Xiaoyu Fu

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.

The multiobjective traveling salesman problem (MOTSP) is a class of classical multiobjective combinatorial optimization problems (MOCOPs), attracting significant interest across various disciplines. Due to the NP-Hard nature, traditional algorithms struggle to find feasible solutions in a short period of time. To this end, this paper proposes a deep reinforcement learning algorithm based on graph weight multi-pointer network (GWMPN), which only needs to perform forward propagation on the GWMPN model to obtain the solution of MOTSP, thus significantly improving the solution efficiency. Specifically, we encode the problem instance and weight vector by means of the graph weight encoder of the GWMPN model to construct the overall encoded feature with enhanced representation capabilities. Subsequently, the encoded feature as the context vector is fed into the multi-pointer decoder to construct solutions through diversity interactions. Experimental results demonstrate that our algorithm solves the MOTSP more rapidly than classical heuristic algorithms and exhibits superior performance and generalization compared with learning-based algorithms within a reasonable time frame.