I have a MILP feasibility problem, so the objective function is constant (0). I have read that strong branching scores measure changes in the objective value. So my question is, what would be the strong branching scores in my case?
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If branching on a variable leads to an infeasible subproblem, then you can either immediately branch on this variable, or change its domain in the current node.
Otherwise, strong branching won't be useful in this case.
A excerpt from "Hybrid Branching" (Achterberg et Berthold, 2009) DOI:
In CSP and SAT, where no objective function is available, one may better estimate the impact of a branching by taking the number of implied reductions of other variable domains into account [4]. In analogy to the pseudocosts, we call the estimated numbers of implied reductions the inference values of a variable.
