Learning-based Neural Combinatorial Optimization (NCO) is an emerging paradigm for various vehicle/robot routing problems. It transitions solution strategies from manual heuristics to data-driven learning. This paper presents a systematic survey of deep learning-based approaches for route optimization. We first unify classical routing models and formulate reinforcement learning methods within a Markov Decision Process (MDP) framework. Existing literature is primarily classified into two categories: (1) end-to-end neural solvers, encompassing constructive and improvement-based methods, constraint-handling techniques, and various encoder–decoder or generative training schemes; and (2) scalability-oriented solvers, which leverage divide-and-conquer strategies to address large-scale routing problems. Finally, we discuss vital future research directions, including the integration of heuristic knowledge into NCO, large-scale multi-objective optimization, and automated modeling/solving. This survey offers a structured taxonomy of learning-based route optimization methods and discusses the potential for extending them to a broader class of combinatorial optimization problems.
Jun Li (Thu,) studied this question.