Towards Generalizable Meta-Deep Reinforcement Learning Algorithm for Multi-Objective Traveling Salesman Problems

The multi-objective traveling salesman problem (MOTSP) is a representative class of multi-objective combinatorial optimization problems, with significant implications for both theoretical research and practical applications. Although deep reinforcement learning (DRL) has shown promise in solving MOTSPs, existing approaches often struggle with generalization to large-scale problem instances. To address this challenge, we propose a novel meta-deep reinforcement learning framework with preference-fused attention networks (MDRL-PFAN). This framework integrates a preference-fused mechanism to jointly encode problem instances and weight preferences into a unified feature space. Moreover, an ensemble meta-learning strategy is adopted to train the meta-model across tasks with varying scales, equipping MDRL-PFAN with robust solving and strong crossscale generalization capabilities. During inference, a lightweight fine-tuning process on small-batch adaptation tasks is employed to further enhance optimization performance. Extensive experiments on diverse MOTSP instances demonstrate that MDRL-PFAN achieves superior performance compared to classic evolutionary algorithms and state-of-the-art DRL algorithms in terms of training efficiency, solution quality, and cross-scale generalization capability.