GeoHopNet: Hopfield-Augmented Sparse Spatial Attention for Dynamic UAV Site Location Problem

TL;DR

GeoHopNet is a novel neural network model that combines Hopfield memory with sparse spatial attention to efficiently solve large-scale UAV site location problems, outperforming existing methods in speed and solution quality.

Contribution

The paper introduces GeoHopNet, a new attention-based model with Hopfield memory and sparse attention, enabling scalable and efficient solutions for dynamic UAV site location problems.

Findings

Successfully solves large-scale instances with 1,000 nodes in under 0.1 seconds.

Achieves 0.22% optimality gap on large problems, outperforming traditional methods.

Improves solution quality by 22.2% over the state-of-the-art ADNet baseline.

Abstract

The rapid development of urban low-altitude unmanned aerial vehicle (UAV) economy poses new challenges for dynamic site selection of UAV landing points and supply stations. Traditional deep reinforcement learning methods face computational complexity bottlenecks, particularly with standard attention mechanisms, when handling large-scale urban-level location problems. This paper proposes GeoHopNet, a Hopfield-augmented sparse spatial attention network specifically designed for dynamic UAV site location problems. Our approach introduces four core innovations: (1) distance-biased multi-head attention mechanism that explicitly encodes spatial geometric information; (2) K-nearest neighbor sparse attention that reduces computational complexity from $O(N^2)$ to $O(NK)$; (3) a modern Hopfield external memory module; and (4) a memory regularization strategy. Experimental results demonstrate that GeoHopNet extends the boundary of solvable problem sizes. For large-scale instances with 1,000 nodes, where standard attention models become prohibitively slow (over 3 seconds per instance) and traditional solvers fail, GeoHopNet finds high-quality solutions (0.22\% optimality gap) in under 0.1 seconds. Compared to the state-of-the-art ADNet baseline on 100-node instances, our method improves solution quality by 22.2\% and is 1.8$\times$ faster.