We address the Diverse Traveling Salesman Problem (D-TSP), a bi-criteria optimization challenge that seeks a set of $k$ distinct TSP tours. The objective requires every selected tour to have a length at most $c|T^*|$ (where $|T^*|$ is the optimal tour length) while minimizing the average Jaccard similarity across all tour pairs. This formulation is crucial for applications requiring both high solution quality and fault tolerance, such as logistics planning, robotics pathfinding or strategic patrolling. Current methods are limited: traditional heuristics, such as the Niching Memetic Algorithm (NMA) or bi-criteria optimization, incur high computational complexity $O(n^3)$, while modern neural approaches (e.g., RF-MA3S) achieve limited diversity quality and rely on complex, external mechanisms. To overcome these limitations, we propose a novel hybrid framework that decomposes D-TSP into two efficient steps. First, we utilize a simple Graph Pointer Network (GPN), augmented with an approximated sequence entropy loss, to efficiently sample a large, diverse pool of high-quality tours. This simple modification effectively controls the quality-diversity trade-off without complex external mechanisms. Second, we apply a greedy algorithm that yields a 2-approximation for the dispersion problem to select the final $k$ maximally diverse tours from the generated pool. Our results demonstrate state-of-the-art performance. On the Berlin instance, our model achieves an average Jaccard index of $0.015$, significantly outperforming NMA ($0.081$) and RF-MA3S. By leveraging GPU acceleration, our GPN structure achieves a near-linear empirical runtime growth of $O(n)$. While maintaining solution diversity comparable to complex bi-criteria algorithms, our approach is over 360 times faster on large-scale instances (783 cities), delivering high-quality TSP solutions with unprecedented efficiency and simplicity.

翻译：本文针对多样化旅行商问题（D-TSP）这一双目标优化挑战，该问题旨在寻找一组$k$条不同的TSP路径。目标要求每条被选路径的长度不超过$c|T^*|$（其中$|T^*|$为最优路径长度），同时最小化所有路径对之间的平均Jaccard相似度。该问题表述对于需要兼顾解决方案质量与容错性的应用场景至关重要，例如物流规划、机器人路径寻优或战略巡逻。现有方法存在局限：传统启发式算法（如小生境模因算法NMA或双目标优化）具有高达$O(n^3)$的计算复杂度，而现代神经方法（如RF-MA3S）则存在多样性质量有限且依赖复杂外部机制的问题。为突破这些限制，我们提出一种新颖的混合框架，将D-TSP分解为两个高效步骤。首先，我们采用增强近似序列熵损失的简易图指针网络（GPN），高效采样大规模高质量路径池。这种简易改进能有效控制质量-多样性权衡，无需复杂的外部机制。其次，我们应用针对分散化问题具有2-近似保证的贪心算法，从生成的路径池中选取最终$k$条最大化多样性路径。实验结果表明我们的方法达到最先进性能：在柏林算例中，模型获得的平均Jaccard指数为$0.015$，显著优于NMA（$0.081$）和RF-MA3S。通过GPU加速，我们的GPN结构实现了接近线性的$O(n)$经验运行时增长。在保持与复杂双目标算法相当的解决方案多样性的同时，本方法在大规模算例（783个城市）上的运行速度提升超过360倍，以前所未有的效率与简洁性提供高质量的TSP解决方案。