Implementing TSP with Lazy constraint callback

问题

I am trying to TSP with Lazy constraint callback. From Answer given here and here, I have tried to use the code from the links and was able to add the call back function. Now I am struggling with add_lazy_constraints.

Here is my current code: It is a 9 Node TSP.

import docplex.mp.model as cpx
from cplex.callbacks import LazyConstraintCallback
from docplex.mp.callbacks.cb_mixin import *


class DOLazyCallback(ConstraintCallbackMixin, LazyConstraintCallback):
    def __init__(self, env):
        LazyConstraintCallback.__init__(self, env)
        ConstraintCallbackMixin.__init__(self)
        self.nb_lazy_cts = 0

    def add_lazy_constraints(self, cts):
        self.register_constraints(cts)

    @print_called('--> lazy constraint callback called: #{0}')
    def __call__(self):
        # fetch variable values into a solution
        sol = self.make_solution()
        # for each lazy constraint, check whether it is verified,
        unsats = self.get_cpx_unsatisfied_cts(self.cts, sol, tolerance=1e-6)
        for ct, cpx_lhs, sense, cpx_rhs in unsats:
            self.add(cpx_lhs, sense, cpx_rhs)
            self.nb_lazy_cts += 1
            print('  -- new lazy constraint[{0}]: {1!s}'.format(self.nb_lazy_cts, ct))


DST = [[0, 0.238, 0.608, 0.5442, 0.6097, 1.2337, 0.5574, 0.8691, 1.3394],
       [0.238, 0, 0.37, 0.6694, 0.6039, 0.9957, 0.6826, 0.8633, 1.23],
       [0.608, 0.37, 0, 1.0394, 0.9739, 0.6257, 1.0526, 1.2333, 0.860],
       [0.5442, 0.6694, 1.0394, 0, 0.0655, 0.903, 0.0132, 0.3249, 0.7952],
       [0.6097, 0.6039, 0.9739, 0.0655, 0, 0.8375, 0.0787, 0.2594, 0.7297],
       [1.2337, 0.9957, 0.6257, 0.903, 0.8375, 0, 0.9162, 0.7046, 0.2343],
       [0.5574, 0.6826, 1.0526, 0.0132, 0.0787, 0.9162, 0, 0.3381, 0.8084],
       [0.8691, 0.8633, 1.2333, 0.3249, 0.2594, 0.7046, 0.3381, 0, 0.4703],
       [1.3394, 1.23, 0.860, 0.7952, 0.7297, 0.2343, 0.8084, 0.4703, 0]]

n = 9

set_n = range(9)
opt_model = cpx.Model(name="MIP Model")

x = {(i, j): opt_model.binary_var(name="x_{0}_{1}".format(i, j)) for i in set_n for j in set_n if not i == j}

objective = opt_model.sum(DST[i][j] * x[i, j] for i in set_n for j in set_n if not i == j)

# one incoming edge one outgoing edge
for i in set_n:
    xp = opt_model.sum(x[j, i] for j in set_n if not i == j) - opt_model.sum(x[i, k] for k in set_n if not i == k)
    opt_model.add_constraint(xp == 0)

for j in set_n:
    opt_model.add_constraint(opt_model.sum(x[i, j] for i in set_n if not i == j) == 1)

lazyct_cb = opt_model.register_callback(DOLazyCallback)

lazyct_cb.add_lazy_constraints( ?? WHAT TO ADD HERE ?? )


opt_model.lazy_callback = lazyct_cb

url = "URLL"
api = "APII"

#opt_model.parameters.mip.tolerances.mipgap = 0
opt_model.minimize(objective)

print(opt_model.print_information())

solv = opt_model.solve(url=url, key=api)
print(solv.solve_status)
print(solv.solve_details)

回答1:

I don't think you want to call add_lazy_constraints beforehand. If you did this, then you could just add the lazy constraints directly to the model.

Instead you want some code in your callback that separates the constraints. Based on the values in sol you find a violated subtour elimination constraint and add it.

来源：https://stackoverflow.com/questions/60543917/implementing-tsp-with-lazy-constraint-callback

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