IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 12, Issue 6 Ver. I (Nov. - Dec. 2015), PP 21-28 www.iosrjournals.org DOI: 10.9790/1684-12612128 www.iosrjournals.org 21 | Page Multi-objective optimization of water distribution system using particle swarm optimization Minakshi Shrivatava 1 , Dr. Vishnu Prasad 2 , Dr. Ruchi Khare 3 1, 2, 3 (Department of Civil Engineering, M.A. National institute of technology Bhopal- 462003, India) Abstract: The cost of water distribution system includes cost of pipes, pumping system, civil works and pumping energy. Out of these, cost of civil works and pumping system are nearly fixed for any specific water supply project. The cost of pipes and pumping energy are variable and can be minimized by suitable selection of pipe size, material of pipes and staging of elevated service reservoir. In the present work, the cost of pipes and energy have been optimized using Particle Swarm Optimization (PSO) method for a water supply system having large pipe network. In addition to this, the effect of swarm size and different inertia weights of PSO is also studied on the optimized cost of the system. Key words: Water supply system, Particle swarm optimization, Inertia weight function I. Introduction Water is a vital commodity for all living beings on earth surface next to air [15]. Therefore water supply systems are the most important public utility for safe supply of potable water. To supply the adequate amount of water at desired pressure with minimum cost is a big challenge for researchers. The pipe and energy cost involved in the water supply contribute major share of any water supply project [7]. These two cost are variable and depend on the commercial pipe sizes, pipe material available and the staging of service reservoir. Many investigators have worked on the minimization of pipe cost taking constant height of reservoir. In this process, the pipes sizes selected for optimization may not be hydraulically efficient. The pipes selected may be either oversized or undersized to give minimum cost. Various deterministic as well as stochastic methods have been used for optimization of water distribution system [3]. Literature reveals that stochastic method are faster and gives good results for optimizing water distribution system.[1] Particle swarm optimization is one of the best stochastic techniques for optimizing water distribution system as it has very simple features and has very fast rate of convergence. It is developed by James Kennedy and Russell Eberhart in 1995[2]. The inertia weighted function ‘w’ is very important parameter in PSO [5, 6]. In the present work, height of service reservoir is also minimized along with pipe cost after putting constraints on hydraulic gradient. It is seen that most of optimization of pipe network using PSO has been done using a single inertia weight function. The effect of different inertia weights on network optimization has also been presented in this paper. A computer program has been developed for the optimisation of network and analysis has been done by finite element method. The code developed is validated with existing optimised network given in literature with fixed tank staging and results are closely matching. II. Problem formulation The optimisation has been achieved by minimisation of pipe cost as well as energy cost by minimising height of service reservoir using following two objective functions: 2.1 Minimization of pipe cost: The commercially available ductile iron pipes are used in design of network and objective function for minimization of pipe cost is:     m i i i i D L C Z Min 1 1 ) , ( (1) 2.2 Minimization of energy cost: The pumping energy required to lift water to service reservoir depends on height of service reservoir for specific flow rate and annual energy cost is given by