A Derivative Free Non-Linear Programming Method for the Optimal Setting of PATs to Be Used in a Hybrid Genetic Algorithm: A Preliminary Work

In recent years, recovering energy while managing excessive pressure in water distribution networks (WDNs) has gradually taken hold through the use of Pumps as Turbines (PATs). Therefore, algorithms commonly used for the optimizations of WDNs require modifications to incorporate these devices. Within this study, an intermediate step toward a new Hybrid Genetic Algorithm (HGA) for the optimal placement and setting of PATs within WDNs is proposed. The described methodology is based on a non‐linear optimization algorithm, the Powell Direction Set (PDS) method. For each WDN configuration with PATs, a non‐linear univariate function, namely the energy production subjected to pressure and technical constraints, is maximized by the PDS method. The promising capabilities of the algorithm are demonstrated with a case study.