Geometry-Aware Reinforcement Learning for 2D Irregular Nesting

arXiv:2606.10611v2 Announce Type: replace 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. In this paper, we argue that Reinforcement Learning is uniquely positioned to overcome this bottleneck. By pairing an optimization policy with a geometry-aware neural encoder, an agent can automatically discover rich geometric priors directly from data, utilizing these learned intuitions to strategically guide exploration. To realize this, we introduce the Polygons Transformer (PoT), a novel architecture that encodes 2D continuous vector geometries while allowing cross-polygon attention. We couple this novel architecture with a Combinatorial Optimization Reinforcement Learning (CORL) training framework to find optimal solutions. To support this paradigm, we release an open-source training dataset derived from complex geographic contours alongside a dedicated evaluation benchmark. Empirically, our agent slightly exceeds Sparrow, the state-of-the-art heuristic, on small (4-polygon) instances, while a clear scaling gap remains on larger (8-polygon) instances.

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. In this paper, we argue that Reinforcement Learning is uniquely positioned to overcome this bottleneck. By pairing an optimization policy with a geometry-aware neural encoder, an agent can automatically discover rich geometric priors directly from data, utilizing these learned intuitions to strategically guide exploration. To realize this, we introduce the Polygons Transformer (PoT), a novel architecture that encodes 2D continuous vector geometries while allowing cross-polygon attention. We couple this novel architecture with a Combinatorial Optimization Reinforcement Learning (CORL) training framework to find optimal solutions. To support this paradigm, we release an open-source training dataset derived from complex geographic contours alongside a dedicated evaluation benchmark. Empirically, our agent slightly exceeds Sparrow, the state-of-the-art heuristic, on small (4-polygon) instances, while a clear scaling gap remains on larger (8-polygon) instances.

20 pages, 6 figures, 7 tables. Under review at the Transaction on Machine Learning Research (TMLR)

Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)

arXiv:2606.10611 [cs.LG]

(or arXiv:2606.10611v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.10611 Focus to learn more arXiv-issued DOI via DataCite

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Geometry-Aware Reinforcement Learning for 2D Irregular Nesting

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