This paper addresses a constrained two-dimensional (2D) non-guillotine cutting problem, where a fixed set of small rectangles has to be cut from a larger stock rectangle so as to maximize the value of the rectangles cut. The algorithm we propose hybridizes a novel placement procedure with a genetic algorithm based on random keys. We propose … Read more
Gomory mixed-integer (GMI) cuts generated from optimal simplex tableaus are known to be useful in solving mixed-integer programs. Further, it is well-known that GMI cuts can be derived from facets of Gomory’s master cyclic group polyhedron and its mixed-integer extension studied by Gomory and Johnson. In this paper we examine why cutting planes derived from … Read more
An algorithm is developed for minimizing nonsmooth convex functions. This algorithm extends Elzinga-Moore cutting plane algorithm by enforcing the search of the next test point not too far from the previous ones, thus removing compactness assumption. Our method is to Elzinga-Moore’s algorithm what a proximal bundle method is to Kelley’s algorithm. Instead of lower approximations … Read more
This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to $q$-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence probem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. … Read more
In this paper we derive new properties of extreme inequalities for infinite group problems. We develop tools to prove that given valid inequalities for the infinite group problem are extreme. These results show that integer infinite group problems have discontinuous extreme inequalities. These inequalities are strong when compared to related classes of continuous extreme inequalities. … Read more
We analyze the problem of finding a point strictly interior to a bounded, fully dimensional set from a finite dimensional Hilbert space. We generalize the results obtained for the LP, SDP and SOCP cases. The cuts added by our algorithm are central and conic. In our analysis, we find an upper bound for the number … Read more
The evolutionary history of species may be described by a phylogenetic tree whose topology captures ancestral relationships among the species, and whose branch lengths denote evolution times. For a fixed topology and an assumed probabilistic model of nucleotide substitution, we show that the likelihood of a given tree is a d.c. (difference of convex) function … Read more
We present an analytic center cutting surface algorithm that uses mixed linear and multiple second-order cone cuts. Theoretical issues and applications of this technique are discussed. From the theoretical viewpoint, we derive two complexity results. We show that an approximate analytic center can be recovered after simultaneously adding $p$ second-order cone cuts in $O(p\log(p+1))$ Newton … Read more
The semidefinite programming formulation of the Lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number and the clique number of a graph, but also leads to heuristics for graph coloring and extracting large cliques. This semidefinite programming formulation can be tightened toward either number by adding … Read more
We investigate a network design problem under traffic uncertainty which arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network so as to support all … Read more