# 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')