Hybrid Modified Particle Swarm Optimization Algorithm for Adjustment of Water Distribution Network Coefficients

Regarding the complexity of WDNs, the need for computerized modelling of WDNs is felt more than ever for monitoring their performance at the operational stage. One of the most important issues in modelling is to adjust the results of modelling with the real status of the system. So it is necessary to calibrate the model by observed data. Finding a suitable method for adjusting the model's coefficients is one of the main challenges in computerized modelling. In this paper, a modified particle swarm method is presented to adjustment of water distribution network coefficients by modifying the velocity equation of the particle swarm and Combining it with the mutation operator. Thus by defining the coefficients of the models, four models such as standard particle swarm optimization model (SPSO), modified standard particle swarm optimization model (MSPSO), standard particle swarm optimization model with a mutation (SPSOM) and modified standard particle swarm optimization model with a mutation (MSPSOM) are constructed. The Rastrigin test function is used for verification of the modified particle swarm equation and the two-loop network is used for verification of models and also the four-loop network and real water distribution network are used for detailed analysis. The optimization is done in MATLAB by combining the particle swarm optimization algorithm and the EPANET software. Comparison of the results of the standard particle swarm model and the modified standard particle swarm model for the Rastrigin test function showed that modifying the particle swarm velocity equation increased the model's ability to determine the actual answers and reduced the costs. The MSPSOM model finds the optimal answer for two-loop and four-loop networks with a probability of 96.7 and 95 percent respectively. So it is the best model among all models in this criteria. Also, the MSPSO model finds the optimal answer for two-loop and four-loop networks in lowest time compared to other models. So it is the best model among all models in this criteria. Comparing the results of the models in the Ahar water distribution network showed that the modified standard particle swarm with the mutation model have the lowest minimum and average values of the modeling data error. So it has the best performance among the particle swarm models. In general, the correction of the particle swarm velocity equation in the form of the standard particle swarm model, and the correction of the particle swarm velocity and its integration with the mutation operator in the form of a modified standard particle swarm with a mutation has a higher ability to adjust the water distribution network coefficients.