From Global Assessment to Local Selection: Efficiently Solving Traveling Salesman Problems of All Sizes
Keywords: Traveling salesman problem, neural combinatorial optimization, size generalization
Abstract: The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem with broad real-world applications. Recent advancements in neural network-based TSP solvers have shown promising results. Nonetheless, these models often struggle to efficiently solve both small- and large-scale TSPs using the same set of pre-trained model parameters, limiting their practical utility. To address this issue, we introduce a novel neural TSP solver named GELD, built upon our proposed broad global assessment and refined local selection framework. Specifically, GELD integrates a lightweight Global-view Encoder (GE) with a heavyweight Local-view Decoder (LD) to enrich embedding representation while accelerating the decision-making process. Moreover, GE incorporates a novel low-complexity attention mechanism, allowing GELD to achieve low inference latency and scalability to larger-scale TSPs. Additionally, we propose a two-stage training strategy that utilizes training instances of different sizes to bolster GELD's generalization ability. Extensive experiments conducted on both synthetic and real-world datasets demonstrate that GELD outperforms seven state-of-the-art models considering both solution quality and inference speed. Furthermore, GELD can be employed as a post-processing method to exchange affordable computing time for significantly improved solution quality, capable of solving TSPs with up to 744,710 nodes without relying on divide-and-conquer strategies.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 13204
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