The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound

The Traveling Tournament Problem is a well-known benchmark problem in tournament timetabling, which asks us to design a schedule of home/away games of n teams (n is even) under some feasibility requirements such that the total traveling distance of all the n teams is minimized. In this paper, we study TTP-2, the traveling tournament problem where at most two consecutive home games or away games are allowed, and give an effective algorithm for n/2 being odd. Experiments on the well-known benchmark sets show that we can beat previously known solutions for all instances with n/2 being odd by an average improvement of 2.66%. Furthermore, we improve the theoretical approximation ratio from 3/2+O(1/n) to 1+O(1/n) for n/2 being odd, answering a challenging open problem in this area.

A new approach based on graph matching and evolutionary approach for sport scheduling problem

The Traveling Tournament Problem (TTP) is concerned with finding a double round-robin tournament schedule that minimizes the total distances traveled by the teams. It has attracted significant interest recently since a favorable TTP schedule can result in significant savings for the league. This paper proposes an original evolutionary algorithm for TTP. We first propose a quick and effective constructive algorithm to construct a Double Round Robin Tournament (DRRT) schedule with low travel cost. We then describe an enhanced genetic algorithm with a new crossover operator to improve the travel cost of the generated schedules. A new heuristic for ordering efficiently the scheduled rounds is also proposed. The latter leads to significant enhancement in the quality of the schedules. The overall method is evaluated on publicly available standard benchmarks and compared with other techniques for TTP and UTTP (Unconstrained Traveling Tournament Problem). The computational experiment shows that the proposed approach could build very good solutions comparable to other state-of-the-art approaches or better than the current best solutions on UTTP. Further, our method provides new valuable solutions to some unsolved UTTP instances and outperforms prior methods for all US National League (NL) instances.