Rethinking Supervised Learning-Based Neural Combinatorial Optimization for Routing Problem

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving complex combinatorial optimization problems such as the traveling salesman problem (TSP), the vehicle routing problem (VRP), and the orienteering problem (OP). However, how to efficiently train a powerful NCO solver for routing problems remains a crucial challenge. The widely used reinforcement learning method suffers from sparse rewards and low data efficiency, while the supervised learning approach requires a large number of high-quality solutions (i.e., labels) that could be costly to obtain. In this work, we find that simple data augmentation operations can drastically reduce the number of required high-quality solutions for supervised learning. Moreover, simple boosting strategies that leverage the property of multiple optima can significantly improve training efficiency. With only a small set of \(50{,}000\) labeled instances, supervised learning can achieve a competitive in-distribution performance with the widely used reinforcement learning counterpart. Furthermore, we also investigate the generalization ability for larger out-of-distribution problems. We believe the findings from this work may lead to a rethinking of the value of data-efficient supervised learning for NCO solver training.