Neural Solver Selection for Combinatorial Optimization

TL;DR

This work tackles the uneven strengths of neural COP solvers by introducing an instance-level solver selection framework built from three components: feature extraction to capture instance structure, a selection model to predict solver compatibility, and strategies to balance efficiency and accuracy. It instantiates the framework with diverse solvers for TSP and CVRP, employing graph-attention and hierarchical encoders, and trains with both classification and ranking losses. Empirical results show the framework surpasses the best single solver and approaches Oracle-level performance, with notable generalization to out-of-distribution benchmarks like TSPLIB and CVRPLIB Set-X. The approach is adaptable to other COPs and supports zero-shot generalization to unseen solvers via solver features, offering a practical path to more efficient, ensemble-like neural optimization.

Abstract

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.

Figures (6)

• Figure 1: (a), (b): Observation from the comparison of prevailing neural solvers at instance level. Details of the settings are provided in Section \ref{['settings']}. (c): Our proposed selection framework.
• Figure 2: Illustration of the hierarchical graph encoder.
• Figure 3: Performance of introducing an extra neural solver based on the neural solver feature. The results of top-$k$ selection with and without extra neural solver are presented. The horizontal axis represents the number of selected solvers.
• Figure 4: Comparisons of the proposed top-$k$ selection and the solver portfolio with size $k$.
• Figure 5: Performance of the rejection-based and top-$p$ selection.