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.

Meta-solver approaches exploit many individual solvers to potentially build a better solver. To assess the performance of meta-solvers, one can adopt the metrics typically used for individual solvers (e.g., runtime or solution quality) or employ more specific evaluation metrics (e.g., by measuring how close the meta-solver gets to its virtual best performance). In this paper, based on some recently published works, we provide an overview of different performance metrics for evaluating (meta-)solvers by exposing their strengths and weaknesses.

Meta-solver approaches exploits a number of individual solvers to potentially build a better solver. To assess the performance of meta-solvers, one can simply adopt the metrics typically used for individual solvers (e.g., runtime or solution quality), or employ more specific evaluation metrics (e.g., by measuring how close the meta-solver gets to its virtual best performance). In this paper, based on some recently published works, we provide an overview of different performance metrics for evaluating (meta-)solvers, by underlying their strengths and weaknesses.