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This research advances Transformer-based routing by integrating Relative Positional Encoding directly into the attention mechanism, enabling models to better capture spatial relationships in graph structures like those found in logistics and network optimization. By explicitly modeling pairwise distances between nodes, the approach achieves superior performance on complex combinatorial problems such as the Team Orienteering Problem compared to standard architectures. The findings underscore a critical direction for AI infrastructure: enhancing geometric awareness within deep learning models is essential for scaling solutions to large-scale operational challenges.
Enhancing Transformer-based Routing by Encoding Distance via Relative Positional Encoding
arXiv:2607.18909v1 Announce Type: new Abstract: This paper explores Relative Positional Encoding (RPE) as an additive bias in Transformer architectures to solve the Team Orienteering Problem. By embedding in the attention mechanism pairwise spatial relationships among nodes of the graph that represents the routing problem, the transformer encoder can compute a richer spatial-aware graph embedding that allows the decoder to estimate better routes. Experimental results involving instances up to 100 nodes demonstrate consistent improvements in collected rewards and optimality gaps over vanilla Transformer architectures used by other state-of-the-art works. These findings highlight that explicit relational modeling significantly enhances scalability and generalization for complex combinatorial optimization.
Abstract:This paper explores Relative Positional Encoding (RPE) as an additive bias in Transformer architectures to solve the Team Orienteering Problem. By embedding in the attention mechanism pairwise spatial relationships among nodes of the graph that represents the routing problem, the transformer encoder can compute a richer spatial-aware graph embedding that allows the decoder to estimate better routes. Experimental results involving instances up to 100 nodes demonstrate consistent improvements in collected rewards and optimality gaps over vanilla Transformer architectures used by other state-of-the-art works. These findings highlight that explicit relational modeling significantly enhances scalability and generalization for complex combinatorial optimization.
Artificial Intelligence (cs.AI)
arXiv:2607.18909 [cs.AI]
(or arXiv:2607.18909v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.18909 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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