A Generative Graph Method to Solve the Travelling Salesman Problem

TL;DR

This paper introduces a novel generative graph learning approach called GLN for approximately solving the Traveling Salesman Problem, demonstrating promising results in reducing optimality gap and computational effort.

Contribution

The paper presents a new generative graph learning network that directly learns TSP patterns and encodes graph properties for efficient approximate solutions.

Findings

Low optimality gap compared to exact solutions

Significant computational savings

Effective encoding of graph properties

Abstract

The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph Learning Network (GLN), a generative approach, to approximately solve the TSP. GLN model learns directly the pattern of TSP instances as training dataset, encodes the graph properties, and merge the different node embeddings to output node-to-node an optimal tour directly or via graph search technique that validates the final tour. The preliminary results of the proposed novel approach proves its applicability to this challenging problem providing a low optimally gap with significant computation saving compared to the optimal solution.