In this paper we present a cutting plane algorithm for the Set Covering problem. Cutting planes are generated by a “general” (i.e. not based on the “template paradigm”) separation algorithm based on the following idea: i) identify a suitably small subproblem defined by a subset of the constraints of the formulation; ii) run an exact … Read more
In this paper, we propose lifting techniques for generating strong cuts for nonlinear programs that are globally-valid. The theory is geometric and provides intuition into lifting-based cut generation procedures. As a special case, we find short proofs of earlier results on lifting techniques for mixed-integer programs. Using convex extensions, we obtain conditions that allow sequence-independent … Read more
A finite test set for an integer maximization problem enables us to verify whether a feasible point attains the global maximum. We establish in this paper several general results that apply to integer maximization problems with nonlinear objective functions. Citation Operations Research Letters 36 (2008) 439–443 Article Download View On Test Sets for Nonlinear Integer … Read more
We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints … Read more
We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially … Read more
Chvatal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or 1/2, such cuts are known as {0, 1/2}-cuts. It has been proven by Caprara and Fischetti (1996) that separation of {0, 1/2}-cuts is NP-hard. In this paper, we study … Read more
Consider the problem that consists in maximizing the revenue generated by tolls set on a subset of arcs of a transportation network, and where origin-destination flows are assigned to shortest paths with respect to the sum of tolls and initial costs. In this work, we address the instance where toll arcs must be connected, as … Read more
We introduce a new measure of complexity of integer hulls of rational polyhedra called the small Chvatal rank (SCR). The SCR of an integer matrix A is the number of rounds of a Hilbert basis procedure needed to generate all normals of a sufficient set of inequalities to cut out the integer hulls of all … Read more
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: 1. polynomial-time algorithms to exactly determine the number of Pareto optima and Pareto strategies; 2. a polynomial-space polynomial-delay prescribed-order enumeration algorithm … Read more
We propose a very simple preconditioning method for integer programming feasibility problems: replacing the problem b’ ≤ Ax ≤ b, x ∈ Zn with b’ ≤ (AU)y ≤ b, y ∈ Zn, where U is a unimodular matrix computed via basis reduction, to make the … Read more