Hierarchical Neural Constructive Solver for Real-world TSP Scenarios

TL;DR

This paper introduces a hierarchical neural approach for real-world TSP scenarios, leveraging learnable choice and clustering modules to improve routing efficiency over traditional transformer-based methods.

Contribution

It proposes a novel hierarchical neural solver with learnable choice and clustering modules tailored for realistic TSP scenarios, outperforming existing models.

Findings

Hierarchical approach outperforms classical and transformer models.

Learnable choice layer biases decisions based on current location.

Approximate clustering improves unvisited node management.

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.