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:2504. 16595v2 Announce Type: replace-cross Abstract: Packing objects efficiently is a fundamental problem in logistics, warehouse automation, and robotics.
By Gojko Perovic, Nuno Ferreira Duarte, Atabak Dehban, Gon\c{c}alo Teixeira, Egidio Falotico, Jos\'e Santos-Victor
arXiv:2510. 10057v2 Announce Type: replace Abstract: The three-dimensional bin packing problem (3D-BPP) is widely applied in logistics and warehousing.
By Lei Gao, Shihong Huang, Shengjie Wang, Hong Ma, Feng Zhang, Hengda Bao, Qichang Chen, Weihua Zhou
arXiv:2606. 10611v1 Announce Type: new Abstract: Traditional heuristic solvers for the 2D irregular nesting problem share a fundamental limitation: they are blind to polygon geometry, relying on guided brute-force to navigate the continuous placement space with minimal geometrical guidance.
By Auguste Lehuger, Guillaume Henon-Just
arXiv:2606. 26399v1 Announce Type: new Abstract: We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints.
By Luoning Zhang, Xu Zhuang, Tianhao Wang, Nathan Kaplan
We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits.
Traditional heuristic solvers for the 2D irregular nesting problem share a fundamental limitation: they are blind to polygon geometry, relying on guided brute-force to navigate the continuous placement space with minimal geometrical guidance. In this paper, we argue that Reinforcement Learning is uniquely positioned to overcome this bottleneck.
GeoPAR is a geometry-guided parallel autoregressive reinforcement learning framework designed for large-scale multi-agent combinatorial optimization. It introduces a projection-window sparse geometry mechanism, sparse edge-biased attention, and cache-guided conflict-aware assignment to better model local geometric structures and reduce duplicate task selections. Experiments on heterogeneous vehicle routing and multi-depot pickup-and-delivery problems demonstrate improved zero-shot generalization, fewer rollout steps, and efficient inference.
By Wenjian Wu, Zesheng Jia, Jiaying Tang, Benyuan Yang, Jin Wang
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
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.
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
arXiv:2605. 19748v2 Announce Type: replace Abstract: Automatic generation of computer-aided design (CAD) models is a core technology for enabling intelligence in advanced manufacturing.
By Yin Xiaolong, Liu Yu, Shen Jiahang, Lu Xingyu, Ni Jingzhe, Fan Fengxiao, Sang Fan