The Capacitated Arc Routing Problem (CARP) stands among the hardest combinatorial problems to solve or to find high quality solutions. This becomes even more true when dealing with large instances. This paper investigates methods to improve on lower and upper bounds of instances on graphs with over two hundred vertices and three hundred edges, dimensions … Read more
This paper introduces interdiction branching, a new branching method for binary integer programs that is designed to overcome the difficulties encountered in solving problems for which branching on variables is inherently weak. Unlike traditional methods, selection of the disjunction in interdiction branching takes into account the best feasible solution found so far. In particular, the … Read more
We study solution approaches for the design of reliably connected networks. Speci fically, given a network with arcs that may fail at random, the goal is to select a minimum cost subset of arcs such the probability that a connectivity requirement is satis ed is at least 1-\epsilon, where \epsilon is a risk tolerance. We consider two … Read more
We prove that any minimal valid function for the k-dimensional infinite group relaxation that is piecewise linear with at most k+1 slopes and does not factor through a linear map with non-trivial kernel is extreme. This generalizes a theorem of Gomory and Johnson for k=1, and Cornu\’ejols and Molinaro for k=2. Article Download View A … Read more
We are given a digraph G = (N, A), where each arc is colored with one among k given colors. We look for a spanning arborescence T of G rooted at a given node and having minimum changeover cost. We call this the Minimum Changeover Cost Arborescence problem. To the authors’ knowledge, it is a … Read more
Valid inequalities or cutting planes for (mixed-) integer programming problems are an essential theoretical tool for studying combinatorial properties of polyhedra. They are also of utmost importance for solving optimization problems in practice; in fact any modern solver relies on several families of cutting planes. The Chvátal-Gomory procedure, one such approach, has a peculiarity that … Read more
This paper presents some strong valid inequalities for the Maximum Common Induced Subgraph Problem (MCIS) and the proofs that the inequalities are facet-defining under certain conditions. The MCIS is an NP-hard problem and, therefore, no polynomial time algorithm is known to solve it. In this context, the study of its polytope can help in the … Read more
We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has focused on the special case in which … Read more
In this paper, we examine a mixed integer linear programming (MIP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to … Read more
We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with nite 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 nd provably good solutions in certain very special cases. Our approach … Read more