Related papers: A geometric way to build strong mixed-integer prog…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…
This paper presents a mixed-integer quadratic programming formulation of an existing data-driven approach to computational elasticity. This formulation is suitable for application of a standard mixed-integer programming solver, which finds…
A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
In this paper, we investigate the constraint typology of mixed-integer linear programming MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning,…
Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…
The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of…
Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer…
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…
Mixed-Integer Programming (MIP), particularly Mixed-Integer Linear Programming (MILP) and Mixed-Integer Quadratic Programming (MIQP), has found extensive applications in domains such as portfolio optimization and network flow control, which…
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have…
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…
In project scheduling under processing times uncertainty, the Anchor-Robust Project Scheduling Problem is to find a baseline schedule of bounded makespan and a max-weight subset of jobs whose starting times are guaranteed. The problem was…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
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…
Morse matchings capture the essential structural information of discrete Morse functions. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present polyhedral…