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This paper considers a modification of the branch-and-cut algorithm for Mixed Integer Linear Programming where branching is performed on general disjunctions rather than on variables. We select promising branching disjunctions based on a heuristic measure of disjunction quality. This measure exploits the relation between branching disjunctions and intersection cuts. In this work, we focus on disjunctions defining the mixed integer Gomory cuts at an optimal basis of the linear programmingdoi:10.1007/s10107-009-0332-3 fatcat:nfbmlsuv65bqlf4z4w6d7jboba