def test_tsp_mipstart(solver: str):
"""tsp related tests"""
announce_test("TSP - MIPStart", 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)
route = ['a', 'g', 'f', 'c', 'd', 'e', 'b', 'a']
m.start = [(x[route[i - 1], route[i]], 1.0) for i in range(1, len(route))]
m.optimize()
check_result("mip model status", m.status == OptimizationStatus.OPTIMAL)
check_result("mip model objective",
(abs(m.objective_value - 262)) <= 0.0001)
print('')
C, U = S.C, [i for i in range(S.u_max + 1)]
m = Model(sense=MINIMIZE)
x = [[m.add_var('x({},{})'.format(i, c), var_type=BINARY) for c in U]
for i in N]
z = m.add_var('z')
m.objective = minimize(z)
for i in N:
m += xsum(x[i][c] for c in U) == r[i]
for i, j, c1, c2 in product(N, N, U, U):
if i != j and c1 <= c2 < c1 + d[i][j]:
m += x[i][c1] + x[j][c2] <= 1
for i, c1, c2 in product(N, U, U):
if c1 < c2 < c1 + d[i][i]:
m += x[i][c1] + x[i][c2] <= 1
for i, c in product(N, U):
m += z >= (c + 1) * x[i][c]
m.start = [(x[i][c], 1.0) for i in N for c in C[i]]
m.optimize(max_seconds=100)
C = [[c for c in U if x[i][c] >= 0.99] for i in N]
print(C)
