The project is dedicated to uncovering algorithms that can deliver optimal team
configurations within the bounds of predefined team composition constraints. These
constraints encompass diverse team structures, including individual athletes, female and
male pairs, female trios, male quartets, and mixed-gender pairs. A key methodological
aspect of your approach is the employment of a fully connected weighted graph, modeled
as a matrix, to represent the network of athletes. In this model, the nodes symbolize team
members, while the edges reflect the connectivity strength between athletes, with higher
edge weights indicating stronger connections. This foundational setup aims at facilitating
the identification and formation of teams characterized by optimal synergy and
performance potential.
To tackle the challenge of optimizing team compositions, our project employed two distinct
polynomial complexity methods: Simulated Annealing (SA) and Cross Entropy (CE).
Simulated Annealing (SA): SA is inspired by the metallurgical process of annealing, where
materials are heated and then cooled to increase their strength. The algorithm mimics this
process by starting with a high “temperature” to allow for exploration of the solution space,
including less optimal solutions, to avoid local minima. As the temperature decreases, the
algorithm increasingly focuses on improving the quality of solutions, aiming for
convergence towards an optimal solution.
Cross Entropy (CE): CE is an iterative method that builds a probabilistic model of potential
solutions. By continuously updating the model parameters based on the performance of
the best solutions in each iteration, the algorithm narrows down to the most promising
areas of the solution space, aiming to converge to the optimal solution.
Our approach involved first adapting these algorithms to the specific context of our
problem, implementing them within the MATLAB environment. We conducted thorough
performance evaluations to assess factors such as the complexity of the algorithms, their
accuracy in identifying optimal solutions, and their scalability in terms of managing
diPerent group sizes under fixed parameters.
In our project, we explored the integration of Simulated Annealing (SA) and Cross Entropy
(CE) methods. The process began with the creation of an initial solution using CE, which
was then further refined with the application of the SA algorithm.
The ultimate goal of our project was to develop tool for coaches and sports professionals,
facilitating optimized team compositions. This, in turn, is expected to contribute to
enhanced performance and more strategic decision-making in sports contexts