We consider the construction of minimal multi-layered perceptrons for solving combinatorial optimization problems. Though general in nature, the construction method is presented as a case study for the sorting problem. The presentation starts with an O((n!)^2) three-layered perceptron based on complete enumeration, that solves the sorting problem of n numbers. This network is then gradually reduced to an O(n^2) three-layered perceptron, which can be viewed as a neural implementation of Preparata's parallel enumerative sorting algorithm. Key words: minimal multi-layered percept1'Ons, feed-forward neural networks, combinatorial optimization problems, sorting.