# TSP example using numpy functions (for efficiency)
#
# (C) Fair Isaac Corp., 1983-2025
import xpress as xp
import numpy as np
def cb_preintsol(prob, data, soltype, cutoff):
'''Callback for checking if solution is acceptable
'''
n = data
xsol = prob.getCallbackSolution()
xsolf = np.array(xsol) # flattened
xsol = xsolf.reshape(n,n) # matrix-shaped
nextc = np.argmax(xsol, axis=1)
i = 0
ncities = 1
# Scan cities in order until we get back to 0 or the solution is
# wrong and we're diverging
while nextc[i] != 0 and ncities < n:
ncities += 1
i = nextc[i]
reject = False
if ncities < 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:
# Obtain an order by checking the maximum of the variable matrix
# for each row
unchecked = np.zeros(n)
ngroup = 0
# Initialize the vectors to be passed to addcuts
cut_mstart = [0]
cut_ind = []
cut_coe = []
cut_rhs = []
nnz = 0
ncuts = 0
while np.min(unchecked) == 0 and ngroup <= n:
'''Seek a tour
'''
ngroup += 1
firstcity = np.argmin(unchecked)
assert (unchecked[firstcity] == 0)
i = firstcity
ncities = 0
# Scan cities in order
while True:
unchecked[i] = ngroup # mark city i with its new group, to be used in addcut
ncities += 1
i = nextc[i]
if i == firstcity or ncities > n + 1:
break
assert ncities < n # we know solutions is infeasible
# unchecked[unchecked == ngroup] marks nodes to be made part of
# subtour elimination inequality
# Find indices of current subtour. S is the set of nodes
# traversed by the subtour, compS is its complement.
S = np.where(unchecked == ngroup)[0].tolist()
compS = np.where(unchecked != ngroup)[0].tolist()
indices = [i*n+j for i in S for j in compS]
# Check if solution violates the cut, and if so add the cut to
# the list.
if sum(xsolf[i] for i in indices) < 1 - 1e-3:
mcolsp, dvalp = [], []
# Presolve cut in order to add it to the presolved problem
drhsp, status = prob.presolverow(rowtype='G',
origcolind=indices,
origrowcoef=np.ones(len(indices)),
origrhs=1,
maxcoefs=prob.attributes.cols,
colind=mcolsp,
rowcoef=dvalp)
# 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
nnz += len(mcolsp)
ncuts += 1
cut_ind.extend(mcolsp)
cut_coe.extend(dvalp)
cut_rhs.append(drhsp)
cut_mstart.append(nnz)
if ncuts > 0:
assert (len(cut_mstart) == ncuts + 1)
assert (len(cut_ind) == nnz)
prob.addcuts(cuttype=[0] * ncuts,
rowtype=['G'] * ncuts,
rhs=cut_rhs,
start=cut_mstart,
colind=cut_ind,
cutcoef=cut_coe)
return (reject, None)
def print_sol(p, n):
'''Print the solution: order of nodes and cost
'''
xsol = np.array(p.getSolution()).reshape(n,n)
nextc = np.argmax(xsol, axis=1)
i = 0
# Scan cities in order
tour = []
while i != 0 or len(tour) == 0:
tour.append(str(i))
i = nextc[i]
print('->'.join(tour), '->0; cost: ', p.attributes.objval, sep='')
def create_initial_tour(n):
'''Returns a permuted trivial solution 0->1->2->...->(n-1)->0
'''
sol = np.zeros((n, n))
p = np.random.permutation(n)
for i in range(n):
sol[p[i], p[(i + 1) % n]] = 1
return sol.flatten()
def solve_opttour():
'''Create a random TSP problem
'''
n = 50
CITIES = range(n) # set of cities: 0..n-1
np.random.seed(3)
X = 100 * np.random.rand(n)
Y = 100 * np.random.rand(n)
# Compute distance matrix
dist = np.ceil(np.sqrt ((X.reshape(n,1) - X.reshape(1,n))**2 +
(Y.reshape(n,1) - Y.reshape(1,n))**2))
p = xp.problem()
# Create variables as a square matrix of binary variables. Note
# the use of dtype=xp.npvar (introduced in Xpress 8.9) to ensure
# NumPy uses the Xpress operations for handling these vectors.
fly = np.array([p.addVariable(vartype=xp.binary, name='x_{0}_{1}'.format(i,j))
for i in CITIES for j in CITIES], dtype=xp.npvar).reshape(n,n)
# Degree constraints
p.addConstraint(xp.Sum(fly[i,:]) - fly[i,i] == 1 for i in CITIES)
p.addConstraint(xp.Sum(fly[:,i]) - fly[i,i] == 1 for i in CITIES)
# Fix diagonals (i.e. city X -> city X) to zero
p.addConstraint(fly[i,i] == 0 for i in CITIES)
# Objective function
p.setObjective (xp.Sum((dist * fly).flatten()))
# Add callbacks
p.addcbpreintsol(cb_preintsol, n)
# 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
# Create 10 trivial solutions: simple tour 0->1->2...->n->0
# randomly permuted
for k in range(10):
InitTour = create_initial_tour(n)
p.addmipsol(solval=InitTour, name="InitTour_{}".format(k))
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:
print_sol(p,n) # print solution and cost
if __name__ == '__main__':
solve_opttour()
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