Graph Neural Network-based Algorithm Selection for the Traveling Salesman Problem: A Systematic Study of Cost and Rank Losses under Distinct Budget Regimes

תקציר מקורי באנגליתarXiv:2607.18632v1 Announce Type: new Abstract: Automated Algorithm Selection (AS) aims to improve problem-solving performance by selecting, for each problem instance, the most suitable algorithm from a predefined portfolio. This is particularly relevant to the Traveling Salesman Problem (TSP), where solver performance is strongly instance-dependent. We introduce GNNAS-TSP, a Graph Neural Network (GNN)-based AS framework that learns TSP instance representations directly from raw graph data, avoiding manual feature engineering. GNNAS-TSP formulates AS as a joint cost-prediction and ranking task. We evaluate cost-based (mean squared error (MSE), mean absolute error (MAE), and Huber), rank-based (RankNet, ListNet, and LambdaRank), and hybrid learning objectives for a portfolio comprising Chai