Related papers: Parameterized Algorithms for MILPs with Small Tree…

This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By…

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the…

We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-independence number. In [Dallard, Milani\v{c}, and…

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…

A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…

Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…

In this paper, we address the problem of time-optimal coordination of mobile robots under kinodynamic constraints along specified paths. We propose a novel approach based on time discretization that leads to a mixed-integer linear…

While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…

Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is…

This paper addresses the problem of tightening the mixed-integer linear programming (MILP) formulation for continuous piecewise linear (CPWL) approximations of data sets in arbitrary dimensions. The MILP formulation leverages the…

We consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…

Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…

We study two classic variants of block-structured integer programming. Two-stage stochastic programs are integer programs of the form $\{A_i \mathbf{x} + D_i \mathbf{y}_i = \mathbf{b}_i\textrm{ for all }i=1,\ldots,n\}$, where $A_i$ and…

The Steiner Forest problem is among the fundamental network design problems. Finding tight linear programming bounds for the problem is the key for both fast Branch-and-Bound algorithms and good primal-dual approximations. On the…

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…

Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…

Mixed-integer (MI) quadratic models subject to quadratic constraints, known as All-Quadratic MI Programs, constitute a challenging class of NP-complete optimization problems. The particular scenario of unbounded integers defines a subclass…