Branching

• LP/AAP_lp_branch.cpp::select_branching_candidates()
  We branch using a disjunction on the original variables $x_{ijk}$. The choice for which variables to select as candidates for branching is determined in the function branch_close_to_half(), in which we pick variables with high cost that are closest to 0.5. The number of branching candidates is determined by the parameter AAP_StrongBranch_Can.

  In the function append_branching_vars(), for each candidate we construct a BCP_lp_branching_object. For our case, the branching object simply contains information about which variables we will change the bounds on. Since we are branching on the original variables $x_{ijk} = \sum_{s \in {\cal F}'} s_{ijk} \lambda_s$, we have to reset a set of variables in the master formulation. In one child, we set $x_{ijk} = 0$, which forces $\lambda _s = 0$ for all $s \in {\cal F}'$ that contain index $(i,j,k)$. In the other child, we set $x_{ijk} = 1$, which forces $\lambda _s = 0$ for all $s \in {\cal F}'$ that do not contain index $(i,j,k)$.

• LP/AAP_lp_branch.cpp::set_user_data_for_children()
  In this method, we update the user data with the branching information.