DISTANCE VS. COORDINATE: DISTANCE-BASED EM-BEDDING IMPROVES MODEL GENERALIZATION FOR ROUTING PROBLEMS

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 DL 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.

1. INTRODUCTION

Inspired by the success of deep models, such as Transformer (Vaswani et al., 2017) in tackling language tasks and graph neural network (GNN) (Scarselli et al., 2008) in dealing with unstructured data, growing number of researchers have been attracted to explore the potential of deep learning (DL) models in dealing with routing problems, a research direction historically being dominated by operations research (OR) methods for decades. Numerous DL models, which have achieved success in other research areas, are applied to solve traditional routing problems, such as traveling salesman problem (TSP) and vehicle routing problem (VRP). More recently, with the urgent requirements from online logistics service platforms, route prediction has also become an emerging research topic. For example, the platform usually needs to predict and evaluate whether a package is 'distanceconsuming' if it is dispatched to a courier. The predicted route, as well as related route properties, can be used in these evaluations and is vital for improving platform performance. These two kinds of problems, namely route optimization and route prediction, are also the main focus of this paper. Routing problems, to a great extent, can be defined by the properties of route points (or called nodes in some literature) and the relationship among them. In light of this, it is not surprising to understand that route point characterization plays an irreplaceable role in the algorithm design. To the best of our knowledge, almost all existing DL models tend to take the route point coordinates or their corresponding embedding as the model input. With such coordinate information, competitive performance are achieved via numerical experiments, mostly conducted on synthetic data. However, when it comes to the real-world data, we empirically note that the coordinate information turns to be 'poisonous', rather than informative. A DL model which employs the coordinate information often

