عنوان مقاله [English]
As for the severe limitation of water resources, costly construction and operation of water supply systems and rapid population growth, the optimal design of these networks is essential. The problem of cost minimization is done by minimizing the diameter of the network pipes, which reduces the pressure in the network. Since providing adequate pressure in the nodes is one of the important design principles, so in this study, the problem of optimization in several sample networks was defined with the objectives of minimizing the cost and lack of pressure in the whole network. EPANET software was used for hydraulic analysis of sample networks and the multi-objective optimization process through coding of PESA-II and SPEA-II algorithms in MATLAB software and their connection to EPANET face Took. The cost function was initially defined only by considering the relationship between cost, diameter, and pipe length. Then, in the next definition, the cost of exceeding the allowable pressure range, where the minimum and maximum allowable pressures are 30 and 60 meters, respectively, was added to this function, and the program again with the number of repetitions that ended in the best answer Was implemented. The results showed that these algorithms have a high ability to find optimal solutions. In these algorithms, considering the cost of exceeding the allowable pressure limits results in the best answer that other researchers have ever obtained for sample networks, which for the two-loop and lansey network, The cost was 419000 and 1069393 $ respectively, and the pressure shortage was zero and with a low number of iterations, in the two-loop network for both algorithms with 20 iterations and in the lansey network for PESA-II and SPEA-II algorithms with 200 and 140 iterations respectively, to achieve a higher number of optimal answers and the time to achieve convergence is significantly reduced, so that in the two-loop network, the execution time of PESA-II and SPEA-II algorithms are 0.55 and 0.59 minutes respectively, and in the lansey network It was 1/8 and 7.4 minutes respectively.