Should I describe failed iterations in methodology?
I wouldn't outright reject the utility of discussing failed iterations in your thesis. If handled deftly, a discussion of failures could be just as informative as a discussion of your final approach. Far too often, such discussions are omitted from papers owing to lack of space.

Think of it from your reader's point of view. What does s/he stand to gain from reading about failed approaches? If you could provide an analysis of the "nature of problem" and the "ill fitting approach", and put it in a larger perspective, it might help readers avoid repeating your (very tempting) mistakes in their works.