Subset Algebra Lift Operators for 0-1 Integer Programming

Subset Algebra Lift Operators for 0-1 Integer Programming

We extend the Sherali-Adams, Lovász-Schrijver, Balas-Ceria-Cornuéjols and Lasserre lift-and-project methods for 0-1 optimization by considering liftings to subset algebras. Our methods yield polynomialtime algorithms for solving a relaxation of a set-covering problem at least as strong as that given by the set of all valid inequalities with small coefficients, and, more generally, all valid ine...

Lift-and-project for Mixed 0-1 programming: recent progress

Lift-and-project for 0–1 programming via algebraic geometry

Recently, tools from algebraic geometry have been successfully applied to develop solution schemes for new classes of optimization problems. A central idea in these constructions is to express a polynomial that is positive on a given domain in terms of polynomials of higher degree so that its positivity is readily revealed. This resembles the “lifting” phase of the lift-and-project procedures f...

The Core Concept for 0/1 Integer Programming

In this paper we examine an extension of the core concept for the 0/1 Multidimensional Knapsack Problem (MKP) towards general 0/1 Integer Programming (IP) by allowing negative profits, weights and capacities. The core concept provides opportunities for heuristically solving the MKP, achieving higher quality solutions and shorter runtimes than general IP methods. We provide the theoretical found...

Best-First AND/OR Search for 0/1 Integer Programming

AND/OR search spaces are a unifying paradigm for advanced algorithmic schemes for graphical models. The main virtue of this representation is its sensitivity to the structure of the model, which can translate into exponential time savings for search algorithms. In this paper we introduce an AND/OR search algorithm that explores a context-minimal AND/OR search graph in a best-first manner for so...