Related papers: Mixed-integer linear representability, disjunction…
In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related…
Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…
There has been growing interest in implementing massive MIMO systems by one-bit analog-to-digital converters (ADCs), which have the benefit of reducing the power consumption and hardware complexity. One-bit MIMO detection arises in such a…
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…
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…
This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the…
Machine Reassignment is a challenging problem for constraint programming (CP) and mixed-integer linear programming (MILP) approaches, especially given the size of data centres. The multi-objective version of the Machine Reassignment Problem…
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…
Developing Machine Learning (ML) algorithms for heterogeneous/mixed data is a longstanding problem. Many ML algorithms are not applicable to mixed data, which include numeric and non-numeric data, text, graphs and so on to generate…
Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…
Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is…
Mixed Integer Linear Programming (MILP) is a well-known approach for the cryptanalysis of a symmetric cipher. A number of MILP-based security analyses have been reported for non-linear (SBoxes) and linear layers. Researchers proposed word-…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
This paper is concerned with adaptive signal control problems on a road network, using a link-based kinematic wave model (Han et al., 2012). Such a model employs the Lighthill-Whitham-Richards model with a triangular fundamental diagram. A…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
Discrete black-box optimization problems are challenging for model-based optimization (MBO) algorithms, such as Bayesian optimization, due to the size of the search space and the need to satisfy combinatorial constraints. In particular,…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
We study the mixed-integer optimization (MIO) approach to feature subset selection in nonlinear kernel support vector machines (SVMs) for binary classification. First proposed for linear regression in the 1970s, this approach has recently…
Over the past few decades, neuroscience experiments have become increasingly complex and naturalistic. Experimental design has in turn become more challenging, as experiments must conform to an ever-increasing diversity of design…
Birkhoff's representation theorem (Birkhoff, 1937) defines a bijection between elements of a distributive lattice and the family of upper sets of an associated poset. Although not used explicitly, this result is at the backbone of the…