Neural Solver Selection for Combinatorial Optimization
This addresses the challenge of complementary performance among neural solvers for NP-hard problems like TSP and CVRP, offering a practical improvement for researchers and practitioners in optimization.
The paper tackles the problem of selecting the best neural solver for each instance in combinatorial optimization, proposing a coordination framework that reduces the optimality gap by 0.88% on TSPLIB and 0.71% on CVRPLIB compared to the best individual solver.
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.