GNNAS-TSP Selects Optimal Algorithms for Traveling Salesman Problem

A new framework called GNNAS-TSP has been developed to automate the selection of the most suitable algorithm for solving the Traveling Salesman Problem (TSP). The performance of TSP solvers varies significantly depending on the specific problem instance, making automated selection a valuable tool. GNNAS-TSP leverages Graph Neural Networks (GNNs) to directly learn representations of TSP instances from their raw graph data, thereby eliminating the need for laborious manual feature engineering. The framework approaches algorithm selection as a dual task: predicting the solution cost and ranking potential algorithms. It was evaluated using various learning objectives, including cost-based (MSE, MAE, Huber) and rank-based (RankNet, ListNet, LambdaRank) methods, as well as hybrid approaches. The portfolio of solvers included well-known algorithms like Chained Lin-Kernighan, Edge Assembly Crossover, Lin-Kernighan-Helsgaun, Multiagent Optimization System, and Concorde. Experiments conducted with fixed computational budgets of 10 and 60 seconds demonstrated that GNNAS-TSP consistently improved normalized solution costs on a held-out test set compared to the Single Best Solver (SBS). Notably, for the 10-second budget, the cost improvement was substantial and statistically significant. These findings suggest that GNNAS-TSP is an effective meta-solving strategy, particularly when there is considerable performance variation among available solvers.