# constraint : enter each city only once
for i in V:
model += xsum(x[j][i] for j in V - {i}) == 1
# (weak) subtour elimination
# subtour elimination
for (i, j) in product(V - {0}, V - {0}):
if i != j:
model += y[i] - (n+1)*x[i][j] >= y[j]-n
# no subtours of size 2
for (i, j) in Arcs:
model += x[i][j] + x[j][i] <= 1
# computing farthest point for each point, these will be checked first for
# isolated subtours
F, G = [], nx.DiGraph()
for (i, j) in Arcs:
G.add_edge(i, j, weight=c[i][j])
for i in V:
P, D = nx.dijkstra_predecessor_and_distance(G, source=i)
DS = list(D.items())
DS.sort(key=lambda x: x[1])
F.append((i, DS[-1][0]))
model.cuts_generator = SubTourCutGenerator(F, x, V)
model.optimize()
print('status: %s route length %g' % (model.status, model.objective_value))
def test_tsp_cuts(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 = 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()
assert m.status == OptimizationStatus.OPTIMAL # "mip model status"
assert abs(m.objective_value - 262) <= TOL # "mip model objective"
F, G = [], nx.DiGraph()
for (i, j) in Routes:
G.add_edge(i, j, weight=cost[i][j])
# nx.draw(G, with_labels = True)
for i in places:
P, D = nx.dijkstra_predecessor_and_distance(G, source=i)
# print(P, D)
DS = list(D.items())
# print('\n', DS)
DS.sort(key=lambda x: x[1])
# print('\n', DS, '\n')
F.append((i, DS[-1][0]))
m.cuts_generator = SubTourCutGenerator(F, x, places)
for i in places:
for j in places:
# prob += vars_2[i][j] >= max(0,-demand[i],demand[j])*vars[i][j]
if i != j:
m += f[i][j] >= 0
for i in places:
for j in places:
# prob += vars_2[i][j] <= min(Q,Q-demand[i],Q + demand[j])*vars[i][j]
if i != j:
m += f[i][j] <= Q * x[i][j]
# The problem is solved using PuLP's choice of Solver
m.optimize()
