Related papers: Solving Integer Linear Programs with a Small Numbe…
Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a "small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching…
We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it.…
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…
Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…
We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary…
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
Integer linear programs (ILPs) are a widely applied framework for dealing with combinatorial problems that arise in practice. It is known, e.g., by the success of CPLEX, that preprocessing and simplification can greatly speed up the process…
Solving (mixed) integer linear programs, (M)ILPs for short, is a fundamental optimization task. While hard in general, recent years have brought about vast progress for solving structurally restricted, (non-mixed) ILPs: $n$-fold, tree-fold,…
In this paper, we show how a resource allocation problem can be solved through Integer Linear Programming (ILP). A detailed illustrative example is presented, together with an exhaustive overview of the mathematical model. The size of the…
State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the so-called Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit the conflicts…