MVRSM optimizes expensive functions with mixed variables, outperforming state-of-the-art methods.
problem Minimizing expensive functions with mixed continuous and integer variables.
method Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) using rectified linear units.
result MVRSM outperforms state-of-the-art methods on synthetic and real-life benchmarks.
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.
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.
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.
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.
Paper introduces DP methods for high-dimensional variable selection.
problem Sparse variable selection in high-dimensional learning.
method Pure differentially private estimators using Integer Programming.
result Achieves state-of-the-art empirical support recovery.
A new distance for mixed-variable, hierarchical datasets with meta variables.
problem Heterogeneous datasets limit generalizability and performance in machine learning and optimization.
method Developed a modeling framework for mixed-variable and hierarchical domains with meta variables, and a novel distance function.
result The novel distance function allows comparison of heterogeneous datasets, improving model performance.
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
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.
Bayesian optimization reduces hyperparameters for mixed variable design problems.
problem Optimizing designs with a large number of mixed continuous, integer, and categorical variables.
method Adaptive dimension reduction using partial least squares for fewer hyperparameters.
result Significant improvement in performance compared to genetic algorithms.
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.
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.
Proposes a method to select variables for kernel two-sample tests.
problem Determining whether two samples have the same distribution using informative variables.
method A framework based on kernel maximum mean discrepancy (MMD) for selecting a subset of variables.
result The sample size requirements for the three kernels depend on the number of selected variables, not the data dimension.
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…
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.
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 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.
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.
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 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.
The paper analyzes financial networks with default charges and defines a model using fixpoint problems.
problem Modeling systemic risk in interbank networks with crossholdings and default charges.
method Mixed integer-linear programming and Gaussian elimination algorithm for computing clearing pairs.
result Developed methods to compute maximal and minimal clearing pairs.
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.
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.
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.
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…
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.
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.
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.
We study the AutoML problem of automatically configuring machine learning pipelines by jointly selecting algorithms and their appropriate hyper-parameters for all steps in supervised learning pipelines. This black-box (gradient-free) optimization with mixed integer & continuous variables is a challenging problem. We pr…
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.
CPP solves chance constrained optimization problems with a framework that combines samples and quantile lemma.
problem Chance constrained optimization problems with constraints on random variables.
method CPP framework using samples and quantile lemma to transform into deterministic problem.
result CPP provides a posteriori guarantees on constraint satisfaction and can handle different types of chance constraints.
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.
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capit…
In this paper, we present a novel approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of widely used measures for misclassifying observations where the \textit{kernel tr…
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
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…
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.
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.
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not p…
This paper presents a novel end-to-end methodology for enabling the deployment of low-error deep networks on microcontrollers. To fit the memory and computational limitations of resource-constrained edge-devices, we exploit mixed low-bitwidth compression, featuring 8, 4 or 2-bit uniform quantization, and we model the i…
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…
Unified Bayesian Optimisation for mixed variables improves performance.
problem Efficient optimisation of problems with both categorical and continuous variables.
method Derive value proposals from the Expected Improvement criterion to optimise both categorical and continuous variables under a single acquisition metric.
result Unified approach significantly outperforms existing methods across mixed-variable tasks.
Paper optimizes battery storage in multiple energy markets for better profits.
problem Optimizing battery storage participation in multiple energy markets to balance supply and demand.
method Developed a joint bidding strategy combining intraday and frequency markets using mixed integer linear programming and a learned classifier strategy.
result The LCS increases overall profits by over 4% compared to static strategies and by more than 3% over a naive dynamic benchmark.
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.
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.
The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO), special cases of this problem that consider fully continuous or fully discrete doma…
Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition f…