I am trying to learn about neural networks. I was reading the paper An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem which uses graph neural networks such that given a graph we get a hamiltonian cycle which hopefully is nearly optimal. However, they use as ground truth the concorde algorithm, which when I ask google and chat-GPT seems seem to be an exact algorithm but in section E (solution visualization), there are some cases where the author say :
The model predicts a shorter tour than Concorde for this instance by choosing a different contour around the nodes at the top-left of the graph
But how can it be better? Doesn't concord compute the optimal solution already? Did I get something wrong about the traveling salesman problem?