Deep Learning as a Competitive Feature-Free Approach for Automated Algorithm Selection on the Traveling Salesperson Problem
This work addresses algorithm selection for TSP solvers, offering an incremental improvement by demonstrating that feature-free deep learning can compete with traditional feature-based methods in this domain.
The study tackled the per-instance algorithm selection problem for the Euclidean Traveling Salesperson Problem (TSP) by comparing feature-based models with a feature-free deep learning approach using visual representations. The result showed that the deep neural network matched classical model performance, indicating potential for future research, though it did not achieve the virtual best solver's performance in terms of penalized average runtime.
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.