At least Wikipedia disagrees with your view. https://en.wikipedia.org/wiki/Travelling_salesman_problem#Heuristic_and_approximation_algorithms https://en.wikipe

At least Wikipedia disagrees with your view. https://en.wikipedia.org/wiki/Travelling_salesman_problem#Heuristic_and_approximation_algorithms https://en.wikipedia.org/wiki/Travelling_salesman_problem#He... I'm not confused. For the ACO, Genetic algorithms,... approaches you still need to show that the tour that was found has the lowest possible length... which you cannot without iterating all tours (or doing a branch and bound, which is the same but you prune bad partial tours early). Obviously, people typically work with well known problems where the best tour is already known. They then typically determine the quality of their 'solution' as the relative difference to the best tour in some metric.