A method is described for identification in a communication network of a sequence of circuit movement steps therein to change with the movement of a single circuit at a time from an initial routing in which are satisfied a certain number of service demands to a feasible target routing that satisfies the same service demands with better utilization of the network resources and that is identified as the one which best approximates or identifies a new predetermined desired target routing. In accordance with the method the steps are made of calculating for each demand still to be processed a replacement circuit reducing the cost difference with the circuit that satisfies the same demand in the desired target routing, choosing from among all the calculated replacement circuits the one having less cost and replacing it, marking the corresponding demand as processed, and repeating the steps from the beginning until all the demands have been processed. Then the sequence with which the circuits were replaced is used as a sequence of steps in moving of circuits for re-routing the network.