Generating Diverse TSP Tours via a Combination of Graph Pointer Network and Dispersion

Abstract

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.