Title: Rethinking Distance Metric Generalization in Neural Combinatorial Optimization for Vehicle Routing Problems
Primary area: optimization
Keywords: Neural Combinatorial Optimization, Vehicle Routing Problem

Abstract: Neural combinatorial optimization (NCO) has emerged as a promising approach for solving the vehicle routing problem (VRP). However, its ability to generalize across diverse instances is a key challenge for practical applications. Current research on generalization primarily focuses on problem scale and node distribution. The distance metric between nodes, such as 2D Euclidean distance or geographical distance, is also an important characteristic of VRP instances. Unfortunately, existing NCO methods typically use a single distance metric for both training and testing, neglecting the diversity of distance metrics. To fill this gap, this paper systematically investigates the impact of distance metrics. First, we introduce a benchmarking framework that supports multiple distance metrics and evaluates model generalization across them. Experimental results reveal that models trained on instances with a single distance metric perform poorly on instances with different metrics. This suggests that variations in distance metrics pose a significant challenge to model generalization. Second, we examine several training data configurations and find that jointly training on data with diverse distance metrics significantly improves model generalization across different metrics. Moreover, by integrating our proposed method for distance metric generalization with prior advances for problem scale and node distribution generalization, the performance of NCO models on various real-world VRP instances is substantially improved.