MIP-GNN uses graph neural networks to predict variable biases for MIP solvers.
problem Improving combinatorial optimization through data-driven insights.
method Encoding MILP interactions as graphs, training a graph neural network to predict variable biases, and guiding the MIP solver with these predictions.
result Significant improvements in solving binary MILPs compared to default settings of state-of-the-art solvers.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
Transformers improve solving mixed-integer programs, especially CLSP.
problem Solving Capacitated Lot Sizing Problem (CLSP) with mixed-integer programming.
method Employing transformer models to predict binary variables in CLSP.
result Transformer model outperforms CPLEX and LSTM in solving CLSP.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
New MIP methods improve training of integer-valued neural networks.
problem Training integer-valued neural networks with limited data and resources.
method Formulated new MIP models to optimize training efficiency and handle more data.
result Significantly outperforms previous state-of-the-art methods in accuracy, training time, and data usage.
Mixed integer programming identifies critical neurons in neural networks.
problem Identifying neurons critical for network performance and generalization.
method Developed a mixed integer program (MIP) to assign importance scores to neurons, guiding pruning decisions.
result The method identifies multiple 'lucky' sub-networks resulting in optimized architectures that generalize across datasets.
Paper uses RL to optimize branching strategy in B&B algorithms.
problem Optimizing Branch and Bound algorithms for mixed integer linear programs.
method FMSTS, a Reinforcement Learning approach for variable selection.
result FMSTS outperforms commercial solvers in efficiency and generalization.
ExDBN learns dynamic Bayesian networks using mixed-integer programming.
problem Learning dynamic causal relationships from time series data.
method Score-based learning algorithm using mixed-integer quadratic programming with branch-and-cut method.
result The proposed method produces more accurate results than state-of-the-art approaches.
Generalizes neural network verification by adding arbitrary cutting planes.
problem Handling general cutting plane constraints in neural network verification.
method Generalized bound propagation method (GCP-CROWN) that allows arbitrary cutting plane constraints.
result GCP-CROWN significantly improves neural network verification performance.
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the…
NeuralCut learns to select cutting planes by looking ahead, outperforming traditional methods.
problem Selecting effective cutting planes for MILP optimization.
method Imitation learning on a lookahead expert to train a neural network for cut selection.
result NeuralCut outperforms standard baselines in cut selection for MILP benchmarks.
Quantum algorithm speeds up MIP solving by a near-quadratic factor.
problem Solving Mixed Integer Programs (MIPs) efficiently.
method Incremental-Quantum-Branch-and-Bound algorithm combining quantum speedup with classical search heuristics.
result Universal near-quadratic speedup over classical Branch-and-Bound algorithms.
ODTLearn learns optimal decision trees for predictive and prescriptive tasks.
problem Learning optimal decision trees for high-stakes predictive and prescriptive tasks.
method Mixed-integer optimization framework and object-oriented design.
result Implementation of optimal decision trees for various tasks.
This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed pol…
New hybrid model reduces MILP solver time by up to 26%.
problem Improving CPU-based MILP solver efficiency.
method Combines GNN and MLP for efficient CPU-based branching.
result Up to 26% reduction in solver running time compared to state-of-the-art methods.
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mix…
Graph Neural Networks learn to mimic strong branching in MILP solvers.
problem Improving variable selection in MILP solvers using Graph Neural Networks.
method Proposed methods include target smoothing and a Parent-as-Target Lookback regularizer.
result Up to 22% decrease in B&B tree size and 15% improvement in solving times.
A new decision tree induction method using MIP for faster optimization.
problem Optimizing decision tree split rules for better classification performance.
method Mixed-integer programming (MIP) for Gini reduction maximization, efficient search algorithm.
result bsnsing trees outperform other tree models in new case discrimination.
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs…
This paper proposes exact and approximation algorithms for Sparse PCA, improving interpretability and scalability.
problem Selecting a prespecified-size principal submatrix from a covariance matrix to maximize its largest eigenvalue.
method Proposes two exact mixed-integer SDPs and a mixed-integer linear program (MILP) for SPCA, analyzes theoretical optimality gaps, and develops approximation algorithms.
result The proposed algorithms achieve strong theoretical optimality and effective scalability, with continuous relaxations close to optimality and MILP solving small to medium-size instances.
Estimates sparse Gaussian graphical models using discrete optimization.
problem Learning a sparse graph from Gaussian graphical models.
method Proposes GraphL0BnB, an ℓ0-penalized MIP solved with a custom BnB framework. result Significant runtime and statistical performance improvements over existing methods.
Classifier evasion consists in finding for a given instance x the nearest instance x′ such that the classifier predictions of x and x′ are different. We present two novel algorithms for systematically computing evasions for tree ensembles such as boosted trees and random forests. Our first algorithm uses a Mixe…
New method learns BN structures from data efficiently.
problem Learning sparse DAG structure of BN from continuous data.
method Consistent second-order conic integer programming with early stopping criterion.
result Near-optimal solutions to medium-size problems within reasonable time.
Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesia…
Graph neural networks improve solving linear optimization problems.
problem Improving the efficiency of solving linear optimization problems.
method Using graph neural networks to simulate standard interior-point methods for linear optimization problems.
result Graph neural networks can solve linear optimization problems close to optimality, often outperforming conventional solvers.
A scalable gradient-based framework for sparse portfolio selection.
problem Sparse minimum-variance portfolio selection with cardinality constraint.
method Gradient-based optimization with Boolean relaxation and tunable parameter.
result Matches commercial solvers in most instances, differing by a few assets with negligible error in portfolio variance.
Optimizes marketing strategies with practical constraints.
problem Adjusting marketing activities with minimum and maximum changes.
method Formulated as a mixed integer nonlinear program (MINLP), reformulated for computational efficiency.
result Significant improvements in solution process for realistic problems.
A new model tracks indices without rebalancing, solving NP-hard problems.
problem Tracking indices without rebalancing and minimizing deviations.
method Metaheuristic algorithms and local branching for solving mixed integer linear programming.
result The heuristic generates portfolios that outperform commercial solvers in both in-sample and out-of-sample data.
New method builds robust trees from noisy data.
problem Building accurate classification trees from noisy labeled data.
method Combines SVM-like splitting rules and label noise detection.
result Effective in detecting and mitigating label noise.
New method improves portfolio selection by filtering noisy covariance matrices.
problem Noisy covariance matrices in financial datasets affect portfolio performance evaluation.
method Combinatorial Optimization approach using Mixed Integer Quadratic Programming.
result Our method outperforms existing filtering strategies for real financial datasets.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
problem Solving parametric mixed-integer linear optimization problems with changing data.
method Introducing cutting-plane layers (CPLs) for differentiable cutting-plane generation.
result The algorithm computes solutions with low integrality gaps and generalizes to unseen instances.
Security-Constrained Unit Commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via Mixed-Integer Linear Programming, sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine lear…
End-to-end pipeline for data-driven decision making in mixed-integer optimization.
problem Data-driven decision making in mixed-integer optimization with uncertainty.
method Exploiting mixed-integer optimization-representability of machine learning methods, characterizing decision trust regions, and ensembling multiple models.
result Framework generates high-quality prescriptions and controls model robustness.
Global optimization approach for MAP clustering under Gaussian mixtures.
problem Maximum a-posteriori clustering problem under Gaussian mixture model.
method Mixed-integer nonlinear optimization (MINLP) transformed into mixed-integer quadratic program (MIQP).
result Explicit quantification of optimality gap, leading to globally optimal solutions.
Unified framework improves fair classification by selecting representative data points.
problem Improving fair classification outcomes in the presence of unintentional biases.
method Develops a unified framework to jointly optimize accuracy and fairness, recasting as mixed-integer convex programs.
result The framework can be used to enhance classification fairness by selecting more representative data points.
The L0-regularized least squares problem (a.k.a. best subsets) is central to sparse statistical learning and has attracted significant attention across the wider statistics, machine learning, and optimization communities. Recent work has shown that modern mixed integer optimization (MIO) solvers can be used to addre…
BackboneLearn speeds up MIO-based machine learning problems.
problem Scaling mixed-integer optimization problems in machine learning.
method An open-source Python framework for MIO problems with indicator variables.
result Solves MIO problems faster and more accurately than existing methods.
This paper uses MIO to select features for kernel SVM classification.
problem Feature selection for kernel SVM classification.
method Mixed-integer optimization (MIO) for feature subset selection.
result The MIO approach can often outperform linear-SVM-based methods in prediction performance.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
Unified framework for intersectionally fair AI models using MIO.
problem Bias in AI models for high-risk domains.
method Mixed-Integer Optimization (MIO) for fairness and interpretability.
result Improved performance in detecting and mitigating bias at intersections.
Mixed-integer optimization improves fairness and transparency in machine learning models.
problem Ensuring fairness and transparency in machine learning models deployed in sensitive areas.
method Embedding responsible ML considerations directly into the learning process using mixed-integer optimization.
result MIO enables the learning of inherently transparent models that can incorporate fairness or other constraints.
Two clustering algorithms optimize edge controller placement in wireless networks.
problem Optimizing edge controller placement in wireless edge networks.
method Deterministic annealing based clustering algorithms ECP-LL and ECP-LB.
result The algorithms achieve better balance between synchronization and delay costs.
New MIP approach for efficient change-point detection.
problem Offline multiple change-point detection in data streams.
method Mixed-integer programming (MIP) for globally optimal PWL fitting.
result Provable tighter relaxations for segment assignment variables.
Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus, there is a pressing need for developing techniques to verify neural networks to …
VNA solves large portfolio optimization problems efficiently.
problem Large-scale portfolio optimization under real-world constraints.
method Mapped to Ising-like Hamiltonian and solved with VNA.
result Identifies near-optimal solutions for over 2,000 assets.
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
New MIP algorithms improve sparse classifier learning times.
problem Sparse classifier learning at large scales.
method Developed exact and approximate MIP algorithms for ℓ0-regularized classification. result Significantly improved statistical performance compared to existing methods.