Distance VS. Coordinate: Distance Based Embedding Improves Model Generalization for Routing Problems

Hongsen Liao, Ruiyuan Wu, Yuyang Han, Yuncong Hu, Ke Xing, Jinghua Hao, Renqing He

Keywords: routing problems, travelling salesman problem, combinatorial optimization, pickup and delivery, embedding

TL;DR: Distance based embedding is a better choice for routing problems, compared to coordinate based embedding.

Abstract: Routing problems, such as traveling salesman problem (TSP) and vehicle routing problem, are among the most classic research topics in combinatorial optimization and operations research (OR). In recent years, with the rapid development of online service platforms, there has been renewed interest in applying this study to facilitate emerging industrial applications, such as food delivery and logistics services. While OR methods remain the mainstream technique, increasing efforts have been put into exploiting deep learning (DL) models for tackling routing problems. The existing ML methods often consider the embedding of the route point coordinate as a key model input and are capable of delivering competing performance in synthetic or simplified settings. However, it is empirically noted that this line of work appears to lack robustness and generalization ability that are crucial for real-world applications. In this paper, we demonstrate that the coordinate can unexpectedly lead to these problems. There are two factors that make coordinate rather `poisonous' for DL models: i) the definition of distance between route points is far more complex than what coordinate can depict; ii) the coordinate can hardly be sufficiently `traversed' by the training data. To circumvent these limitations, we propose to abandon the coordinate and instead use the relative distance for route point embedding. We show in both synthetic TSP and real-world food pickup and delivery route prediction problem that our design can significantly improve model's generalization ability, and deliver competitive or better performance with existing models.

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