An Improved Approximation Algorithm for the Traveling Tournament Problem with Maximum Trip Length Two

The Traveling Tournament Problem is a complex combinatorial optimization problem in tournament timetabling, which asks a schedule of home/away games meeting specific feasibility requirements, while also minimizing the total distance traveled by all the n teams (n is even). Despite intensive algorithmic research on this problem over the last decade, most instances with more than 10 teams in well-known benchmarks are still unsolved. In this paper, we give a practical approximation algorithm for the problem with constraints such that at most two consecutive home games or away games are allowed. Our algorithm, that generates feasible schedules based on minimum perfect matchings in the underlying graph, not only improves the previous approximation ratio from (1+16/n) to about (1+4/n) but also has very good experimental performances. By applying our schedules on known benchmark sets, we can beat all previously-known results of instances with n being a multiple of 4 by 3% to 10%

An Improved Scheduling Algorithm for Traveling Tournament Problem with Maximum Trip Length Two

The Traveling Tournament Problem(TTP) is a combinatorial optimization problem where we have to give a scheduling algorithm which minimizes the total distance traveled by all the participating teams of a double round-robin tournament maintaining given constraints. Most of the instances of this problem with more than ten teams are still unsolved. By definition of the problem the number of teams participating has to be even. There are different variants of this problem depending on the constraints. In this problem, we consider the case where number of teams is a multiple of four and a team can not play more than two consecutive home or away matches. Our scheduling algorithm gives better result than the existing best result for number of teams less or equal to 32

A 55-approximation Algorithm for the Traveling Tournament Problem

The Traveling Tournament Problem (TTP-$k$) is a well-known benchmark problem in tournament timetabling, which asks us to design a double round-robin schedule such that the total traveling distance of all $n$ teams is minimized under the constraints that each pair of teams plays one game in each other's home venue, and each team plays at most $k$-consecutive home games or away games. Westphal and Noparlik (Ann. Oper. Res. 218(1):347-360, 2014) claimed a $5.875$-approximation algorithm for all $k\geq 4$ and $n\geq 6$. However, there were both flaws in the construction of the schedule and in the analysis. In this paper, we show that there is a $5$-approximation algorithm for all $k$ and $n$. Furthermore, if $k \geq n/2$, the approximation ratio can be improved to $4$

The Traveling Tournament Problem

In this thesis we study the Traveling Tournament problem (TTP) which asks to generate a feasible schedule for a sports league such that the total travel distance incurred by all teams throughout the season is minimized. Throughout our three technical chapters a wide range of topics connected to the TTP are explored. We begin by considering the computational complexity of the problem. Despite existing results on the NP-hardness of TTP, the question of whether or not TTP is also APX-hard was an unexplored area in the literature. We prove the affirmative by constructing an L-reduction from (1,2)-TSP to TTP. To reach the desired result, we show that given an instance of TSP with a solution of cost K, we can construct an instance of TTP with a solution of cost at most 20m(m+1)cK where m = c(n-1)+1, n is the number of teams, and c > 5, c ∈ ℤ is fixed. On the other hand, we show that given a feasible schedule to the constructed TTP instance, we can recover a tour on the original TSP instance. The next chapter delves into a popular variation of the problem, the mirrored TTP, which has the added stipulation that the first and second half of the schedule have the same order of match-ups. Building upon previous techniques, we present an approximation algorithm for constructing a mirrored double round-robin schedule under the constraint that the number of consecutive home or away games is at most two. We achieve an approximation ratio on the order of 3/2 + O(1)/n. Lastly, we present a survey of local search methods for solving TTP and discuss the performance of these techniques on benchmark instances

Hybridization of Biologically Inspired Algorithms for Discrete Optimisation Problems

In the field of Optimization Algorithms, despite the popularity of hybrid designs, not enough consideration has been given to hybridization strategies. This paper aims to raise awareness of the benefits that such a study can bring. It does this by conducting a systematic review of popular algorithms used for optimization, within the context of Combinatorial Optimization Problems. Then, a comparative analysis is performed between Hybrid and Base versions of the algorithms to demonstrate an increase in optimization performance when hybridization is employed