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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…

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…

Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NNs). However the intriguing approach of training NNs with MIP solvers is under-explored.…

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…

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…

Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics,…

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…

Deep neural networks (DNNs) are widely studied in various applications. A DNN consists of layers of neurons that compute affine combinations, apply nonlinear operations, and produce corresponding activations. The rectified linear unit…

Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…

To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the…

We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a \emph{strong formulation} for each neuron in a network using piecewise linear activation functions. Additionally, as in…

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…

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…

Pruning has emerged as the primary approach used to limit the resource requirements of large neural networks (NNs). Since the proposal of the lottery ticket hypothesis, researchers have focused either on pruning at initialization or after…

Large Neighborhood Search (LNS) is a combinatorial optimization heuristic that starts with an assignment of values for the variables to be optimized, and iteratively improves it by searching a large neighborhood around the current…

In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization.…

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…

This paper presents how a mixed-integer programming (MIP) formulation for influence diagrams, based on a gradual rooted junction tree representation of the diagram, can be generalized to incorporate risk considerations such as conditional…

The identification of essential proteins in protein-protein interaction networks (PINs) can help to discover drug targets and prevent disease. In order to improve the accuracy of the identification of essential proteins, researchers…

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…