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Telecommunication problems Description
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 12: Telecommunication problems
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
Data Files
g1rely.mos (!****************************************************** Mosel Example Problems ====================== file g1rely.mos ``````````````` Reliability of a telecommunications network A military telecommunications network has eleven sites connected by bidirectional lines for data transmission. Due to reliability reasons, node 10 and 11 must remain able to communicate even if any three other sites are destroyed. Is this possible given the current network configuration? This problem can be modeled as a maximum flow problem where the graph with N nodes is encoded as an adjacency matrix. To create a more compact model, the variables 'flow' are only defined for existing arcs. Since there is a bidirectional connection between each node, only one direction is provided in the data and we define the opposite direction within the code. We use the function 'round' to transform the result of 'getsol' from 'real' to 'integer'. (c) 2008-2022 Fair Isaac Corporation author: S. Heipcke, Mar. 2002, rev. Mar. 2022 *******************************************************!) model "G-1 Network reliability" uses "mmxprs" 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 'g1rely.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 sum(m in NODES) flow(m,n) = sum(m in NODES) flow(n,m) sum(m in NODES) flow(n,m) <= 1 end-do ! No return to SOURCE node 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 and getsol(flow(SOURCE,n))>0) do 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-do ! Alternative solution display storing paths in a list structure declarations SolPath: array(range) of list of integer end-declarations forall(n in NODES | n<>SOURCE and n<>SINK and getsol(flow(SOURCE,n))>0, i as counter) do SolPath(i):= [SOURCE, n] while (SolPath(i).last<>SINK) SolPath(i) += [round(getsol(sum(m in NODES) m*flow(SolPath(i).last,m)))] end-do writeln("Paths: ", SolPath) end-model | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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