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
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
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...
By Jessica D. Elrefaei, Kaixun Hua, Seungbae Kim, Hoang Nam Tran, Juan S. Borrero
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
The paper introduces Variational Graph-to-Scheduler (VG2S), a framework that applies variational inference to the Job Shop Scheduling Problem (JSSP). By decoupling representation learning from policy optimization using a variational graph encoder and an ELBO-based objective, VG2S improves training stability and robustness to hyperparameter changes. Experiments show that VG2S outperforms state‑of‑the‑art deep reinforcement learning baselines and traditional dispatching rules, especially on large‑scale benchmark instances such as DMU and SWV.
By Seung Heon Oh, Jiwon Baek, Hyunjin Oh, Kiyoung Cho, Heechang Yoon, Jong Hun Woo
arXiv:2606. 06300v1 Announce Type: new Abstract: We propose MResOpt, a staged residual neural network architecture for constrained optimization problems.
By Merve Karakas, Christopher J. Williams, Emmanuel O. Balogun, Sadegh Sadeghi Tabas, Christian Brown, Nikhil Rao
arXiv:2410. 04818v2 Announce Type: replace-cross Abstract: We present PINCO, an unsupervised learning framework that integrates Graph Neural Networks with physics-informed neural networks for AC optimal power flow (AC-OPF) solutions.
By Anna Varbella, Damien Briens, Blazhe Gjorgiev, Giuseppe Alessio D'Inverno, Priya L. Donti, Giovanni Sansavini
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...
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
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
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
By Zohair Shafi, Serdar Kadioglu
The paper introduces a fully differentiable message‑passing neural network (MPNN) designed to approximate the Uniform Facility Location (UniFL) problem. Unlike many learning‑based approaches that require supervision or reinforcement learning, this model incorporates principles from classical approximation algorithms, providing provable approximation guarantees. Empirical results show that it outperforms standard approximation algorithms and reduces the performance gap to integer linear programming solutions.
By Chendi Qian, Christopher Morris, Stefanie Jegelka, Christian Sohler