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Adaptive Mutated Momentum Shuffled Frog Leaping Algorithm for Design of Water Distribution Networks

  • Research Article - Civil Engineering
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Abstract

With the introduction of intelligent heuristic optimization strategies, there has been an increasing interest in the use of these methods for solving the design problem of water distribution networks (WDN). This paper proposes the use of a new version of heuristic shuffled frog leaping (SFL) algorithm for solving the problem of WDN design. First, in order to speed up the original SFL algorithm, an adaptive parameter is introduced. Then, momentum parts are added to the SFL to increase the ability of the algorithm in escaping from local optimums. Finally, a mutation operator is proposed to increase the diversification property of the algorithm. The new version of the SFL algorithm is called adaptive mutated momentum shuffled frog leaping (AMMSFL). The proposed AMMSFL is then applied to solve WDN design problems. An illustrative and comparative illustrative example is presented to show the efficiency and superiority of the introduced AMMSFL compared to the other well-known heuristic algorithms.

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Abbreviations

WDN:

Water distribution network

SFL:

Shuffled frog leaping

AMMSFL:

Adaptive mutated momentum shuffled frog leaping

GA:

Genetic algorithm

PSO:

Particle swarm optimization

ACO:

Ant colony optimization

NLP:

Nonlinear programming

NP:

Non-deterministic polynomial time

HD-DDS:

Hybrid discrete dynamically dimensioned search

EPANET:

Water distribution network simulator

DE:

Differential evolution

PSHS:

Particle swarm harmony search

HS:

Harmony search

GHEST:

Genetic heritage evolution by stochastic transmission

SADE:

Self-adaptive differential evolution

DLL:

Dynamic link library

c i (D i ):

Cost per unit length of pipe diameter

D i :

Pipe diameter

δmax :

Upper bound of the inertia factor

δmin :

Lower bound of the inertia factor

L i :

Length of pipe i

n pipe :

Total number of the network pipes

Q jin :

Flow into of the node j

Q jout :

Flow out of the node j

Q j e :

Flow demand of the node j

N :

Total number of the network nodes

ΔH i :

Head loss in pipe i

NL :

Total number of loops in the network

ΔH i :

Head loss in pipe

S :

Number of variables

H u i and H d i :

Heads of both ends of pipe i

ω:

Conversion constant

C i :

Hazen–Williams loss coefficient

α:

Regression coefficient

β:

Regression coefficient

P j :

Pressure head at node j

P min j :

Minimum required pressure head at node j

D :

Commercially available diameter list

W p :

Penalty multiplier

P :

Number of frogs in population

X i :

Frog i

m :

Number of memeplexes

n :

Number of frogs

p :

m × n

X g :

Frog with the best cost function

X b :

Frog with the best cost function

X w :

Frog with the worst cost function

D max :

Maximum allowed change in a frog’s position

f(X b ):

The best cost function

f(X w):

The worst cost function

f(X g ):

The global best cost function

ɛ :

A small constant

δ :

Inertia factor

γ :

Positive constant

θ :

Positive constant

θ:

Positive constant

\({\Delta X_W^{i-1}}\) :

\({=X_W^{i-1} -X_W^{i-2}}\)

\({\Delta X_W^{i-2}}\) :

\({=X_W^{i-3} -X_W^{i-4}}\)

X k W :

Value of X w in kth iteration

i :

Number of iteration

i max :

Maximum number of iterations

S rate %:

Percentage of superseding frogs

References

  1. Yates, D.F.; Templeman, A.B.; Boffey, T.B.: The computational complexity of the problem of determining least capital cost designs for water supply networks. Eng. Optim. 7, 143–145 (1984)

    Article  Google Scholar 

  2. Schaake, J.C; Lai, D.: Linear programming and dynamic programming applied to water distribution network design. MIT Hydrodynamics Lab Report 116; 1969.

