Facets from gadgets

Abstract

We present a new tool for generating cutting planes for $$\mathcal{NP}$$ -hard combinatorial optimisation problems. It is based on the concept of gadgets—small subproblems that are “glued” together to form hard problems—which we borrow from the literature on computational complexity. Using gadgets, we are able to derive huge (exponentially large) new families of strong (and sometimes facet-defining) cutting planes, accompanied by efficient separation algorithms. We illustrate the power of this approach on the asymmetric traveling salesman, stable set and clique partitioning problems.