# Solve an instance of the TSP with Xpress using callbacks
#
# (C) Fair Isaac Corp., 1983-2024
# Retrieve an example from
#
# http://www.math.uwaterloo.ca/tsp/world/countries.html
#
# and load the TSP instance, then solve it using the Xpress Optimizer
# library with the appropriate callback. Once the optimization is over
# (i.e. the time limit is reached or we find an optimal solution) the
# optimal tour is displayed using matplotlib.
import networkx as nx
import xpress as xp
import re
import math
from matplotlib import pyplot as plt
from urllib.request import urlretrieve
#
# Download instance from TSPLib
#
# Replace with any of the following for a different instance:
#
# ar9152.tsp (9125 nodes)
# bm33708.tsp (33708 nodes)
# ch71009.tsp (71009 nodes)
# dj38.tsp (38 nodes)
# eg7146.tsp (7146 nodes)
# fi10639.tsp (10639 nodes)
# gr9882.tsp (9882 nodes)
# ho14473.tsp (14473 nodes)
# ei8246.tsp (8246 nodes)
# ja9847.tsp (9847 nodes)
# kz9976.tsp (9976 nodes)
# lu980.tsp (980 nodes)
# mo14185.tsp (14185 nodes)
# nu3496.tsp (3496 nodes)
# mu1979.tsp (1979 nodes)
# pm8079.tsp (8079 nodes)
# qa194.tsp (194 nodes)
# rw1621.tsp (1621 nodes)
# sw24978.tsp (24978 nodes)
# tz6117.tsp (6117 nodes)
# uy734.tsp (734 nodes)
# vm22775.tsp (22775 nodes)
# wi29.tsp (29 nodes)
# ym7663.tsp (7663 nodes)
# zi929.tsp (929 nodes)
# ca4663.tsp (4663 nodes)
# it16862.tsp (16862 nodes)
#
filename = 'wi29.tsp'
urlretrieve('https://www.math.uwaterloo.ca/tsp/world/' + filename, filename)
# Read file consisting of lines of the form "k: x y" where k is the
# point's index while x and y are the coordinates of the point. The
# distances are assumed to be Euclidean.
instance = open(filename, 'r')
coord_section = False
points = {}
G = nx.Graph()
#
# Coordinates of the points in the graph
#
for line in instance.readlines():
if re.match('NODE_COORD_SECTION.*', line):
coord_section = True
continue
elif re.match('EOF.*', line):
break
if coord_section:
coord = line.split(' ')
index = int(coord[0])
cx = float(coord[1])
cy = float(coord[2])
points[index] = (cx, cy)
G.add_node(index, pos=(cx, cy))
instance.close()
print("Downloaded instance, created graph.")
# Callback for checking if the solution forms a tour
#
# Returns a tuple (a,b) with
#
# a: True if the solution is to be rejected, False otherwise
# b: real cutoff value
def cbpreintsol(prob, G, soltype, cutoff):
"""
Use this function to refuse a solution unless it forms a tour
"""
# Obtain solution, then start at node 1 to see if the solutions at
# one form a tour. The vector s is binary as this is a preintsol()
# callback.
s = prob.getCallbackSolution()
reject = False
nextnode = 1
tour = []
while nextnode != 1 or len(tour) == 0:
# Find the edge leaving nextnode
edge = None
for j in V:
if j != nextnode and s[xind[nextnode, j]] > 0.5:
edge = x[nextnode, j]
nextnode = j
break
if edge is None:
break
tour.append(edge)
# If there are n arcs in the loop, the solution is feasible
if len(tour) < n:
# The tour given by the current solution does not pass through
# all the nodes and is thus infeasible.
# If soltype is non-zero then we reject by setting reject=True.
# If instead soltype is zero then the solution came from an
# integral node. In this case we can reject by adding a cut
# that cuts off that solution. Note that we must NOT set
# reject=True in that case because that would result in just
# dropping the node, no matter whether we add cuts or not.
if soltype != 0:
reject = True
else:
# The solution is infeasible and it was obtained from an integral
# node. In this case we can generate and inject a cut that cuts
# off this solution so that we don't find it again.
# Presolve cut in order to add it to the presolved problem
colind, rowcoef = [], []
drhsp, status = prob.presolverow(rowtype='L',
origcolind=tour,
origrowcoef=[1] * len(tour),
origrhs=len(tour) - 1,
maxcoefs=prob.attributes.cols,
colind=colind, rowcoef=rowcoef)
# Since mipdualreductions=0, presolving the cut must succeed, and
# the cut should never be relaxed as this would imply that it did
# not cut off a subtour.
assert status == 0
prob.addcuts(cuttype=[1],
rowtype=['L'],
rhs=[drhsp],
start=[0, len(colind)],
colind=colind,
cutcoef=rowcoef)
# To accept the cutoff, return second element of tuple as None
return (reject, None)
#
# Formulate problem, set callback function and solve
#
n = len(points) # number of nodes
V = range(1, n+1) # set of nodes
# Set of arcs (i.e. all pairs since it is a complete graph)
A = [(i, j) for i in V for j in V if i != j]
p = xp.problem()
x = {(i, j): p.addVariable(name='x_{0}_{1}'.format(i, j),
vartype=xp.binary) for (i, j) in A}
conservation_in = [xp.Sum(x[i, j] for j in V if j != i) == 1 for i in V]
conservation_out = [xp.Sum(x[j, i] for j in V if j != i) == 1 for i in V]
p.addConstraint(conservation_in, conservation_out)
xind = {(i, j): p.getIndex(x[i, j]) for (i, j) in x.keys()}
# Objective function: total distance travelled
p.setObjective(xp.Sum(math.sqrt((points[i][0] - points[j][0])**2 +
(points[i][1] - points[j][1])**2) * x[i, j]
for (i, j) in A))
# Should find a reasonable solution within 20 seconds
p.controls.timelimit = 20
p.addcbpreintsol(cbpreintsol, G, 1)
# Disable dual reductions (in order not to cut optimal solutions)
# and nonlinear reductions, in order to be able to presolve the
# cuts.
p.controls.mipdualreductions = 0
p.optimize()
if p.attributes.solstatus not in [xp.SolStatus.OPTIMAL, xp.SolStatus.FEASIBLE]:
print("Solve status:", p.attributes.solvestatus.name)
print("Solution status:", p.attributes.solstatus.name)
else:
# Read solution and store it in the graph
sol = p.getSolution()
try:
for (i, j) in A:
if sol[p.getIndex(x[i, j])] > 0.5:
G.add_edge(i, j)
# Display best tour found
pos = nx.get_node_attributes(G, 'pos')
nx.draw(G, points) # create a graph with the tour
plt.show() # display it interactively
except:
print('Could not draw solution')
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