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.
By Zherong Zhang, Guanlin Li, Chengrui Gao, Haopu Shang, Ke Xue, Jixiang Lu, Weiyong Yang, Chao Qian
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.
By Ousema Bouaneni, Mathis Le Bail, Cl\'ement Elliker, Ma\"el Jenny, Sonia Vanier
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
By Zohair Shafi, Serdar Kadioglu
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
The paper introduces a novel end‑to‑end, size‑agnostic graph reinforcement learning framework for the one‑dimensional bin packing problem (1D‑BPP). It models packing as a Markov decision process on an item‑compatibility graph, where a graph neural network actor‑critic policy learns to merge compatible partial bins. Empirical results on the BPPLIB benchmark show that the learned policy reduces the mean optimality gap of a constructive heuristic from 2.66 % to 2.31 %, performs competitively against other learned methods, and outperforms a state‑of‑the‑art learned solver on the hardest benchmark family.
By M. Asl{\i} Ayd{\i}n
EnerGNN is a framework that learns energy functions over complete binary configurations and performs exact constrained inference via mixed integer programming. It combines a graph neural network encoder, an optimization‑compatible readout, and a nonlinear energy head, and is trained with an optimality‑aware contrastive loss to reflect solution quality and constraint violations. In experiments on Quadratic Knapsack, Combinatorial Auctions, and a personalized cell therapy supply chain problem, EnerGNN achieves near‑optimal solutions with 100% feasibility, a 0.05% mean primal gap, and a 17.4× speedup over a monolithic MIP, while also generalizing to larger instances and supporting zero‑shot constraint injection.
By Niki Triantafyllou, Maria M. Papathanasiou
arXiv:2602.13106v2 Announce Type: replace-cross
Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...
By Solveig Wittig, Antonis Vasileiou, Robert R. Nerem, Timo Stoll, Floris Geerts, Yusu Wang, Christopher Morris
arXiv:2512.20270v2 Announce Type: replace-cross
Abstract: Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. T...
By Matthias K. Hoffmann, Amine Othmane, Kathrin Fla{\ss}kamp
arXiv:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.
By Noah Schwartz, Chandra Kanth Nagesh, Sriram Sankaranarayanan, Ramneet Kaur, Tuhin Sahai, Susmit Jha
arXiv:2606. 01425v1 Announce Type: new Abstract: Mixed-combinatorial nonlinear programming (MCNLP) problems arise in many engineering design and planning applications, e.
By Gishnu Madhu, Feng Liu, Souma Chowdhury
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.