arXiv:2604. 23053v2 Announce Type: replace Abstract: Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization.
The paper introduces ReMILP, a reformulation‑contrastive learning framework that uses self‑supervision from equivalent formulations of mixed‑integer linear programs (MILPs). By distinguishing re‑descriptions and substitutions, the method trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables, achieving invariance and equivariance without solver‑derived labels. The learned representations prove useful for tasks such as binary solution, constraint activity, and integrality gap prediction, and serve as a strong initialization for fine‑tuning.
Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making. Owing to their NP-hardness, however, modern solvers may struggle to find high-quality solutions for challenging MILP instances within practical time limits.
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
arXiv:2608. 19953v1 Announce Type: new Abstract: Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making.
arXiv:2607. 22550v1 Announce Type: cross Abstract: We propose a learning-augmented Benders decomposition framework to solve large-scale two-stage stochastic mixed-integer programs.
arXiv:2609.25728v1 Announce Type: new Abstract: Self-supervised learning for combinatorial optimization has emerged as a promising paradigm for solving discrete optimization problems with neural netw...
CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.
arXiv:2606. 13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications.
arXiv:2608. 02343v1 Announce Type: cross Abstract: Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints.
arXiv:2606. 10112v1 Announce Type: cross Abstract: Characterizing revenue-optimal auctions for multi-item, multi-bidder settings remains a fundamental open problem, with no known closed-form solution existing beyond restrictive binary-type instances.
The paper extends Mixed-Integer Differentiable Predictive Control (MI‑DPC) to handle multi‑modal discrete decisions and nonconvex polynomial dynamics in Underground Pumped Hydro Energy Storage Systems (UPHES). It introduces a neural policy that maps problem parameters to continuous setpoints and integer mode selections using a Gumbel‑Softmax layer, trained via self‑supervised differentiation of the finite‑horizon control objective. Key methodological advances include a parallel differentiable simulator, a Transformer encoder for long‑range temporal dependencies, and a Gumbel‑Softmax temperature annealing schedule, enabling the framework to achieve only 1.6% suboptimality compared to a mixed‑integer quadratic programming baseline while providing a five‑order‑of‑magnitude speedup in online scheduling.