Novel neighborhood structures for incomplete round robin sports tournaments

TL;DR

This paper introduces two novel neighborhood structures for scheduling incomplete round robin sports tournaments, improving solution quality through an adaptive hill climbing algorithm.

Contribution

It proposes new graph-theoretic neighborhood structures for incomplete tournaments and demonstrates their effectiveness in optimizing tournament schedules.

Findings

The neighborhoods enable high-quality solutions for various instances.

One neighborhood fully connects the solution space, enhancing search effectiveness.

The proposed algorithm finds new best solutions in literature instances.

Abstract

The incomplete round robin sports tournament format, where each team plays the same number of games but faces only a subset of the other teams, is becoming increasingly popular in both youth and professional competitions. In contrast to conventional round robin tournaments, however, neighborhood structures for scheduling incomplete round robin tournaments have largely remained unexplored. We fill this gap by proposing two novel neighborhood structures and describe them in graph theory terms. One of them introduces a single new game followed by a minimal repair chain, while the other introduces possibly many new games but only affects a single round. The latter is shown to fully connect the solution space. We embed the neighborhoods in an adaptive late acceptance hill climbing algorithm and show that the proposed algorithm obtains high quality and new best solutions for several sets of instances from the literature, thereby empirically confirming the effectiveness of the proposed neighborhoods.