基于图神经网络的旅行商问题算法选择：不同预算机制下成本和排序损失的系统研究
Graph Neural Network-based Algorithm Selection for the Traveling Salesman Problem: A Systematic Study of Cost and Rank Losses under Distinct Budget Regimes
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中文总结 AI 辅助
研究旅行商问题的算法选择，提出基于图神经网络的GNNAS - TSP框架，将其作为联合成本预测和排序任务，通过实验评估多种学习目标，在不同预算下所选配置优于单一最佳求解器，证明该框架是有用的元求解策略。
中文摘要 AI 辅助
自动算法选择（AS）旨在通过为每个问题实例从预定义的算法组合中选择最合适的算法来提高问题解决性能，这对于旅行商问题（TSP）尤为重要，因为求解器性能强烈依赖于实例。我们引入了GNNAS - TSP，这是一个基于图神经网络（GNN）的AS框架，它直接从原始图数据学习TSP实例表示，避免手动特征工程。GNNAS - TSP将AS表述为联合成本预测和排序任务。我们评估了基于成本（均方误差（MSE）、平均绝对误差（MAE）和Huber）、基于排序（RankNet、ListNet和LambdaRank）以及混合学习目标，用于包含Chained Lin - Kernighan、Edge Assembly Crossover、Lin - Kernighan - Helsgaun、Multiagent Optimization System和Concorde的算法组合。实验使用10秒和60秒的固定计算预算。在留出的测试集上，所选配置在两个预算下的归一化解成本方面均优于单一最佳求解器（SBS）。对于10秒预算，AS相对于SBS实现了显著且具有统计意义的成本改进。总体而言，结果表明当求解器性能存在可利用的差异时，GNNAS - TSP是一种有用的元求解策略。
英文摘要
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 Chained Lin-Kernighan, Edge Assembly Crossover, Lin-Kernighan-Helsgaun, Multiagent Optimization System, and Concorde. Experiments use fixed computational budgets of 10 and 60 seconds. On the held-out test set, the selected configurations improve on the Single Best Solver (SBS) in normalized solution cost at both budgets. For the 10s budget, AS achieves substantial and statistically significant cost improvement over SBS. Overall, the results suggest that GNNAS-TSP is a useful meta-solving strategy when exploitable variation exists across solver performance.
