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.
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.
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.
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.
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.
We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model.Our approach can accommodate side constraints and it preserves the combinatorial structure of the MAP clustering problem by formulating it asa mixed-integer nonlinear optimization pro…
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.
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.
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.
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.
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.
Optimizes risk assessment tools using mixed-integer programming.
problem Challenges in healthcare risk assessment due to label scarcity and asymmetric misclassification costs.
method Jointly optimizes scoring weights and category thresholds via mixed-integer programming (MIP).
result Prevents label-scarce category collapse and achieves more accurate risk categorization.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
Optimizes routing in decentralized exchanges with gas fees.
problem Routing in decentralized exchanges with fixed gas fees.
method General optimization framework with mixed-integer model, incorporating gas fees.
result Explicit Karush-Kuhn-Tucker system linking prices, fees, and activation.
Stochastic cutting planes improve data-driven optimization speed.
problem Data-driven Mixed-Integer Nonlinear Optimization problems.
method Stochastic version of cutting-plane method.
result Stochastic algorithm converges to ε-optimal solution with high probability.
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.
Paper proposes a novel optimization method for disaggregating smart meter data.
problem Energy disaggregation, inferring appliance-specific energy consumption from aggregate meter data.
method Two-stage optimization approach: first phase uses mixed integer programming, second phase binary quadratic optimization with penalty terms and appliance constraints.
result Proposed method successfully reconstructs appliance signatures, overcoming previous optimization-based methods' limitations.
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…
Proposes a method to learn both constraints and objective functions from data.
problem Data-driven inverse optimization for mixed-integer linear programs (MILPs).
method Two-stage approach: first learns constraints, then estimates objective-function weights conditioned on learned constraints.
result Proposes and validates a method for learning both objective functions and constraints from data.
AF improves classification models by adaptively weighting trees.
problem Improving classification model performance.
method AF combines OP2T for input-dependent weights and MIO for dynamic refinement.
result AF consistently outperforms RF, XGBoost, and other weighted RF.
Develops a new method for optimizing with uncertain data.
problem Uncertainty in real-world optimization problems.
method Combines chance constraints and constraint learning for mixed-integer linear optimization.
result Data-driven solution for setting probabilistic bounds on learned constraints.
The paper tackles robust classification trees for distribution shifts, improving accuracy in public health and social work.
problem Learning robust classification trees for high-stakes settings with distribution shifts.
method Mixed-integer robust optimization technology to reformulate as a two-stage linear robust optimization problem.
result Increase of up to 12.48% in worst-case accuracy and 4.85% in average-case accuracy.
Proposes an efficient method for ordered counterfactual explanations.
problem Insufficient explanation of perturbation vectors for executing actions.
method Mixed-Integer Linear Optimization (MILP) approach for evaluating and extracting optimal pairs of actions and orders.
result Demonstrated effectiveness of the proposed method on real datasets.
Intelligent motion planning is one of the core components in automated vehicles, which has received extensive interests. Traditional motion planning methods suffer from several drawbacks in terms of optimality, efficiency and generalization capability. Sampling based methods cannot guarantee the optimality of the gener…
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
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.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
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 solve (to optimality) ℓ0-regularized regression problems at scales much larg…
New algorithms optimize neural networks with ReLU activations using sampling.
problem Optimizing trained neural networks with ReLU activations.
method Iterative algorithm and enhanced algorithm using sampling and neighborhood search.
result The methods reduce the initial MIP problem into smaller LP or MIP problems.
A Ph.D. thesis proposes an efficient approach for optimizing aircraft eco-design with high-dimensional mixed integer variables.
problem Optimizing aircraft eco-design with high-dimensional mixed integer variables.
method EGO optimization approach based on sequential enrichment of adaptive surrogate models, adapted for high-dimensional and mixed variable spaces.
result Effective parameterization tools significantly reduce the number of design variables, enabling optimization of complex aircraft concepts.
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.
Best-of-∞ improves LLM performance by efficiently allocating inference-time computation.
problem Achieving optimal performance in test-time LLM ensembling with infinite budget.
method Adaptive generation scheme and weighted ensembles of LLMs, formulated as mixed-integer linear program.
result Optimal ensemble weighting improves performance over individual models.
Optimizes electric aircraft deployment for Canadian aviation to reduce emissions.
problem Limited fleet capacity and operational structure hinder electric aircraft transition.
method Multi-period mixed-integer linear programming (MILP) framework.
result Electric aircraft can reduce emissions by over 70% within five years.
A new framework for predictive clustering and optimization.
problem Finding clusters of data that yield low error on a supervised target.
method Generalized optimization framework using MILP and MM for scalability.
result Models can uncover different interpretable discrete cluster structures.
New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
New research limits how deep neural networks can be for certain functions.
problem Understanding the depth required for neural networks to represent specific functions.
method Mixed-integer optimization, polyhedral theory, tropical geometry.
result Neural networks with more than one layer are necessary to represent certain functions.
Optimizes experimental design using synthetic controls for better outcomes.
problem Estimating average treatment effects in studies with pre-treatment data.
method Mixed-integer programming for selecting treated and control units and weights.
result Improves mean squared error and statistical power compared to simple alternatives.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
Method learns optimal treatment policies from observational data.
problem Learning interpretable treatment assignment policies from observational data.
method Mixed-integer optimization (MIO) technology.
result Asymptotically exact in converging to optimal treatment policies.
We introduce a mixed integer program (MIP) for assigning importance scores to each neuron in deep neural network architectures which is guided by the impact of their simultaneous pruning on the main learning task of the network. By carefully devising the objective function of the MIP, we drive the solver to minimize th…
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.
Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
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…
Paper introduces methods to create fair and accurate regression models.
problem Creating fair and accurate regression models.
method Mixed-integer optimization methods, exact formulations, branch-and-bound algorithm, coordinate descent algorithm.
result Developed methods produce fair and accurate models with reduced training times.
New model optimizes oil product distribution via pipelines.
problem Optimizing oil product distribution via pipelines.
method Discrete-time mixed integer linear programming model.
result Significant reductions in pipeline operational cost.
This work analyzes machine learning for Lagrangian Relaxation in MILP.
problem Improving efficiency in solving large-scale MILP problems.
method Data-driven Algorithm Design approach to learn Lagrangian multipliers.
result Stochastic Gradient Ascent achieves the minimax optimal rate for learning multipliers.
Proposes a new method for subgroup analysis using optimal trees with parameter fusion.
problem Challenges of greedy heuristics and overfitting in tree-based recursive partitioning methods.
method Fused optimal causal tree method leveraging mixed integer optimization (MIO) for globally optimal partitions and parameter fusion.
result Substantial improvement in subgroup discovery accuracy and statistical efficiency.