Journal of Water Resource and Protection, 2015, 7, 715-729
Published Online July 2015 in SciRes. http://www.scirp.org/journal/jwarp
http://dx.doi.org/10.4236/jwarp.2015.79059
How to cite this paper: Mansouri, R., Torabi, H., Hoseini, M. and Morshedzadeh, H. (2015) Optimization of the Water Dis-
tribution Networks with Differential Evolution (DE) and Mixed Integer Linear Programming (MILP). Journal of Water Re-
source and Protection, 7, 715-729. http://dx.doi.org/10.4236/jwarp.2015.79059
Optimization of the Water Distribution
Networks with Differential Evolution (DE)
and Mixed Integer Linear Programming
(MILP)
Ramin Mansouri
1
, Hasan Torabi
1
, Mohammd Hoseini
1
, Hosein Morshedzadeh
2
1
Water Engineering Department, Lorestan University, Khoram Abad, Iran
2
Economics and Management Department, Tehran University, Tehran, Iran
Email: ramin_mansouri@yahoo.com
Received 20 April 2015; accepted 6 July 2015; published 9 July 2015
Copyright © 2015 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Abstract
Nowadays, due to increasing population and water shortage and competition for its consumption,
especially in the agriculture, which is the largest consumer of water, proper and suitable utilization
and optimal use of water resources is essential. One of the important parameters in agriculture
field is water distribution network. In this research, differential evolution algorithm (DE) was
used to optimize Ismail Abad water supply network. This network is pressurized network and
includes 19 pipes and 18 nodes. Optimization of the network has been evaluated by developing an
optimization model based on DE algorithm in MATLAB and the dynamic connection with EPANET
software for network hydraulic calculation. The developing model was run for the scale factor (F),
the crossover constant (Cr), initial population (N) and the number of generations (G) and was
identified best adeptness for DE algorithm is 0.6, 0.5, 100 and 200 for F and Cr, N and G, respec-
tively. The optimal solution was compared with the classical empirical method and results showed
that Implementation cost of the network by DE algorithm 10.66% lower than the classical empiri-
cal method.
Keywords
Differential Evolution Algorithm, Optimization, Distribution Systems, Crossover Constant, Scale
Factor