In this work, due to the nature of

In this work, due to the nature of the two examples we have chosen, one uses an objective function which only takes into account the pipeline costs and penalty costs, if not complying with minimal values for the pressure at each node of the network. Nevertheless, a generalization to a broader class of objective functions is straightforward. The examples we use have traditionally been employed in the literature and provide a standardized and simplified environment to carry out a wide range of tests and analyses. Hence, in order to facilitate the comparison with results obtained by other authors, we employ the following objective function to estimate the costs