A new lift-and-project operator

In this paper, we analyze the strength of split cuts in a lift-and-project framework. We first observe that the Lovasz-Schrijver and Sherali-Adams lift-and-project operator hierarchies can be viewed as applying specific 0-1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts. More precisely, we define a … Read more

A Study of Three-Period Ramp-Up Polytope

We study the polyhedron of the unit commitment problem, and consider a relaxation involving the ramping constraints. We study the three-period ramp-up polytope, and describe the convex-hull using a new class of inequalities. Citation [1] J. Ostrowski, M. F. Anjos, and A. Vannelli, \Tight mixed integer linear programming formulations for the unit commitment problem,” Power … Read more

Divisive heuristic for modularity density maximization

In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more

Solving MIPs via Scaling-based Augmentation

Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e., number of iterations needed, can theoretically be improved by scaling methods. We extend these results by an … Read more

Integer Programming Approaches for Appointment Scheduling with Random No-shows and Service Durations

We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional … Read more

The Uncapacitated Single Allocation p-Hub Median Problem with Stepwise Cost Function

In this paper, we address a new version of the Uncapacitated Single Allocation p-Hub Median Problem (USApHMP) in which transportation costs on each edge are given by piecewise constant cost functions. In the classical USApHMP, transportation costs are modelled as linear functions of the transport volume, where a fixed discount factor on hub-hub connections is … Read more

Constructing a Small Compact Binary Model for the Travelling Salesman Problem

A variety of formulations for the Travelling Salesman Problem as Mixed Integer Program have been proposed. They contain either non-binary variables or the number of constraints and variables is large. We want to give a new formulation that consists solely of binary variables; the number of variables and the number of constraints are of order … Read more

On Sublinear Inequalities for Mixed Integer Conic Programs

This paper studies $K$-sublinear inequalities, a class of inequalities with strong relations to K-minimal inequalities for disjunctive conic sets. We establish a stronger result on the sufficiency of $K$-sublinear inequalities. That is, we show that when $K$ is the nonnegative orthant or the second-order cone, $K$-sublinear inequalities together with the original conic constraint are always … Read more

A Stabilised Scenario Decomposition Algorithm Applied to Stochastic Unit Commitment Problems

In recent years the expansion of energy supplies from volatile renewable sources has triggered an increased interest in stochastic optimization models for hydro-thermal unit commitment. Several studies have modelled this as a two-stage or multi-stage stochastic mixed-integer optimization problem. Solving such problems directly is computationally intractable for large instances, and alternative approaches are required. In … Read more

Using the Johnson-Lindenstrauss lemma in linear and integer programming

The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean distances. In this paper we … Read more