Improved Heuristics for Finding Balanced Teams
This research addresses the problem of dividing a group of people into a collection of teams that need to be ``balanced'' across a variety of different attributes. This type of problem arises, for example, in an academic setting where it is necessary to partition students into a number of balanced study teams and also in a youth camp in which children need to be formed into sports teams that are competitive with each other. Recent work has resulted in both linear and nonlinear integer programming models for solving this problem. In the research here, improvements to the models are made together with a linear approximation to the nonlinear objective function that significantly reduce the number of integer variables and constraints. Computational experiments are performed on random instances of the problem as well as on instances for which there are almost perfectly balanced teams, the latter providing a way to determine the quality of the optimal solution obtained by the heuristics. These tests show that the approach developed here almost always obtain better balanced teams than those from prior research.