Branch and Bound (B&B) is the exact tree search method typically used to solve Mixed-Integer Linear Programming problems (MILPs). Learning branching policies for MILP has become an active research area, with most works proposing to imitate the strong branching rule and specialize it to distinct classes of problems. We …
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32 results for “MILP”
ReLU networks trained with MILPs match deep learning accuracy.
problem Training deep neural networks efficiently.
method Iterative training with Mixed Integer Linear Programs (MILPs).
result ReLU networks can be trained with MILPs achieving similar accuracy to deep learning methods.
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.
Binarized Neural Networks (BNNs) have recently attracted significant interest due to their computational efficiency. Concurrently, it has been shown that neural networks may be overly sensitive to "attacks" - tiny adversarial changes in the input - which may be detrimental to their use in safety-critical domains. Desig…
Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimizationmath.OC
Plain vanilla K-means clustering has proven to be successful in practice, yet it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outl…
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.
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.
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.
Algorithm finds near-optimal VaR portfolios using MILP, improving risk management.
problem Computing optimal VaR portfolios is hard due to non-convexity and combinatorial nature.
method Formulates VaR portfolio problem as MILP, uses alternate formulations for guarantees.
result Near-optimal VaR portfolios with near-optimality guarantees.
The paper verifies the robustness of classifier ensembles against randomized attacks.
problem Ensuring classifier ensembles are robust against arbitrary randomized attacks.
method Formal verification procedure using SMT and MILP encodings to assess robustness.
result Proves the NP-hardness of the robustness-checking problem and provides upper bounds on attack sets.
Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspectiveq-fin.PM
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.
We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However, enumerating these regions is prohibitive and the known analytical bounds are identical for…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct problem for which one looks for a (non-necessarily contiguous) rectangular sub-matrix…
Glitches cause unreliable AI decisions with steep boundaries.
problem Glitches impair the reliability of AI models with steep decision boundaries.
method Formal definition of glitches, algorithmic search using MILP encoding.
result Glitches are widespread and indicate potential model inconsistencies.
We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existin…
We address the problem of verifying neural-based perception systems implemented by convolutional neural networks. We define a notion of local robustness based on affine and photometric transformations. We show the notion cannot be captured by previously employed notions of robustness. The method proposed is based on re…
Efficiently computes quasiconcave envelope with limited data.
problem Approximating unknown quasiconcave function with partial information.
method Solves value problem and interpolation problem with polynomial and logarithmic LPs.
result Efficiently computes quasiconcave envelope with limited data.
New framework detects model weaknesses in decision tree ensembles.
problem Detecting feature sensitivity in decision tree ensembles.
method Data-aware sensitivity framework using MILP and SMT.
result Realistic and interpretable examples of model weaknesses.
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.
This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by including a budget constraint that sets in advance a limit on the number of features …
We formalize the problem of trading-off DNN training time and memory requirements as the tensor rematerialization optimization problem, a generalization of prior checkpointing strategies. We introduce Checkmate, a system that solves for optimal rematerialization schedules in reasonable times (under an hour) using off-t…
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.
Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work…
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.
Introduces CCR for constructing confidence regions from conformal predictions.
problem Challenges in constructing confidence regions for model parameters.
method Combines conformal prediction intervals for model outputs to establish confidence regions for parameters under minimal assumptions.
result Valid coverage guarantees for finite sample regime, applicable to various model types.
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.
POET enables large neural network training on tiny devices with reduced energy.
problem Training large neural networks on memory-limited edge devices.
method Jointly optimizes rematerialization and paging for memory reduction, formulating an MILP for energy-efficient training.
result POET trains ResNet-18 and BERT within Cortex-M memory constraints, outperforming current methods in energy efficiency.
New method closes certification gap for adversarially trained models.
problem Certifying robustness of adversarially trained neural networks.
method Nonconvex low-rank SDP relaxation with polynomial-time optimization.
result Strong certifications comparable to SDP methods, but with fewer variables.
Paper proposes a network framework for prosumers to manage peak loads in Iran.
problem Balancing renewable prosumers' self-sufficiency with grid integration under uncertainty.
method Distributed contextual stochastic optimization (DCSO) framework with consensus-based sharing.
result Integration of prediction and optimization reduces peak loads and costs.
Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identificationstat.ML
Optimal design for multinomial logit models improves assortment selection efficiency.
problem Optimal experimental design for multinomial logit models with feedback.
method Two complementary approaches: MILP reformulation and lifted design.
result Achieves statistical efficiency and scalability for MNL bandits.
Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACV…
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.