  3. Alperovits, E.; Shamir, U.: Design of optimal water distribution systems. Water Resour. Res. 13(6), 885–900 (1977)

    Article  Google Scholar 

  4. Varma, K.; Narasimhan, S.; Bhallamudi, S.M.: Optimal design of water distribution systems using NLP method. J. Environ. Eng. 123, 381–388 (1997)

    Article  Google Scholar 

  5. Sherali, H.D.; Totlani, R.; Loganathan, G.V.: Enhanced lower bounds for the global optimization of water distribution networks. Water Resour. Res. 34, 1831–1841 (1998)

    Article  Google Scholar 

  6. Prasad, D.T.; Park, N.S.: Multiobjective genetic algorithms for design of water distribution networks. J. Water Resour. Plan. Manag. 130, 73–82 (2004)

    Article  Google Scholar 

  7. Kadu, M.S.; Gupta, R.; Bhave, P.R.: Optimal design of water networks using a modified genetic algorithm with reduction in search space. J. Water Resour. Plan. Manag. 134, 147–160 (2008)

    Article  Google Scholar 

  8. Bolognesi, A.; Bragalli, C.; Marchi, A.; Artina, S.: Genetic heritage evolution by stochastic transmission in the optimal design of water distribution networks. Adv. Eng. Softw. 41, 792–801 (2010)

    Article  MATH  Google Scholar 

  9. Banos, R.; Gil, C.; Reca, J.; Montoya, F.G.: A memetic algorithm applied to the design of water distribution networks. Appl. Softw. Comput. 10, 261–266 (2010)

    Article  Google Scholar 

  10. Eusuff, M.M.; Lansey, K.E.: Optimization of water distribution network design using the shuffled frog leaping algorithm. J. Water Resour. Plan. Manag. 129, 210–225 (2003)

    Article  Google Scholar 

  11. Tospornsampan, J.; Kita, I.; Ishii, M.; Kitamura, Y.: Split-pipe design of water distribution network using simulated annealing. Int. J. Comput. Inform. Syst. Sci. Eng. 1, 153–163 (2007)

    Google Scholar 

  12. Zecchin, A.C.; Maier, H.R.; Simpson, A.R.; Leonard, M.; Nixon, J.B.: Ant colony optimization applied to water distribution system design: comparative study of five algorithms. J. Water Resour. Plan. Manag. 133, 87–92 (2007)

    Article  Google Scholar 

  13. Geem, Z.W.: Optimal cost design of water distribution networks using harmony search. Eng. Optim. 38, 259–280 (2006)

    Article  Google Scholar 

  14. Sung, Y.H.; Lin, M.D.; Lin, Y.H.; Liu, Y.L.: Tabu search solution of water distribution network optimization. J. Environ. Eng. Manag. 17, 177–187 (2007)

    Google Scholar 

  15. Montalvo, I.; Izquierdo, J.; Perez, R.; Tung, M.M.: Particle swarm optimization applied to the design of water supply systems. Comput. Math. Appl. 56, 769–776 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Geem, Z.W.: Particle-swarm harmony search for water networks design. Eng. Optim. 41, 297–311 (2009)

    Article  Google Scholar 

  17. Montalvo, I.; Izquierdo, J.; Perez, R.; Herrera, M.: Improved performance of PSO with self-adaptive parameters for computing the optimal design of water supply systems. Eng. Appl. Artif. Intell. 23, 727–735 (2010)

    Article  Google Scholar 

  18. Aghdam, K.M.; Mirzaee, I.; Pourmahmood, N.; Aghababa, M.P.: Design of water distribution networks using accelerated momentum particle swarm optimisation technique. J. Exp. Theoret. Artif. Intell. (2014). doi:10.1080/0952813X.2013.863227

  19. Chu, C.W.; Lin, M.D.; Liu, G.F.; Sung, Y.H.: Application of immune algorithms on solving minimum-cost problem of water distribution network. Math. Comput. Model. 48, 1888–1900 (2008)

    Article  MATH  Google Scholar 

  20. Dong, X.L.; Liu, S.-Q.; Tao, T.; Li, S.P.; Xin, K.L.: A comparative study of differential evolution and genetic algorithms for optimizing the design of water distribution systems. J. Zhejiang Univ. Sci. A (Appl. Phys. Eng.) 13, 674–686 (2012)

    Article  Google Scholar 

  21. Zheng, F.; Simpson, A.R.; Zecchin, A.C.: A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems. Water Resour. Res. 47, W08531 (2011)

