The Sherali-Adams lift-and-project hierarchy is a fundamental construct in integer programming, which provides successively tighter linear programming relaxations of the integer hull of a polytope. We initiate a new approach to understanding the Sherali-Adams procedure by relating it to methods from computational algebraic geometry. Our main result is a refinement of the Sherali-Adams procedure that … Read more
This paper proposes a linear integer programming formulation and several heuristics based on GRASP and path relinking for the antibandwidth problem. In the antibandwidth problem, one is given an undirected graph with N nodes and must label the nodes in a way that each node receives a unique label from the set {1, 2, …, … Read more
Branching variable selection can greatly a ffect the eff ectiveness and efficiency of a branch-and- bound algorithm. Traditional approaches to branching variable selection rely on estimating the eff ect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from … Read more
We study the multidimensional knapsack problem, present some theoretical and empirical results about its structure, and evaluate different Integer Linear Programming (ILP) based, metaheuristic, and collaborative approaches for it. We start by considering the distances between optimal solutions to the LP-relaxation and the original problem and then introduce a new core concept for the MKP, … Read more
Abstract: We present new valid inequalities for 0-1 programming problems that work in similar ways to well known cover inequalities. Discussion and analysis of these cuts is followed by their revision and use in integer programming as a new generation of cuts that excludes not only portions of polyhedra containing noninteger points, also parts with … Read more
We extend the classical 0-1 knapsack problem by introducing disjunctive constraints for pairs of items which are not allowed to be packed together into the knapsack. These constraints are represented by edges of a conflict graph whose vertices correspond to the items of the knapsack problem. Similar conditions were treated in the literature for bin … Read more
The rectangular assignment problem is a generalization of the linear assignment problem (LAP): one wants to assign a number of persons to a smaller number of jobs, minimizing the total corresponding costs. Applications are, e.g., in the fields of object recognition and scheduling. Further, we show how it can be used to solve variants of … Read more
This paper studies location routing and scheduling problems, a class of problems in which the decisions of facility location, vehicle routing, and route assignment are optimized simultaneously. For a version with capacity and time restrictions, two formulations are presented, one graph-based and one set-partitioning-based. For the set-partitioning-based formulation, valid inequalities are identified and their effectiveness … Read more
We apply the level-3 Reformulation Linearization Technique (RLT3) to the Quadratic Assignment Problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm, based on this RLT3 formulation. This algorithm is not guaranteed to calculate the RLT3 lower bound exactly, but approximates it very closely and reaches it in some … Read more
We prove that the subset sum problem has a polynomial time computable certificate of infeasibility for all $a$ weight vectors with density at most $1/(2n)$ and for almost all integer right hand sides. The certificate is branching on a hyperplane, i.e. by a methodology dual to the one explored by Lagarias and Odlyzko; Frieze; Furst … Read more