In this paper, we prove that the Chvatal-Gomory closure of a set obtained as an intersection of a strictly convex body and a rational polyhedron is a polyhedron. Thus, we generalize a result of Schrijver which shows that the Chvatal-Gomory closure of a rational polyhedron is a polyhedron. Article Download View The Chvatal-Gomory Closure of … 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
Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover … Read more
The Single Row Facility Layout Problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [Discrete Applied Mathematics 157(1)(2009)183-190]. For any number … Read more
In this paper, we study the relationship between {\em 2D lattice-free cuts}, the family of cuts obtained by taking two-row relaxations of a mixed-integer program (MIP) and applying intersection cuts based on maximal lattice-free sets in $\R^2$, and various types of disjunctions. Recently, Li and Richard (2007) studied disjunctive cuts obtained from $t$-branch split disjunctions … Read more
We consider a complex planning problem in integrated steel production. A sequence of coils of sheet metal needs to be color coated in consecutive stages. Di erent coil geometries and changes of coatings may necessitate time-consuming setup work. In most coating stages one can choose between two parallel color tanks in order to reduce setup times. … Read more
We consider two approaches for solving the classical minimum vertex coloring problem�that is, the problem of coloring the vertices of a graph so that adjacent vertices have different colors and minimizing the number of used colors, namely, constraint programming and column generation. Constraint programming is able to solve very efficiently many of the benchmarks but … Read more
The cone of Completely Positive (CP) matrices can be used to exactly formulate a variety of NP-Hard optimization problems. A tractable relaxation for CP matrices is provided by the cone of Doubly Nonnegative (DNN) matrices; that is, matrices that are both positive semidefinite and componentwise nonnegative. A natural problem in the optimization setting is then … Read more
We present a proactive energy management framework that integrates predictive dynamic building models and day-ahead forecasts of disturbances affecting efficiency and costs. This enables an efficient management of resources and an accurate prediction of the daily electricity demand profile. The strategy is based on the on-line solution of mixed-integer nonlinear programming problems. The framework is … Read more
We report on experiments with turning the branch-cut-and-price framework SCIP into a generic branch-cut-and-price solver. That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themselves, … Read more