  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.
