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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 By clicking on a file name, a preview is opened at the bottom of this page.
Data Files airport_nl_graph.mos (!********************************************************************* Mosel NL examples ================= file airport_nl_graph.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, graph drawing - (c) 2008 Fair Issac Corporation author: S. Heipcke, May 2008, rev. Sep. 2017 *********************************************************************!) model "airport" uses "mmxnlp", "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) svgaddellipse(CX(i), CY(i), sqrt(R(i)), sqrt(R(i))) ! Draw the solution points svgaddgroup("S", "Solution", SVG_BLUE) forall(i in RN) svgaddpoint(x(i).sol, y(i).sol) svgsave("airport.svg") svgrefresh svgwaitclose("Close browser window to terminate model execution.", 1) end-model | |||||||||||||

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