Solving Optimization Problems through Fully Convolutional Networks: an Application to the Travelling Salesman Problem

TL;DR

This paper introduces a novel approach using fully convolutional networks to solve the Traveling Salesman Problem by converting it into an image representation, enabling rapid and effective solutions with good generalization.

Contribution

It proposes a new image-based representation for TSP and applies FCNs to learn optimal solutions, demonstrating fast inference and strong generalization across different problem sizes.

Findings

FCN can effectively learn TSP solutions from image representations.

The method achieves millisecond prediction times.

The model generalizes well to TSPs with varying city counts.

Abstract

In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still insufficient. Is there any efficient way to solve certain optimization problem through deep learning? The key is to convert the optimization to a representation suitable for deep learning. In this paper, a traveling salesman problem (TSP) is studied. Considering that deep learning is good at image processing, an image representation method is proposed to transfer a TSP to an image. Based on samples of a 10 city TSP, a fully convolutional network (FCN) is used to learn the mapping from a feasible region to an optimal solution. The training process is analyzed and interpreted through stages. A visualization method is presented to show how a FCN can understand the training task of a TSP. Once the training is completed, no significant effort is required to solve a new TSP and the prediction is obtained on the scale of milliseconds. The results show good performance in finding the global optimal solution. Moreover, the developed FCN model has been demonstrated on TSP's with different city numbers, proving excellent generalization performance.