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'cycle' constraint: formulating a TSP problem

Description
'cycle' constraints can be used to formulate problems of the TSP (traveling sales person) type, including cyclic scheduling problems with setup times. Two model versions showing definition of callbacks via subroutine references or by name.

Further explanation of this example: 'Xpress Kalis Mosel Reference Manual'

Source Files
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cycle.mos

(!****************************************************************
CP example problems
===================

file cycle.mos

Cycle constraint example, solving a small TSP problem.

(c) 2008 Artelys S.A. and Fair Isaac Corporation
Creation: 2005, rev. Apr. 2022
*****************************************************************!)

model "TSP"
uses "kalis"

parameters
S = 14  ! Number of cities to visit
end-parameters

declarations
TC : array(0..3*S) of integer
end-declarations

! TSP DATA
TC :: [
1 , 1647,  9610,
2 , 1647,  9444,
3 , 2009,  9254,
4 , 2239,  9337,
5 , 2523,  9724,
6 , 2200,  9605,
7 , 2047,  9702,
8 , 1720,  9629,
9 , 1630,  9738,
10, 1405,  9812,
11, 1653,  9738,
12, 2152,  9559,
13, 1941,  9713,
14, 2009,  9455]

forward procedure print_solution
forward public function bestregret(Vars: cpvarlist): integer
forward public function bestneighbor(x: cpvar): integer

setparam("KALIS_DEFAULT_LB", 0)
setparam("KALIS_DEFAULT_UB", S-1)

declarations
CITIES = 0..S-1                  ! Set of cities
succ: array(CITIES) of cpvar     ! Array of successor variables
prev: array(CITIES) of cpvar     ! Array of predecessor variables
end-declarations

setparam("KALIS_DEFAULT_UB", 10000)

declarations
dist_matrix: array(CITIES,CITIES) of integer  ! Distance matrix
totaldist: cpvar                 ! Total distance of the tour
succpred: cpvarlist              ! Variable list for branching
end-declarations

! Setting the variable names
forall(p in CITIES) do
setname(succ(p),"succ("+p+")")
setname(prev(p),"prev("+p+")")
end-do

! Add succesors and predecessors to succpred list for branching
forall(p in CITIES) succpred += succ(p)
forall(p in CITIES) succpred += prev(p)

! Build the distance matrix
forall(p1,p2 in CITIES | p1<>p2)
dist_matrix(p1,p2) :=  round(sqrt((TC(3*p2+1) - TC(3*p1+1)) *
(TC(3*p2+1) - TC(3*p1+1)) + (TC(3*p2+2) - TC(3*p1+2)) *
(TC(3*p2+2) - TC(3*p1+2))))

! Set the name of the distance variable
setname(totaldist, "total_distance")

! Posting the cycle constraint
cycle(succ, prev, totaldist, dist_matrix)

! Print all solutions found
cp_set_solution_callback(->print_solution)

! Set the branching strategy
cp_set_branching(assign_and_forbid("bestregret", "bestneighbor",
succpred))
setparam("KALIS_MAX_COMPUTATION_TIME", 10)

! Find the optimal tour
if cp_minimize(totaldist) then
if getparam("KALIS_SEARCH_LIMIT")=KALIS_SLIM_BY_TIME then
writeln("Search time limit reached")
else
writeln("Done!")
end-if
end-if

!---------------------------------------------------------------
! **** Solution printing ****
procedure print_solution
writeln("TOUR LENGTH = ", getsol(totaldist))

thispos:=getsol(succ(0))
nextpos:=getsol(succ(thispos))
write("  Tour: ", thispos)
while (nextpos <> getsol(succ(0))) do
write(" -> ", nextpos)
thispos:=nextpos
nextpos:=getsol(succ(thispos))
end-do
writeln
end-procedure

!---------------------------------------------------------------
! **** Variable choice ****
public function bestregret(Vars: cpvarlist): integer

! Get the number of elements of "Vars"
listsize:= getsize(Vars)
minindex := 0
mindist := 0

! Set on uninstantiated variables
forall(i in 1..listsize) do
if not is_fixed(getvar(Vars,i)) then
if i <= S then
bestn := getlb(getvar(Vars,i))
v:=bestn
mval:=dist_matrix(i-1,v)
while (v < getub(getvar(Vars,i))) do
v:=getnext(getvar(Vars,i),v)
if dist_matrix(i-1,v)<=mval then
mval:=dist_matrix(i-1,v)
bestn:=v
end-if
end-do
sbestn := getlb(getvar(Vars,i))
mval2:= 10000000
v:=sbestn
if dist_matrix(i-1,v)<=mval2 and v <> bestn then
mval2:=dist_matrix(i-1,v)
sbestn:=v
end-if
while (v < getub(getvar(Vars,i))) do
v:=getnext(getvar(Vars,i),v)
if (dist_matrix(i-1,v)<=mval2 and v <> bestn) then
mval2:=dist_matrix(i-1,v)
sbestn:=v
end-if
end-do

else

bestn := getlb(getvar(Vars,i))
v:=bestn
mval:=dist_matrix(v,i-S-1)
while (v < getub(getvar(Vars,i))) do
v:=getnext(getvar(Vars,i),v)
if dist_matrix(v,i-S-1)<=mval then
mval:=dist_matrix(v,i-S-1)
bestn:=v
end-if
end-do
sbestn := getlb(getvar(Vars,i))
mval2:= 10000000
v:=sbestn
if dist_matrix(v,i-S-1)<=mval2 and v <> bestn then
mval2:=dist_matrix(v,i-S-1)
sbestn:=v
end-if
while (v < getub(getvar(Vars,i))) do
v:=getnext(getvar(Vars,i),v)
if dist_matrix(v,i-S-1)<=mval2 and v <> bestn then
mval2:=dist_matrix(v,i-S-1)
sbestn:=v
end-if
end-do
end-if

dsize := getsize(getvar(Vars,i))

rank := integer(10000/ dsize +(mval2 - mval))
if mindist<= rank then
mindist := rank
minindex := i
end-if

end-if
end-do

returned := minindex

end-function

!---------------------------------------------------------------
! **** Value choice: choose value resulting in smallest distance
public function bestneighbor(x: cpvar): integer

issucc := false
idx := -1
forall (i in CITIES)
if (is_same(succ(i),x)) then
idx:= i
issucc := true
end-if
forall (i in CITIES)
if (is_same(prev(i),x)) then
idx:= i
end-if

if issucc then
returned:= getlb(x)
v:=getlb(x)
mval:=dist_matrix(idx,v)
while (v < getub(x)) do
v:=getnext(x,v)
if dist_matrix(idx,v)<=mval then
mval:=dist_matrix(idx,v)
returned:=v
end-if
end-do
else
returned:= getlb(x)
v:=getlb(x)
mval:=dist_matrix(v,idx)
while (v < getub(x)) do
v:=getnext(x,v)
if dist_matrix(v,idx)<=mval then
mval:=dist_matrix(v,idx)
returned:=v
end-if
end-do
end-if

end-function

end-model