def test_tsp(solver: str):
"""tsp related tests"""
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 = 1
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.relax()
m.optimize()
assert m.status == OptimizationStatus.OPTIMAL # "lp model status"
assert abs(m.objective_value - 238.75) <= TOL # "lp model objective"
# setting all variables to integer now
for v in m.vars:
v.var_type = INTEGER
m.optimize()
assert m.status == OptimizationStatus.OPTIMAL # "mip model status"
assert abs(m.objective_value - 262) <= TOL # "mip model objective"
Ain = {n: [a for a in A if a[1] == n] for n in N}
m = Model()
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 n in N:
m += xsum(x[a] for a in Aout[n]) == 1, 'out({})'.format(n)
m += xsum(x[a] for a in Ain[n]) == 1, 'in({})'.format(n)
newConstraints = True
m.relax()
while newConstraints:
m.optimize()
print('objective value : {}'.format(m.objective_value))
G = DiGraph()
for a in A:
G.add_edge(a[0], a[1], capacity=x[a].x)
newConstraints = False
for (n1, n2) in [(i, j) for (i, j) in product(N, N) if i != j]:
cut_value, (S, NS) = minimum_cut(G, n1, n2)
if cut_value <= 0.99:
m += xsum(x[a]
for a in A if (a[0] in S and a[1] in S)) <= len(S) - 1
