We investigate several complexity issues related to branch-and-cut algorithms for 0-1 integer programming based on lifted cover inequalities (LCIs). We show that given a fractional point, determining a violated LCI over all minimal covers is NP-hard. The main result is that there exists a class of 0-1 knapsack instances for which any branch-and-cut algorithm based on LCIs has to evaluate an exp...

We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to find provably good solutions in certain very special cases. Our approach uses both...

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic,...

We study the hub location and routing problem where we jointly decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and s...

We discuss the variability in the performance of multiple runs of branchand-cut mixed integer linear programming solvers, and we concentrate on the one deriving from the use of different optimal bases of the linear programming relaxations. We propose a new algorithm exploiting more than one of those bases and we show that different versions of the algorithmcanbeused to stabilize and improve the...

In this paper we develop a characterisation of minimal non-planarity of level graphs. We show that a level minimal non-planar (LMNP) graph is completely characterised by either a tree, a level non-planar cycle or a level planar cycle with certain path augmentations. We discuss the usefulness of these characterisations in the context of an branch-and-cut Integer Linear Programming implementation...

0377-2217/$ see front matter 2010 Elsevier B.V. A doi:10.1016/j.ejor.2010.04.019 * Corresponding author. E-mail addresses: [email protected] (M.W. Ta Ntaimo). We present a new method for solving stochastic programs with joint chance constraints with random technology matrices and discretely distributed random data. The problem can be reformulated as a large-scale mixed 0–1 integer program. We de...

An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem. Areas where symmetric ILPs arise range from applied settings (scheduling on identical machines), to combinatorics (code construction), and to statistics (statistical designs construction). Relatively small symmetric ILPs are extremely difficult to solve using branch-and-c...

Deciding c-planarity for a given clustered graph C = (G, T ) is one of the most challenging problems in current graph drawing research. Though it is yet unknown if this problem is solvable in polynomial time, latest research focused on algorithmic approaches for special classes of clustered graphs. In this paper, we introduce an approach to solve the general problem using integer linear program...

In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called bordered block diagonal form. More precisely, given some matrix A, we try to assign as many rows as possible to some number β of blocks of size κ such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirab...