Improvement of the performance of NSGA-II and MOPSO algorithms in multi-objective optimization of urban water distribution networks based on modification of decision space

Water distribution networks require huge investment for construction. Involved people, especially researchers, are always seeking to find a way for decreasing costs and achieving an efficient design. One of the main factors of the network design is the selection of proper diameters based on costs and deficit of flow pressure and velocity in the network. The reduction in construction costs is accomplished by minimizing the diameter of network pipes which leads to the pressure drop in the network. Supplying proper pressure in nodes is one of the important design principles, and low pressure will not provide a complete water supply at the consumption site. Therefore, in this research, the problem of optimization in several sample networks was defined with the objectives of cost minimization and minimization of pressure deficit in the whole network. The EPANET software was used for hydraulic analysis of sample networks, and the multi-objective optimization process was performed by coding NSGA-II and MOPSO algorithms in the MATLAB software environment and linking them to EPANET. The cost function was initially defined only by considering the relationship between cost and diameter and the length of pipes, and in the next definition, the cost resulted by violation of the allowable pressure range was added to this function In both cases, the schedule for achieving the optimal answer was executed. The results showed that these algorithms have a high ability to find optimal solutions and are able to optimize the network in terms of cost and pressure by finding the appropriate pipe diameter. The time for reaching convergence was reduced by considering the cost of violation of the allowable pressure limits significantly and the optimal answer is obtained in a small number of repetitions. In NSGA-II and MOPSO algorithms in two-looped network with 20 and 30 iterations and run time of 0.66 and 0.8 s, respectively, and in Lansey network with 150 and 250 iterations and run time of 5.7 and 9.5 s, the optimal solutions were obtained.