Further explanation of this example: 'Mosel User Guide', Section 17.4.2 Xpress NonLinear


Source Files

Data Files





airport_nl.mos

(!*********************************************************************
   Mosel NL examples
   =================
   file airport_nl.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.

   - XNLP version -

   (c) 2008 Fair Issac Corporation
       author: S. Heipcke, May 2008rev. Mar 2013
*********************************************************************!)

model "airport"
 uses "mmxnlp"

 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)))

end-model

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