def test_tsp_cuts(solver: str):
"""tsp related tests"""
announce_test("TSP - Branch & Cut", solver)
N = ['a', 'b', 'c', 'd', 'e', 'f', 'g']
n = len(N)
i0 = N[0]
A = {
('a', 'd'): 56,
('d', 'a'): 67,
('a', 'b'): 49,
('b', 'a'): 50,
('d', 'b'): 39,
('b', 'd'): 37,
('c', 'f'): 35,
('f', 'c'): 35,
('g', 'b'): 35,
('b', 'g'): 25,
('a', 'c'): 80,
('c', 'a'): 99,
('e', 'f'): 20,
('f', 'e'): 20,
('g', 'e'): 38,
('e', 'g'): 49,
('g', 'f'): 37,
('f', 'g'): 32,
('b', 'e'): 21,
('e', 'b'): 30,
('a', 'g'): 47,
('g', 'a'): 68,
('d', 'c'): 37,
('c', 'd'): 52,
('d', 'e'): 15,
('e', 'd'): 20
}
# input and output arcs per node
Aout = {n: [a for a in A if a[0] == n] for n in N}
Ain = {n: [a for a in A if a[1] == n] for n in N}
m = Model(solver_name=solver)
m.verbose = 0
x = {
a: m.add_var(name='x({},{})'.format(a[0], a[1]), var_type=BINARY)
for a in A
}
m.objective = xsum(c * x[a] for a, c in A.items())
for i in N:
m += xsum(x[a] for a in Aout[i]) == 1, 'out({})'.format(i)
m += xsum(x[a] for a in Ain[i]) == 1, 'in({})'.format(i)
# continuous variable to prevent subtours: each
# city will have a different "identifier" in the planned route
y = {i: m.add_var(name='y({})'.format(i), lb=0.0) for i in N}
# subtour elimination
for (i, j) in A:
if i0 not in [i, j]:
m.add_constr(y[i] - (n + 1) * x[(i, j)] >= y[j] - n)
m.cuts_generator = SubTourCutGenerator()
# tiny model, should be enough to find the optimal
m.max_seconds = 10
m.max_nodes = 100
m.max_solutions = 1000
m.optimize()
check_result("mip model status", m.status == OptimizationStatus.OPTIMAL)
check_result("mip model objective",
(abs(m.objective_value - 262)) <= 0.0001)
print('')
# constraint : enter each city coming from another city
for i in N:
model += xsum(x[a] for a in OUT[i]) == 1
# constraint : leave each city coming from another city
for i in N:
model += xsum(x[a] for a in IN[i]) == 1
# subtour elimination
for (i, j) in [a for a in A.keys() if n0 not in [a[0], a[1]]]:
model += \
y[i] - (n+1)*x[(i, j)] >= y[j]-n, 'noSub({},{})'.format(i, j)
print('model has {} variables, {} of which are integral and {} rows'.format(
model.num_cols, model.num_int, model.num_rows))
print("Adding SOSs")
for i in N:
sosOut = [(x[(i, j)], A[(i, j)]) for (i, j) in OUT[i]]
sosIn = [(x[(i, j)], A[(i, j)]) for (i, j) in IN[i]]
model.add_sos(sosOut, 1)
model.max_nodes = 1000
st = model.optimize(max_seconds=120)
print('best route found has length {}, best possible (obj bound is) {} st: {}'.
format(model.objective_value, model.objective_bound, st))
arcs = [(a) for a in A.keys() if x[a].x >= 0.99]
print('optimal route : {}'.format(arcs))