arXiv:2601. 04509v2 Announce Type: replace Abstract: Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness.
Mixed-Integer Linear Programming (MILP) is a fundamental optimization paradigm in combinatorial optimization and has been widely applied across real-world domains. Due to its NP-hard nature, obtaining...
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.
The paper introduces SHSP, a Structure-Aware Hierarchical Solution Prediction framework for Mixed-Integer Linear Programming. SHSP replaces one-shot marginal decoding with a hierarchical conditional decoding that sequentially predicts variables based on a coupling graph derived from constraints, and includes a confidence-aware mask-and-repair step to correct errors. Experiments on four MILP benchmarks show SHSP reduces the solution gap by an average of 54% compared to existing one-shot methods.
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
Collab‑Solver introduces a multi‑agent policy learning framework for mixed‑integer linear programming (MILP) that enables collaborative optimization of multiple solver modules. By modeling the interaction between cut selection and branching as a Stackelberg game, the approach employs a two‑phase learning paradigm—data‑communicated policy pretraining followed by coordinated policy refinement. Experiments on synthetic and large‑scale real‑world MILP datasets show that the jointly learned policies markedly improve solving performance and generalize well across diverse instance sets.
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.
The paper introduces TPR-Attention, an attention mechanism that operates over tensor‑product representations to embed structured inductive bias into deep learning models. Experiments on compositional tasks demonstrate that TPR‑Attention outperforms existing architectural components in achieving combinatorial generalization. The results suggest that incorporating explicit compositional structure into neural attention can improve systematic generalization.
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:2608.30103v1 Announce Type: cross Abstract: Bilevel mixed-integer linear optimization problems model hierarchical decision processes in which a leader anticipates the optimal response of a foll...
arXiv:2510. 04567v3 Announce Type: replace-cross Abstract: Graph Neural Networks (GNNs) are powerful tools for processing relational data but often struggle to generalize to unseen graphs, giving rise to the development of Graph Foundational Models (GFMs).
arXiv:2605. 09382v2 Announce Type: replace Abstract: The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness.
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.