Related papers: Mixed-integer linear representability, disjunction…
Jeroslow and Lowe gave an exact geometric characterization of subsets of $\mathbb{R}^n$ that are projections of mixed-integer linear sets, also known as MILP-representable or MILP-R sets. We give an alternate algebraic characterization by…
Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several…
This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by…
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…
Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in…
A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the…
We study the continuous set covering problem on networks and propose several new MILP formulations and valid inequalities. In contrast to state-of-the-art formulations, the new formulations only use edges to index installed points, and the…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…
We propose a new method for separating valid inequalities for the epigraph of a function of binary variables. The proposed inequalities are disjunctive cuts defined by disjunctive terms obtained by enumerating a subset $I$ of the binary…
We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer…
Cutting planes (cuts) are crucial for solving Mixed Integer Linear Programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and…
Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…
In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…