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Frequency assignment problem

Description
Frequency assignment problem: 'abs', 'distance', and 'all-different' constraints; branching strategy for variables; solution callback; interrupting and restarting the search.

Further explanation of this example: 'Xpress Kalis User Guide', Section 3.4 abs and distance: Frequency assignment


Source Files





freqasgn.mos

(!****************************************************************
   CP example problems
   ===================
   
   file freqasgn.mos
   `````````````````
   Frequency assignment problem from telecommunications.

   We are given a network of cells (nodes) with requirements of 
   discrete frequency bands. Each cell has a demand of a number of 
   frequencies (bands).
   The objective is to minimize the number of frequencies used in 
   the network so that
   (1) Neighboring nodes all use different frequencies (interference).
   (2) If a cell uses several frequencies they must all be different
       by at least 2.

   (c) 2008 Artelys S.A. and Fair Isaac Corporation
       Creation: 2005, rev. Mar. 2013       
*****************************************************************!)

model "Frequency assignment"
 uses "kalis"
 
 forward public procedure print_solution
  
 declarations
  NODES = 1..10                               ! Range of nodes
  LINKS = 1..18                               ! Range of links between nodes
  DEM: array(NODES) of integer                ! Demand of nodes
  LINK: array(LINKS,1..2) of integer          ! Neighboring nodes
  INDEX: array(NODES) of integer              ! Start index in 'use'
  NUMDEM: integer                             ! Upper bound on no. of freq.
 end-declarations

 DEM :: (1..10)[4, 5, 2, 3, 2, 4, 3, 4, 3, 2]
 LINK:: (1..18,1..2)[1, 3, 1, 4, 1, 6, 
                     2, 4, 2, 7, 
                     3, 4, 3, 6, 3, 8, 3, 9,
                     4, 7, 4, 9, 4,10, 
                     5, 7, 5, 8, 5, 9, 
                     6, 9, 7, 8, 8,10]
 NUMDEM:= sum(n in NODES) DEM(n)

! Correspondence of nodes and demand indices:
! use(d) d = 1, ..., DEM(1) correspond to the demands of node 1
!            d = DEM(1)+1, ..., DEM(1)+DEM(2))     - " -     node 2  etc.
 INDEX(1):= 1
 forall(n in NODES | n > 1) INDEX(n) := INDEX(n-1) + DEM(n-1)

 declarations
  DEMANDS = 1..NUMDEM                         ! Range of frequency demands
  use: array(DEMANDS) of cpvar                ! Frequency used for a demand
  numfreq: cpvar                              ! Number of frequencies used
  Strategy: array(range) of cpbranching
 end-declarations

! Setting the domain of the decision variables
 forall(d in DEMANDS) setdomain(use(d), 1, NUMDEM)

! All frequencies attached to a node must be different by at least 2
 forall(n in NODES, c,d in INDEX(n)..INDEX(n)+DEM(n)-1 | c<d)
  distance(use(c), use(d)) >= 2
!  abs(use(c) - use(d)) >= 2
  
! Neighboring nodes take all-different frequencies
 forall(l in LINKS)
  all_different(
   union(d in INDEX(LINK(l,1))..INDEX(LINK(l,1))+DEM(LINK(l,1))-1) {use(d)} + 
   union(d in INDEX(LINK(l,2))..INDEX(LINK(l,2))+DEM(LINK(l,2))-1) {use(d)},
   KALIS_GEN_ARC_CONSISTENCY)

! Objective function: minimize the number of frequencies used, that is,
! minimize the largest value assigned to 'use'
 setname(numfreq, "NumFreq")
 numfreq = maximum(use)

! Search strategy
 Strategy(1):=assign_var(KALIS_SMALLEST_DOMAIN, KALIS_MIN_TO_MAX, use)
 Strategy(2):=assign_var(KALIS_MAX_DEGREE, KALIS_MIN_TO_MAX, use)
 cp_set_branching(Strategy(1))
 setparam("KALIS_MAX_COMPUTATION_TIME", 1)
 cp_set_solution_callback("print_solution")

! Try to find solution(s) with strategy 1
 if (cp_minimize(numfreq)) then
  cp_show_stats
  sol:=getsol(numfreq)
 end-if

! Restart search with strategy 2
 cp_reset_search
 if sol>0 then                             ! If a solution was found:
  numfreq <= sol-1                         ! Add upper bound on objective
 end-if
 cp_set_branching(Strategy(2))
 setparam("KALIS_MAX_COMPUTATION_TIME", 1000)

 if (cp_minimize(numfreq)) then
  cp_show_stats
 elif sol>0 then
  writeln("Optimality proven")
 else
  writeln("Problem has no solution")
 end-if

!********************************************************************
! **** Solution printout ****
 public procedure print_solution
  writeln("Number of frequencies: ", getsol(numfreq))
  writeln("Frequency assignment: ")
  forall(n in NODES) do
   write("Node ", n, ": ")
   forall(d in INDEX(n)..INDEX(n)+DEM(n)-1) write(getsol(use(d)), " ")
   writeln
  end-do
 end-procedure

end-model

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