Although several surveys on Neural Combinatorial Optimization (NCO) solvers specifically designed to solve Vehicle Routing Problems (VRPs) have been conducted. These existing surveys did not cover the state-of-the-art (SOTA) NCO solvers emerged recently. More importantly, to provide a comprehensive taxonomy of NCO solvers with up-to-date coverage, based on our thorough review of relevant publications and preprints, we divide all NCO solvers into four distinct categories, namely Learning to Construct, Learning to Improve, Learning to Predict-Once, and Learning to Predict-Multiplicity solvers. Subsequently, we present the inadequacies of the SOTA solvers, including poor generalization, incapability to solve large-scale VRPs, inability to address most types of VRP variants simultaneously, and difficulty in comparing these NCO solvers with the conventional Operations Research algorithms. Simultaneously, we propose promising and viable directions to overcome these inadequacies. In addition, we compare the performance of representative NCO solvers from the Reinforcement, Supervised, and Unsupervised Learning paradigms across both small- and large-scale VRPs. Finally, following the proposed taxonomy, we provide an accompanying web page as a live repository for NCO solvers. Through this survey and the live repository, we hope to make the research community of NCO solvers for VRPs more thriving.

Deep reinforcement learning offers notable benefits in addressing combinatorial problems over traditional solvers, reducing the reliance on domain-specific knowledge and expert solutions, and improving computational efficiency. Despite the recent surge in interest in neural combinatorial optimization, practitioners often do not have access to a standardized code base. Moreover, different algorithms are frequently based on fragmentized implementations that hinder reproducibility and fair comparison. To address these challenges, we introduce RL4CO, a unified Reinforcement Learning (RL) for Combinatorial Optimization (CO) library. We employ state-of-the-art software and best practices in implementation, such as modularity and configuration management, to be flexible, easily modifiable, and extensible by researchers. Thanks to our unified codebase, we benchmark baseline RL solvers with different evaluation schemes on zero-shot performance, generalization, and adaptability on diverse tasks. Notably, we find that some recent methods may fall behind their predecessors depending on the evaluation settings. We hope RL4CO will encourage the exploration of novel solutions to complex real-world tasks, allowing the community to compare with existing methods through a unified framework that decouples the science from software engineering. We open-source our library at https://github.com/ai4co/rl4co.