Related papers: Optimizing Objective Functions from Trained ReLU N…

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…

When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local…

We study optimization problems where the objective function is modeled through feedforward neural networks with rectified linear unit (ReLU) activation. Recent literature has explored the use of a single neural network to model either…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

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…

In this paper, it is demonstrated through a case study that multilayer feedforward neural networks activated by ReLU functions can in principle be trained iteratively with Mixed Integer Linear Programs (MILPs) as follows. Weights are…

This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…

The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to…

In this work, we develop a novel input feature selection framework for ReLU-based deep neural networks (DNNs), which builds upon a mixed-integer optimization approach. While the method is generally applicable to various classification…

Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

ReLU neural networks trained as surrogate models can be embedded exactly in mixed-integer linear programs (MILPs), enabling global optimization over the learned function. The tractability of the resulting MILP depends on structural…

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…

We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to…

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…

We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…

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…

Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring…