Travel-aware feasible neighborhoods for the TTP

Determine whether there exist polynomial-time neighborhoods for the Traveling Tournament Problem that explicitly optimize travel distance or are guaranteed to respect the no-repeater constraint, the at-most constraint, or both.

Background

Existing TTP neighborhoods primarily preserve the round-robin structure and repair feasibility after timetable modifications. The paper identifies a gap in neighborhoods that directly account for travel cost or guarantee preservation of the principal TTP constraints. The unresolved question is whether such polynomial-time neighborhoods can be constructed.

References

\begin{open} \label{open:newN} Do there exist polynomial-time neighborhoods that explicitly optimize for travel distance and/or are guaranteed to respect the no-repeater and/or the at-most constraint? \end{open}

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