from mip import Model, INTEGER, CONTINUOUS
from random import randint

m = Model("toy-model")

level1 = m.add_var_tensor(
    (8, 8),
    name='1',
    var_type=INTEGER,
    ub=10,
    lb=-10
)

level1_aux = m.add_var_tensor(
    (8, 8),
    name='1_aux',
    var_type=CONTINUOUS,
    ub=10,
    lb=-10,
    obj=1
)

level2 =  m.add_var_tensor(
    (4, 4),
    name='2',
    var_type=INTEGER,
    ub=10,
    lb=-10
)

level2_aux =  m.add_var_tensor(
    (4, 4),
    name='2_aux',
    var_type=CONTINUOUS,
    ub=10,
    lb=-10,
    obj=1
)

for base_var, aux_var in zip(level1.flatten(), level1_aux.flatten()):
    m += base_var <= aux_var
    m += -base_var <= aux_var
for base_var, aux_var in zip(level2.flatten(), level2_aux.flatten()):
    m += base_var <= aux_var
    m += -base_var <= aux_var

initial_solution = []
for x in range(0, 8):
    for y in range(0,8):
        value = randint(-10, 10)
        m += level1[x][y] + level2[x // 2][y // 2] == value
        initial_solution.append((level1[x][y], value))

m.start = initial_solution
m.optimize()