Randomized Local Search vs. NSGA-II vs. Frequency Fitness Assignment on The Traveling Tournament Problem

Cao Xiang, Zhize Wu, Daan van den Berg, Thomas Weise

2024

Abstract

The classical compact double-round robin traveling tournament problem (TTP) asks us to schedule the games of n teams in a tournament such that each team plays against every other team twice, once at home and once away (doubleRoundRobin constraint). The maxStreak constraint prevents teams from having more than three consecutive home or away games. The noRepeat constraint demands that, before two teams can play against each other the second time, they must at least play one other game in between. The goal is to find a game plan observing all of these constraints and having the overall shortest travel length. We define a game-permutation based encoding that allows for representing game plans with arbitrary numbers of constraint violations and tackle the TTP as a bi-objective problem minimizing both the number of constraint violations and the travel length by applying the well-known NSGA-II. We combine both objectives in a lexicographic prioritization scheme and also apply the randomized local search RLS to this single-objective variant of the problem. We realize that Frequency Fitness Assignment (FFA), which makes algorithms invariant under all injective transformations of the objective function value, would also make optimization algorithms invariant under all lexicographic prioritization schemes for multi-objective problems. The FRLS, i.e., the RLS with FFA plugged in, would therefore solve both possible prioritizations of our TTP variants at once. We thus also explore its performance on the TTP. We find that RLS performs surprisingly well and can find game plans without constraint violations reliably until a scale of 36 teams, whereas FRLS and NSGA-II have an advantage on small- and mid-scale problems.

Paper Citation

in Harvard Style

Xiang C., Wu Z., van den Berg D. and Weise T. (2024). Randomized Local Search vs. NSGA-II vs. Frequency Fitness Assignment on The Traveling Tournament Problem. In Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA; ISBN 978-989-758-721-4, SciTePress, pages 38-49. DOI: 10.5220/0012891500003837

in Bibtex Style

@conference{ecta24,
author={Cao Xiang and Zhize Wu and Daan van den Berg and Thomas Weise},
title={Randomized Local Search vs. NSGA-II vs. Frequency Fitness Assignment on The Traveling Tournament Problem},
booktitle={Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA},
year={2024},
pages={38-49},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012891500003837},
isbn={978-989-758-721-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA
TI - Randomized Local Search vs. NSGA-II vs. Frequency Fitness Assignment on The Traveling Tournament Problem
SN - 978-989-758-721-4
AU - Xiang C.
AU - Wu Z.
AU - van den Berg D.
AU - Weise T.
PY - 2024
SP - 38
EP - 49
DO - 10.5220/0012891500003837
PB - SciTePress