Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To date, the community has created numerous open-source neural solvers with distinct motivations and inductive biases. While considerable efforts are devoted to designing powerful single solvers, our findings reveal that existing solvers typically demonstrate complementary performance across different problem instances. This suggests that significant improvements could be achieved through effective coordination of neural solvers at the instance level. In this work, we propose the first general framework to coordinate the neural solvers, which involves feature extraction, selection model, and selection strategy, aiming to allocate each instance to the most suitable solvers. To instantiate, we collect several typical neural solvers with state-of-the-art performance as alternatives, and explore various methods for each component of the framework. We evaluated our framework on two extensively studied combinatorial optimization problems, Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP). Experimental results show that the proposed framework can effectively distribute instances and the resulting composite solver can achieve significantly better performance (e.g., reduce the optimality gap by 0.88\% on TSPLIB and 0.71\% on CVRPLIB) than the best individual neural solver with little extra time cost.

本研究解决了当前神经求解器在组合优化问题中利用效率不足的难题。我们提出了一种新的协调神经求解器的通用框架，旨在根据实例将其分配给最适合的求解器。实验结果表明，该框架显著提高了求解性能，并在多个优化问题上实现了显著的改进。 

组合优化的神经求解器选择