Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey With Perspectives

Although several surveys on neural combinatorial optimization (NCO) solvers specifically designed to solve vehicle routing problems (VRPs) have been conducted, they did not cover the state-of-the-art (SOTA) NCO solvers emerged recently. More importantly, to establish a comprehensive and up-to-date taxonomy of NCO solvers, we systematically review relevant publications and preprints, categorizing them into four distinct types, namely learning to construct (L2C), learning to improve (L2I), learning to predict (L2P)-once, and L2P-multiplicity (L2P-M) 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 (OR) algorithms. Simultaneously, we discuss ongoing efforts, identify open inadequacies, and propose promising and viable directions to overcome these inadequacies. Notably, existing efforts focus on only one or two of these inadequacies, with none attempting to address all of them concurrently. In addition, we compare the performance of representative NCO solvers from the reinforcement, supervised, and unsupervised learning (UL) paradigms across VRPs of varying scales. 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 aim to foster further advancements in the NCO community.