Hierarchical Neural Constructive Solver for Real-world TSP Scenarios

TL;DR

The paper addresses the gap between neural TSP solvers trained on synthetic random instances and real world routing scenarios by introducing a realistic data generation scheme and a dual architectural strategy. It combines a locality aware hypernetwork based Choice Decoder with an EM inspired soft clustering to form a hierarchical decoder that effectively models both nearby decisions and structured unvisited city representations. Empirical results across uniform and realistic distributions, and even PCB3038, show consistent improvements over state of the art baselines such as POMO, Sym-NCO, and ELG, particularly in realistic maps. The work advances practical neural solvers for TSP by explicitly leveraging locality and problem structure, and it suggests that these components can be integrated with existing models to further boost performance in industrial routing tasks.

Abstract

Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been demonstrated on entirely random problem instances that inadequately capture real-world scenarios. In this paper, we introduce realistic Traveling Salesman Problem (TSP) scenarios relevant to industrial settings and derive the following insights: (1) The optimal next node (or city) to visit often lies within proximity to the current node, suggesting the potential benefits of biasing choices based on current locations. (2) Effectively solving the TSP requires robust tracking of unvisited nodes and warrants succinct grouping strategies. Building upon these insights, we propose integrating a learnable choice layer inspired by Hypernetworks to prioritize choices based on the current location, and a learnable approximate clustering algorithm inspired by the Expectation-Maximization algorithm to facilitate grouping the unvisited cities. Together, these two contributions form a hierarchical approach towards solving the realistic TSP by considering both immediate local neighbourhoods and learning an intermediate set of node representations. Our hierarchical approach yields superior performance compared to both classical and recent transformer models, showcasing the efficacy of the key designs.

Figures (7)

• Figure 1: Comparing subset of TSP drawn from USA map (first row) against a uniform distribution (second row). Left-most plots show the base distribution. The subsets follow certain underlying structures for the USA case compared to completely random problems.
• Figure 2: POMO model making a minor mistake with a poor selection of a local node
• Figure 3: POMO model making a major mistake by not visiting nodes that are near it, causing cross-cluster routes that are inefficient
• Figure 4: Overview of our proposed architecture. Given a TSP instance, we learn contextual embeddings of the cities in a set of cluster representations with an EM-inspired differentiable technique. In addition, our policy is dynamically adapted with a local hypernetwork which emphasises the completion of local cluster before moving on to new distant cities.
• Figure 5: World maps used for experiments