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...
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
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: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.
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.
By Guanlin Li, Chengrui Gao, Chenguang Wang, Haopu Shang, Zherong Zhang, Ke Xue, Jixiang Lu, Weiyong Yang, Chao Qian
The paper proposes that Learning-to-Optimize (L2O) should serve as a missing architectural layer in AI-native communication networks, bridging optimisation and AI intelligence. It redefines optimisation algorithms as offline knowledge generators that produce supervisory data for neural surrogate models, enabling low‑latency inference in dynamic environments. A four‑stage workflow—optimisation, knowledge generation, surrogate learning, and runtime inference—is introduced, and demonstrated on an NR‑V2X relay‑selection problem where a Graph Neural Network learns near‑optimal decisions from MILP solutions.
By Giambattista Amati, Federica Mangiatordi, Pierpaolo Salvo, Emiliano Pallotti, Simone Angelini
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.
By Youcef Magnouche, Abderrahmane Driouch, S\'ebastien Martin, Pierre Bauguion
arXiv:2608. 02343v1 Announce Type: cross Abstract: Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints.
By Patrick Helm, Jan-Niklas Doerr, Joren Gijsbrechts, Stefan Minner