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Maximum flow in a telecom network

Description
We wish to test the reliability of a telecommunications network that consists of eleven sites connected by bidirectional lines for data transmission. The specifications require that the two sites (nodes) 10 and 11 of the network remain able to communicate even if any three other sites of the network are destroyed.

Further explanation of this example: 'Applications of optimization with Xpress-MP', Section 12.1 'Network reliability' Similar problem: Section 15.1 'Water conveyance/water supply management'


Source Files

Data Files





maxflow_graph.mos

(!******************************************************
   Mosel Example Problems
   ======================

   file maxflow.mos
   ````````````````
   TYPE:         Maximum flow with unitary capacities
   DIFFICULTY:   3
   FEATURES:     MIP problem, encoding of arcs, `range', `exists', `create',
                 algorithm for printing paths, `forall-do', `while-do', 
                 `round', graphical representation of results
   DESCRIPTION:  We wish to test the reliability of a telecommunications 
                 network that consists of eleven sites connected by 
                 bidirectional lines for data transmission. The specifications 
                 require that the two sites (nodes) 10 and 11 of the network 
                 remain able to communicate even if any three other sites of 
                 the network are destroyed.    
   FURTHER INFO: `Applications of optimization with Xpress-MP', 
                 Section 12.1 `Network reliability'
                 Similar problem: 
                 Section 15.1 `Water conveyance/water supply management'
   
   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, 2002, rev. Sep. 2107
*******************************************************!)

model "Network reliability"
 uses "mmxprs", "mmsvg"

 declarations
  NODES: range                        ! Set of nodes
  SOURCE = 10; SINK = 11              ! Source and sink nodes

  ARC: dynamic array(NODES,NODES) of integer  ! 1 if arc defined, 0 otherwise
  flow: dynamic array(NODES,NODES) of mpvar   ! 1 if flow on arc, 0 otherwise
 end-declarations

 initializations from 'maxflow.dat'
  ARC
 end-initializations

 forall(n,m in NODES | exists(ARC(n,m)) and n<m ) ARC(m,n):= ARC(n,m)
 forall(n,m in NODES | exists(ARC(n,m)) )  create(flow(n,m))

! Objective: number of disjunctive paths
 Paths:= sum(n in NODES) flow(SOURCE,n)

! Flow conservation and capacities
 forall(n in NODES | n<>SOURCE and n<>SINK) do
  Balance(n):= sum(m in NODES) flow(m,n) = sum(m in NODES) flow(n,m)
  Capacity(n):= sum(m in NODES) flow(n,m) <= 1
 end-do 

! No return to SOURCE node
 NoReturn:= sum(n in NODES) flow(n,SOURCE) = 0

 forall(n,m in NODES | exists(ARC(n,m)) )  flow(n,m) is_binary

! Solve the problem
 maximize(Paths)
 
! Solution printing
 writeln("Total number of paths: ", getobjval)

 forall(n in NODES | n<>SOURCE and n<>SINK) 
  if(getsol(flow(SOURCE,n))>0) then
   write(SOURCE, " - ",n)
   nnext:=n
   while (nnext<>SINK) do
    nnext:=round(getsol(sum(m in NODES) m*flow(nnext,m)))
    write(" - ", nnext)
   end-do
   writeln
  end-if

! Solution drawing
 declarations
  X,Y: array(NODES) of integer        ! x-y-coordinates of nodes
 end-declarations
 
 initializations from 'maxflow.dat'
  [X,Y] as 'POS'
 end-initializations

 svgsetgraphviewbox(0,0,max(n in NODES)X(n)+10, max(n in NODES)Y(n)+10)
 svgsetgraphscale(2)

 svgaddgroup("Arcs", "Network", SVG_GREY)
 forall(n in NODES| n<>SOURCE and n<>SINK) do
  svgaddpoint(X(n), Y(n))
  svgaddtext(X(n), Y(n)+1, text(n))
 end-do
 forall(n,m in NODES | exists(ARC(n,m)) and n<m )
  svgaddline(X(n), Y(n), X(m), Y(m))

 svgaddgroup("Flow", "Disjunctive Paths", SVG_RED)
 forall(n in {SOURCE,SINK}) do
  svgaddpoint(X(n), Y(n))
  svgaddtext(X(n), Y(n)+1, string(n))
 end-do
 forall(n,m in NODES | exists(ARC(n,m)) and getsol(flow(n,m))>0) 
   svgaddline(X(n), Y(n), X(m), Y(m))

 svgsave("maxflow.svg")
 svgrefresh
 svgwaitclose("Close browser window to terminate model execution.", 1)
end-model

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