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dm = (

( 0,86,49,57,31,69,50),

(86, 0,68,79,93,24, 5),

(49,68, 0,16, 7,72,67),

(57,79,16, 0,90,69, 1),

(31,93, 7,90, 0,86,59),

(69,24,72,69,86, 0,81),

(50, 5,67, 1,59,81, 0))



n = len(dm) #how many cities

V = range(n)

E = [(i,j) for i in V for j in V if i!=j]



print "there are %d cities"%n



from pymprog import *

beginModel('TSP by row generation')

x = var(E, 'x', bool)

minimize( sum(dm[i][j]*x[i,j] for i,j in E), 'TravelDist' )

st([sum( x[k,j] for j in V if j!=k ) == 1 for k in V], 'leave')

st([sum( x[i,k] for i in V if i!=k ) == 1 for k in V], 'enter')



solve() #solve the IP problem



def subtour(x):

   "find a subtour in current solution"

   succ = 0

   subt = [succ] #start from node 0

   while True:

      succ=sum(x[succ,j].primal*j 

               for j in V if j!=succ)

      if succ == 0: break #tour found

      subt.append(int(succ+0.5))

   return subt



while True:

   subt = subtour(x)

   if len(subt) == n:

      print "Optimal tour length:", vobj()

      print "Optimal tour:\n", subt

      break

   print "New subtour: ", subt

   if len(subt) == 1: break #something wrong

   #now add a subtour elimination constraint:

   nots = [j for j in V if j not in subt]

   st( sum(x[i,j] for i in subt for j in nots) >= 1 )

   solve() #solve the IP problem again