Survey on Neural Routing Solvers

TL;DR

The heuristic nature of NRSs is highlighted, and existing NRSs are reviewed from the perspective of heuristics, and a hierarchical taxonomy based on heuristic principles is further introduced.

Abstract

Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted counterparts in classic heuristic frameworks, thereby reducing reliance on costly manual design and trial-and-error adjustments. This survey makes two main contributions: (1) The heuristic nature of NRSs is highlighted, and existing NRSs are reviewed from the perspective of heuristics. A hierarchical taxonomy based on heuristic principles is further introduced. (2) A generalization-focused evaluation pipeline is proposed to address limitations of the conventional pipeline. Comparative benchmarking of representative NRSs across both pipelines uncovers a series of previously unreported gaps in current research.

Figures (4)

• Figure 1: Hierarchical structure of the heuristic taxonomy. There are two main heuristic categories: the non-iterative construction-based methods and the iterative improvement-based methods. Construction-based methods can be further divided into single-stage and two-stage methods, based on whether the original graph is decomposed. Improvement-based methods can be further split into single-solution-based and population-based methods, depending on the number of solutions maintained during the improvement process.
• Figure 2: Hierarchical structure of the proposed NRS taxonomy. Each subcategory is presented with the proportion of existing studies. The statistics are obtained from Google Scholar between January 1, 2015, and November 17, 2025. The paper list is further filtered by content relevance and supplemented with relevant experience. Finally, there are a total of 439 papers, including 344 methods across various categories, as well as other related studies such as surveys and benchmarks. Note that an NRS may contribute to the counts of multiple subcategories, due to the adoption of multiple inference strategies.
• Figure 3: Illustration of subcategories of single-stage methods. (a) For appending methods, the selected nodes are linked to the end of partial solutions one at a time. (b) For insertion methods, the positions are not limited.
• Figure 4: Illustration of subcategories of single-solution-based methods. (a) For small neighborhood methods, an example with the 2-opt operator is presented. At each iteration, two edges are replaced. (b) For large neighborhood methods, the classic destroy-and-repair process is illustrated. At each iteration, some nodes are picked out and then reinserted one by one in a prescribed order (indicated by the numbered labels).