Laura Galli The Simple Plant Location Problem (SPLP) is a well-known NP-hard optimisation problem with applications in logistics. Although many families of facet-defining inequalities are known for the associated polyhedron, very little work has been done on separation algorithms. We present the first ever polynomial-time separation algorithm for the SPLP that separates exactly over an exponentially large … Read more
The Dynamic Random Access Memory (DRAM) is among the major points of contention in multi-core systems. We consider a challenging optimization problem arising in worst-case performance analysis of systems architectures: computing the worst-case delay (WCD) experienced when accessing the DRAM due to the interference of contending requests. The WCD is a crucial input for micro-architectural … Read more
In 2013, Buchheim and Wiegele introduced a quadratic optimisation problem, in which the domain of each variable is a closed subset of the reals. This problem includes several other important problems as special cases. We study some convex sets and polyhedra associated with the problem, and derive several families of strong valid inequalities. We also … Read more
We consider non-convex mixed-integer quadratic programs in which all variables are explicitly bounded. Many exact methods for such problems use additional variables, representing products of pairs of original variables. We study the convex hull of feasible solutions in this extended space. Some other approaches use bit representation to convert bounded integer variables into binary variables. … Read more
The Lovasz theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovasz and the other to Groetschel et al. The former SDP is often thought to be preferable … Read more
The Simple Plant Location Problem is a well-known (and NP-hard) combinatorial optimisation problem, with applications in logistics. We present a new family of valid inequalities for the associated family of polyhedra, and show that it contains an exponentially large number of new facet-defining members. We also present a new procedure, called facility augmentation, which enables … Read more
Non-convex quadratic programming with box constraints is a fundamental problem in the global optimization literature, being one of the simplest NP-hard nonlinear programs. We present a new heuristic for this problem, which enables one to obtain solutions of excellent quality in reasonable computing times. The heuristic consists of four phases: binarisation, convexification, branch-and-bound, and local … Read more
In 1996, Laurent and Poljak introduced an extremely general class of cutting planes for the max-cut problem, called gap inequalities. We prove several results about them, including the following: (i) there must exist non-dominated gap inequalities with gap larger than 1, unless NP = co-NP; (ii) there must exist non-dominated gap inequalities with exponentially large … Read more
Quadratic Convex Reformulation (QCR) is a technique that was originally proposed for quadratic 0-1 programs, and then extended to various other problems. It is used to convert non-convex instances into convex ones, in such a way that the bound obtained by solving the continuous relaxation of the reformulated instance is as strong as possible. In … Read more
We compute a complete linear description of the bipartite subgraph polytope, for up to seven nodes, and a conjectured complete description for eight nodes. We then show how these descriptions were used to compute the integrality ratio of various relaxations of the max-cut problem, again for up to eight nodes. Citation L. Galli & A.N. … Read more