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submission: 07/06/2019 | acception: 25/10/2019 | publication: 16/09/2020

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Ali Shakarami
^{1}, Hasan Torabi Poude^{2}*, Hojatt Allah Yonesi^{3}, Azadeh Jabbary^{4}1-Lorestan University.،shakarami27428350@gmail.com 2-Lorestan University.،torabi1976@gmail.com 3-Lorestan University.،yonesi.h@lu.ac.ir 4-Lorestan University.،jabary.az@gmail.com |

A major part of the total cost of water supply systems is related to water transport and distribution systems. So, there have been many studies to enhance network planning. To plan water transport and distribution systems, the characteristics of the network (such as the diameter of the pipes, the height of the reservoirs, the type of pumps applied, etc.) must be known. Then to analyze the network, this information is used as well as the rules that govern pipes and hydraulic systems. Using analysis and optimization, the most cost-effective and reliable design for the network can be chosen. In recent decades, many researches have been done regarding optimizing the design of water distribution networks. So, various optimization methods have been used to minimize the costs of these networks. An appropriate optimization method for the water supply network should be an efficient mathematical approach to optimize the objective function. In the models of hydraulic analysis of the networks, the actual values of the discharges can be determined based on the relationship between pressure and discharge in the nodes. But it should be considered that the issues such as discrete variables (allowable diameters), design constraints (minimum pressure or velocity, etc.), and the complexity of the solving of hydraulic equations of networks, make it difficult to optimize. The optimization methods are only able to use the data given by the objective function and distance themselves from the complexities associated with the estimation of derivatives and other auxiliary functions. Since the pipes with the minimum cost should be within the allowable range in terms of pressure and velocity, another method is needed to solve the hydraulic network. Many researchers have been done to solve the problems of optimization of water transport and distribution systems, applying water distribution system modeling software such as EPANET. They define the objective function in ways which transmit the diameters to the EPANET software and return the hydraulic result of the pipes to the algorithm again. During this process, the EPANET software runes in terms of the evaluation of the objective function, and much time is spent on this process. But in the present study, using the Newton Raphson method, the hydraulic of the pipes was simulated in MATLAB. Thus, the problem solving time was greatly reduced because by the Newton Raphson method the diameters were accepted only if their speed and pressure were within the allowable range. In order to optimize, the combination of Big Bang Big Crunch (BB-BC) and Central Force Optimization (CFO) algorithm was applied. Each of these algorithms has the strengths and weaknesses that were adjusted and modified by combining them together and forming the BB-CFO algorithm. Despite high capabilities of CFO algorithm, it has weak points in acceleration calculation. The advantage of BB-BC is applying the best result in each replication and using inconstant parameters in the algorithm. But, the weaknesses of the two algorithms are such that they are completely complementary. In order to apply BB-CFO algorithm, the distribution networks of the Hanoi network and the Kadu network were selected to be optimized. After their hydraulic coding, the results were analyzed using the Newton-Raphson method with the BB-BC and BB-CFO algorithms. The Hanoi network is characterized by two loops and 34 pipes. After a 6360 evaluation of objective function, the Hanoi network was estimated at $ 6,210,780. As the last network increased difficulty of the problem, the Kadu network with two reservoirs, 34 pipes and 9 loops was selected. The method was able to reach Rs. 130,645,890 with 2288 evaluation of objective function. It should be noted that all pressures and velocities are within the allowable range and had better results compared with the power algorithms such as GA and PSO. Also, due to the lack of use of the software, the time of the program was less than other studies. The advantages of the proposed method in the current study were high speed, not applying hydraulic simulation software, use of inconstant parameters, and its simplicity in application. The present research showed that by understanding abilities and combining the capabilities of different algorithms, a better algorithm could be created. Also, the suggested algorithm could solve the problems more quickly without the use of hydraulic software and only by applying the rules which govern the hydraulic pipes.

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