A Cooperative Local Search Method for Solving the Traveling Tournament Problem

Constrained optimization is the process of optimizing a certain objective function subject to a set of constraints. The goal is not necessarily to find the global optimum. We try to explore the search space more efficiently in order to find a good approximate solution. The obtained solution should verify the hard constraints that are required to be satisfied. In this paper, we propose a cooperative search method that handles optimality and feasibility separately. We take the traveling tournament problem (TTP) as a case study to show the applicability of the proposed idea. TTP is the problem of scheduling a double round-robin tournament that satisfies a set of related constraints and minimizes the total distance traveled by the teams. The proposed method for TTP consists of two main steps. In the first step, we ignore the optimization criterion. We reduce the search only to feasible solutions satisfying the problem's constraints. For this purpose, we use constraints programming model to ensure the feasibility of solutions. In the second step, we propose a stochastic local search method to handle the optimization criterion and find a good approximate solution that verifies the hard constraints. The overall method is evaluated on benchmarks and compared with other well-known techniques for TTP. The computational results are promising and show the effectiveness of the proposed idea for TTP

An instance data repository for the round-robin sports timetabling problem

The sports timetabling problem is a combinatorial optimization problem that consists of creating a timetable that defines against whom, when and where teams play games. This is a complex matter, since real-life sports timetabling applications are typically highly constrained. The vast amount and variety of constraints and the lack of generally accepted benchmark problem instances make that timetable algorithms proposed in the literature are often tested on just one or two specific seasons of the competition under consideration. This is problematic since only a few algorithmic insights are gained. To mitigate this issue, this article provides a problem instance repository containing over 40 different types of instances covering artificial and real-life problem instances. The construction of such a repository is not trivial, since there are dozens of constraints that need to be expressed in a standardized format. For this, our repository relies on RobinX, an XML-supported classification framework. The resulting repository provides a (non-exhaustive) overview of most real-life sports timetabling applications published over the last five decades. For every problem, a short description highlights the most distinguishing characteristics of the problem. The repository is publicly available and will be continuously updated as new instances or better solutions become available