Water distribution networks optimization using GA, SMPSO, and SHGAPSO algorithms based on engineering approach: a real case study

In modern societies, water distribution networks (WDNs) play a significant role in maintaining the standards of the desired life quality. The previous research findings indicated that meta-heuristic algorithms are stunningly capable of choosing the optimal sizes from a set of commercially available diameters in order to minimize the investment cost of WDNs. However, these methods usually suffer from falling in local optima or highly computational efforts. Therefore, in this study, a hybrid method referred to as a simple hybrid of genetic algorithm and particle swarm optimization (SHGAPSO) has been employed for the first time which depends on genetic algorithm (GA) and simple modified particle swarm optimization (SMPSO). SHGAPSO is developed based on a very simple but efficient hybrid use of GA and SMPSO, and then It is implemented on a real-life WDNs in Iran. In addition, an innovative constraint, which is called head loss gradient, is introduced that could replace the maximum velocity constraint. The results demonstrate that the hybrid technique is quite superior, mitigates the weakness of these two methods, and consequently increases the total efficiency. The results also show that the network design cost using SHGAPSO method is reduced by about 11% and 6%, respectively, compared to the GA and SMPSO algorithms. Moreover, using the maximum head loss gradient constraint causes pressure uniformity and creates surplus pressure in the nodes to the minimum permissible pressure, thereby increases the network hydraulic reliability, and velocity uniformity decreases velocity and head loss gradient in the pipes and ultimately reduces energy loss in the network.