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I am trying to understand how local branching is used in Benders Decomposition. I was wondering if someone could kindly explain me how exactly local branching works.

If my understanding is correct, you generate a cut based on Hamming distance in local branching with which the feasible region is divided into two parts. In fact, you might generate multiple cuts. Now, do we add these cuts as user-defined cuts in a callback function? or Do we solve the master problem to the optimality and generate these cuts without worrying about the sub problem just to improve the lower bound (i.e, for a minimization problem)?

Wouldn't that make sense to generate these cuts with the incumbent solutions?

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