I have now completed my implementation of the ascent and the branch and bound method detailed in the 1970 paper The Traveling-Salesman Problem and Minimum Spanning Trees by Micheal Held and Richard M. Karp.
In my last post, titled Understanding the Ascent Method, I completed the first iteration of the ascent method and found an important bug in the find_epsilon() method and found a more efficient way to determine substitutes in the graph.
However the solution being given was still not the optimal solution.
This is a companion discussion topic for the original entry at https://blog.scientific-python.org/networkx/atsp/implementing-the-held-karp-relaxation