Proven optimality of the NL12 instance

Determine a proven optimal solution for the 12-team National League Traveling Tournament Problem instance NL12.

Background

Exact algorithms have established optimal solutions for the principal benchmark instances through ten teams, but larger instances remain unresolved. For NL12, the paper reports a best-known upper bound of 110,729 and a lower bound of 108,629, leaving an approximately two-percent optimality gap. Closing this gap by proving the optimum is identified as a significant milestone.

References

Consequently, we propose the following open problem, whose solution would constitute a significant milestone in the study of the TTP.

\begin{open} Determine a proven optimal solution for the NL12 instance. \end{open}

— The Traveling Tournament Problem: An Overview  (2609.03612 - Bulck et al., 3 Sep 2026) in Section 6, subsection “Exact Methods”