Journal of Environmental Treatment Techniques 2014, Volume 2, Issue 2, Pages: 63-70 63 Optimal Design of Water Distribution Networks Applying Pattern Search Algorithm with Fuzzy Parameters Mohammad Kangazian 1 , Amid Hadi 1, 2 , Mohammad Javad Hashemi 1, 2 1- Department of Civil Engineering, Shahid Bahonar University, Kerman, Iran. 2- Member facticity of Civil and Environment Engineering, Jami Institute of Technology, Isfahan, Iran. Received: 23/04/2014 Accepted: 29/05/2014 Published: 12/06/2014 Abstract Water distribution network optimization has been among the most significant issues that scientists have ever regarded it highly and have done their best to cut the expenses by taking hydraulic constraints into consideration. Accordingly, regardless of the uncertainty in the parameters of network design, optimization seems something unreal. Regarding the attempts made by other scientists to simulate the uncertainties in different systems; in this study, the Fuzzy method is used to model uncertainty in fuzzy uncertainty. Also, the Pattern Search of algorithm is used for optimizing water distribution network devices. By considering Friction coefficient in Darcy-Weisbach equation, a demand in nodes, and tank head as independent fuzzy parameters we can study cost variations, heads in nodes, velocity, and discharge pipes which are known as dependent fuzzy parameters. Key words: Optimization, Fuzzy parameter, Pattern of search, Water distribution network 1 Introduction 1 Water networks optimization has been under research for about four decades, and notwithstanding a myriad of research studies carried out during this period, this subject, contrary to scientists' expectation is still a theory and is not practically employed by engineers dealing with designing distribution network projects. A reason to this can be scientists' neglection to selecting object function and optimization procedure. In all procedures conducted before, object function set for decreasing costs in constructing networks work under hydraulic constraints, and the most important thing in optimization was to earn total profit out of network and in this case, network could be designed at any time according to circumstances. Therefore, network uncertainty resulting from errors necessarily has to be considered as a future need. In this way, optimization can be put into practice. Concerning network designing, there are purposes that seem difficult to be fulfilled and it is because of model disability where there is uncertainty. Among the best procedures for applying uncertainty is fuzzy method. Although fuzzy method has been developed by Professor Zadeh for circa five decades and it is really applicable in engineering, it's not a long time that it has been applied in optimization. Goulter and Bocharat (1988) are pioneers of fuzzy method. They applied trapezoid membership functions for describing pressure deviation Corresponding author: Amid Hadi, (1) Department of Civil Engineering, Shahid Bahonar University, Kerman, Iran. (2) Member facticity of Civil and Environment Engineering, Jami Institute of Technology, Isfahan, Iran. E-mail: amidhadi@yahoo.com. from desirable pressure in each node for designing an optimum network with the help of linear planning. Vamookride (1995) applied fuzzy functions with the help of dynamic planning for designing a convoluted networker [1.2.3]. 2 Uncertainly Models of water distribution network are simulated models that are constructed for expanding water distribution networks into real networks. These models often involve certain and exact values and a large number of these internal parameters are described as a certain value. However, these certain parameters are a part of uncertain parameters. Uncertainty comes down to 3 groups. The first group characterized by measurement devices in which there are errors such as pump characteristics, tank head, pipes length and diagonal. The second group includes inexact information about a variety of parameters like nodes demand that differ by the passage of time and the third group which contains parameters that are simplified in real network[4,5,6,7]. Fuzzy procedure describes any changes in internal parameters by applying fuzzy membership functions in which statistical data are not needed. Parameters can be made fuzzy by using membership functions that are expressed as triangle, trapezoid, Gucci, and…. In these functions, value for membership function is calculated for each different α-cut [8, 9]. In the current research study, triangle membership function is applied (Fig 1), in which we can calculate membership function of fraction in pipes friction by considering 20% uncertainty and calculate tank head by considering half meter uncertainty and estimate Journal web link: http://www.jett.dormaj.com Enviro. Treat. Tech. ISSN: 2309-1185