We present a new tool for generating cutting planes for 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 … Read more
We consider the problem of characterizing the convex hull of the graph of a bilinear function $f$ on the $n$-dimensional unit cube $[0,1]^n$. Extended formulations for this convex hull are obtained by taking subsets of the facets of the Boolean Quadric Polytope (BQP). Extending existing results, we propose the systematic study of properties of $f$ … Read more
In this paper we introduce a new class of bounds for the maximum -cut problem on undirected edge-weighted simple graphs. The bounds involve eigenvalues of the weighted adjacency matrix together with geometrical parameters. They generalize previous results on the maximum (2-)cut problem and we demonstrate that they can strictly improve over other eigenvalue bounds from … Read more
Experimental design is a classical problem in statistics and has also found new applications in machine learning. In the experimental design problem, the aim is to estimate an unknown vector x in m-dimensions from linear measurements where a Gaussian noise is introduced in each measurement. The goal is to pick k out of the given … Read more
We exactly solve the NP-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit … Read more
Uses of drones and unmanned vehicles (UAVs) in ground or aerial are increasing in both civil and military applications. This paper develops a two-stage stochastic optimization model with a recourse for a multiple drone-routing problem with fuel constraints under uncertainty for the travel between any pair of targets/refueling-sites/depot. We are given a set of n … Read more
We study the covering-type k-violation linear program where at most $k$ of the constraints can be violated. This problem is formulated as a mixed integer program and known to be strongly NP-hard. In this paper, we present a simple (k+1)-approximation algorithm using a natural LP relaxation. We also show that the integrality gap of the … Read more
It is common knowledge that symmetries arising in integer programs could impair the solution process, in particular when symmetric solutions lead to an excessively large branch and bound (B&B) search tree. Techniques like isomorphic pruning [11], orbital branching [16] and orbitopal fixing [8] have been shown to be essential to solve very symmetric instances from … Read more
We consider the Resource Constrained Shortest Path problem arising as a subproblem in state-of-the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance … Read more
This paper is motivated by the case of a forwarder in dealing with inland transportation planning from a seaport, where inbound containers from the sea are filled with pallets, which have different destinations in the landside. Although this forwarder does not have or control any vehicle, he is required to plan the assignment of containers … Read more