Authors:
Cao Xiang
1
;
Zhize Wu
1
;
Daan van den Berg
2
and
Thomas Weise
1
Affiliations:
1
Institute of Applied Optimization, School of Artificial Intelligence and Big Data, Hefei University, Jinxiu Dadao 99, Hefei, 230601, Anhui, China
;
2
Department of Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1111, Amsterdam, 1081 HV, The Netherlands
Keyword(s):
Traveling Tournament Problem, NSGA-II, Randomized Local Search, Frequency Fitness Assignment.
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.
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