Bipartición balanceada en grupos homogéneos con correspondencia posicional

In many applications requiring fair comparisons (e.g., control vs. treatment or equitable resource allocation), forming “internally compact” groups is not sufficient: it is necessary to partition a dataset into two balanced subsets that are as similar as possible to each other, and additionally, with an explicit one-to-one correspondence between elements. This work studies the case of two groups (c = 2) as a combinatorial optimization problem, minimizing a cost function based on the sum of squared distances between pairs matched at equivalent positions (positional matching). As the main contribution, a hybrid heuristic is proposed that constructs an initial solution via nearest neighbors supported by spatial indexing (KD-Tree) and refines it with local search through swaps accepted by pure descent, exploiting the additive nature of the cost to evaluate improvements efficiently. The experimental evaluation on synthetic and real datasets shows that the method attains consistently low objective values, practical execution times, and stable behavior across runs. Finally, future directions are discussed to extend the approach to the general case c > 2 and study scalability strategies (e.g., parallelization and ANN structures), maintaining positional correspondence as the central constraint.