A Local Dominance Procedure for Mixed-Integer Linear Programming

Among the hardest Mixed-Integer Linear Programming (MILP) problems, the ones that exhibit a symmetric nature are particularly important in practice, as they arise in both theoretical and practical combinatorial optimization problems. A theoretical concept that generalizes the notion of symmetry is that of dominance. This concept, although known since a long time, is typically not used in generalpurpose MILP codes, due to the intrinsic difficulties arising when using the classical definitions in a completely general context. In this paper we study a general-purpose dominance procedure proposed in the 80’s by Fischetti and Toth, that overcomes some of the main drawbacks of the classical dominance criteria. Both theoretical and practical issues concerning this procedure are considered, and important improvements are proposed. Computational results on a test-bed made of hard (single and multiple) knapsack problems are reported, showing that the proposed method can lead to considerable speedup when embedded in a general-purpose MILP solver.