Deep Learning as a Competitive Feature-Free Approach for Automated Algorithm Selection on the Traveling Salesperson Problem

TL;DR

This paper investigates the use of deep learning as a feature-free method for algorithm selection on the Euclidean TSP, demonstrating that visual representations can match traditional feature-based models in predicting solver performance.

Contribution

It introduces a deep neural network approach that relies solely on visual representations of TSP instances, outperforming feature-based models and showing promise for future research.

Findings

Feature-based models outperform single solvers but are still far from the virtual best.

Deep learning with visual inputs matches classical feature-based algorithm selection results.

Visual representations have significant potential for future TSP algorithm selection methods.

Abstract

In this work we focus on the well-known Euclidean Traveling Salesperson Problem (TSP) and two highly competitive inexact heuristic TSP solvers, EAX and LKH, in the context of per-instance algorithm selection (AS). We evolve instances with 1,000 nodes where the solvers show strongly different performance profiles. These instances serve as a basis for an exploratory study on the identification of well-discriminating problem characteristics (features). Our results in a nutshell: we show that even though (1) promising features exist, (2) these are in line with previous results from the literature, and (3) models trained with these features are more accurate than models adopting sophisticated feature selection methods, the advantage is not close to the virtual best solver in terms of penalized average runtime and so is the performance gain over the single best solver. However, we show that a feature-free deep neural network based approach solely based on visual representation of the instances already matches classical AS model results and thus shows huge potential for future studies.