A mixed-integer exponential cone programming formulation for feature subset selection in logistic regression

Logistic regression is one of the widely-used classification tools to construct prediction models. For datasets with a large number of features, feature subset selection methods are considered to obtain accurate and interpretable prediction models, in which irrelevant and redundant features are removed. In this paper, we address the problem of feature subset selection in logistic … Read more

Deep learning and hyperparameter optimization for assessing one’s eligibility for a subcutaneous implantable cardioverter-defibrillator

In cardiology, it is standard for patients suffering from ventricular arrhythmias (the leading cause of sudden cardiac death) belonging to high risk populations to be treated using Subcutaneous Implantable Cardioverter-Defibrillators (S-ICDs). S-ICDs carry a risk of so-called T Wave Over Sensing (TWOS), which can lead to inappropriate shocks with an inherent health risk. For this … Read more

Machine Learning for K-adaptability in Two-stage Robust Optimization

Two-stage robust optimization problems constitute one of the hardest optimization problem classes.One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizesdecisions corresponding to each of these subsets. In general case, it is solved using the … Read more

Robust Two-Stage Optimization with Covariate Data

We consider a generalization of two-stage decision problems in which the second-stage decision may be a function of a predictive signal but cannot adapt fully to the realized uncertainty. We will show how such problems can be learned from sample data by considering a family of regularized sample average formulations. Furthermore, our regularized data-driven formulations … Read more

A Machine Learning Approach to Solving Large Bilevel and Stochastic Programs: Application to Cycling Network Design

We present a novel machine learning-based approach to solving bilevel programs that involve a large number of independent followers, which as a special case include two-stage stochastic programming. We propose an optimization model that explicitly considers a sampled subset of followers and exploits a machine learning model to estimate the objective values of unsampled followers. … Read more

Revisiting local branching with a machine learning lens

Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce improving solutions and has been highly influential for the development of local search methods in MILP. The algorithm iteratively explores a sequence of solution … Read more

Learning to Use Local Cuts

An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, … Read more

PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming

In deterministic optimization, it is typically assumed that all parameters of the problem are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this … Read more

Learning for Spatial Branching: An Algorithm Selection Approach

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of … Read more