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

TL;DR

This work tackles the Diverse TSP by decomposing the problem into two steps: (i) a fast, GPU-accelerated Graph Pointer Network (GPN) samples a large pool of near-optimal tours with an entropy-based loss to balance quality and diversity, and (ii) a greedy dispersion algorithm selects $k$ tours with maximal structural dissimilarity, achieving a 2-approximation for the dispersion step. The framework integrates two tour-construction strategies—diverse traversal of sampled spanning trees and a Christofides-inspired approach with diverse matchings—followed by a principled edge-based greedy selection. Empirical results on TSPLIB show that the approach attains diversity comparable to or better than traditional heuristics while delivering orders-of-magnitude faster inference than prior neural methods, with particularly strong performance on large-scale instances (e.g., rat783). The entropy parameter $\alpha$ provides a controllable trade-off between diversity and solution quality, enabling practical deployment for applications requiring both resilience and near-optimality. Overall, the paper demonstrates a scalable, interpretable neural-heuristic framework that delivers diverse, high-quality TSP tours efficiently for real-world planning and robotics tasks.

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.

Figures (4)

• Figure 1: A counterexample shows that one cannot preserve the dissimilarity when converting spanning trees into tours. (a) and (b) depict two distinct spanning trees sharing exactly one edge(resulting in a near-zero Jaccard index). Despite this minimal overlap, (c) demonstrates that distinct spanning trees can generate the exact same TSP tour via the double-tree heuristic.
• Figure 2: The proposed architecture integrating GPN for spanning tree and perfect matching generation, respectively, followed by a dispersion module for diverse tour selection.
• Figure 3: Overview of the model architecture.
• Figure 4: Performance comparison across different scales. Top row: berlin52; Bottom row: eil101. The left column displays cost distributions, while the right column shows Jaccard index distributions.