Related papers: Learning to Remove Cuts in Integer Linear Programm…

We consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-cuts) that defines the convex hull of the integer…

This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…

Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…

Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find…

Chvatal-Gomory cutting planes (CG-cuts for short) are a fundamental tool in Integer Programming. Given any single CG-cut, one can derive an entire family of CG-cuts, by `iterating' its multiplier vector modulo one. This leads naturally to…

Inductive logic programming (ILP) is a form of logical machine learning. The goal is to search a hypothesis space for a hypothesis that generalises training examples and background knowledge. We introduce an approach that 'shrinks' the…

In this paper we give a generalization of the well known split cuts of Cook, Kannan and Schrijver to cuts which are based on multi-term disjunctions. They will be called k-disjunctive cuts. The starting point is the question what kind of…

We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). We propose an integer linear programming model for the…

Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…

Large language models (LLMs) have shown remarkable capabilities in language understanding and generation. However, such impressive capability typically comes with a substantial model size, which presents significant challenges in deployment…

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…

Large Language Models (LLMs) have achieved remarkable success across a wide spectrum of natural language processing tasks. However, their ever-growing scale introduces significant barriers to real-world deployment, including substantial…

Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear Programing…

As real logic programmers normally use cut (!), an effective learning procedure for logic programs should be able to deal with it. Because the cut predicate has only a procedural meaning, clauses containing cut cannot be learned using an…

We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…

We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.

The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…

In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general…

We address the issue of generating cutting planes for mixed integer programs from multiple rows of the simplex tableau with the tools of disjunctive programming. A cut from q rows of the simplex tableau is an intersection cuts from a…

This paper addresses the challenge of determining optimal cut-offs for a set of n items with m scores to maximize distinguishability. The term distinguishability is defined as the fraction of item pairs assigned to different buckets, where…