    Google Scholar 

  22. Zheng, F.; Zecchin, A.C.; Simpson, A.R.: A self-adaptive differential evolution algorithm applied to water distribution system optimization. J. Comput. Civ. Eng. ASCE 27, 148–158 (2013)

    Article  Google Scholar 

  23. Tolson, B.A.; Asadzadeh, M.; Maier, H.R.; Zecchin, A.C.: Hybrid discrete dynamically dimensioned search (HD-DDS) algorithm for water distribution system design optimization. Water Resour. Res. 45, W12416 (2009)

    Google Scholar 

  24. Zecchin, A.C.; Simpson, A.R.; Maier, H.R.; Nixon, J.B.: Parametric study for an ant algorithm applied to water distribution system optimization. IEEE Trans. Evol. Comput. 9, 175–191 (2005)

    Article  Google Scholar 

  25. Mohan, S.; Jinesh Babu, K.S.: Optimal water distribution network design with Honey-Bee mating optimization. J. Comput. Civ. Eng. 24, 117–126 (2010)

    Article  Google Scholar 

  26. Adarsh, S.; Sahana, A.S.: Minimum cost design of irrigation canals using probabilistic global search lausanne. Arab. J. Sci. Eng. 38, 2631–2637 (2013)

    Article  Google Scholar 

  27. Al-Qutub, A.; Taleb, J.; Mokheimer, E.M.A.: A novel approach for optimizing two-phase flow in water rockets: Part I. Arab. J. Sci. Eng. (2013). doi:10.1007/s13369-013-0779-7

  28. Vatani, A.; Mehrpooya, M.; Pakravesh, H.: Modification of an industrial ethane recovery plant using mixed integer optimization and shuffled frog leaping algorithm. Arab. J. Sci. Eng. 38, 439–455 (2013)

    Article  Google Scholar 

  29. Vijaychakaravarthy, G.; Marimuthu, S.; Naveen Sait, A.: Comparison of Improved sheep flock heredity algorithm and artificial bee colony algorithm for lot streaming in m-machine flow shop scheduling. Arab. J. Sci. Eng. (2014). doi:10.1007/s13369-014-0994-x

  30. Rossman, L.A.: EPANET 2 users manual. Reports EPA/600/R-00/057. US Environ. Prot. Agency, Cincinnati, Ohio (2000)

  31. Liong, S.Y.; Atiquzzaman, M.D.: Optimal design of water distribution network using shuffled complex evolution. J Inst Eng 44, 93–107 (2004)

    Google Scholar 

  32. EPANET Programmer’s Toolkit, Water Supply and Water Resources Division of the U.S. Environmental Protection Agency’s National Risk Management Research Laboratory

  33. Fujiwara, O.; Khang, D.B.: A two phase decomposition method for optimal design of looped water distribution networks. Water. Resour. Res. 26, 539–549 (1990)

    Article  Google Scholar 

  34. Dandy, G.C.; Simpson, A.R.; Murphy, L.J.: An improved genetic algorithm for pipe network optimization. Water Resour. Res. 32, 449–458 (1996)

    Article  Google Scholar 

  35. Maier, H.R.; Simpsom, A.R.; Zwcchin, A.C.; Foong, W.K.; Phang, K.Y.; Seah, H.Y.; Tan, C.L.: Ant colony optimization for the design of water distribution systems. J. Water. Resour. Plan. Manag. 129, 200–209 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Department, Urmia University of Technology, Urmia, Iran

    Kazem Mohammadi Aghdam & Iraj Mirzaee

  2. Mechanical Engineering Department, Urmia University, Urmia, Iran

    Nader Pourmahmood

  3. Electrical Engineering Department, Urmia University of Technology, Urmia, Iran

    Mohammad Pourmahmood Aghababa

Authors
  1. Kazem Mohammadi Aghdam
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  2. Iraj Mirzaee
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  3. Nader Pourmahmood
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  4. Mohammad Pourmahmood Aghababa
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Correspondence to Mohammad Pourmahmood Aghababa.

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Aghdam, K.M., Mirzaee, I., Pourmahmood, N. et al. Adaptive Mutated Momentum Shuffled Frog Leaping Algorithm for Design of Water Distribution Networks. Arab J Sci Eng 39, 7717–7727 (2014). https://doi.org/10.1007/s13369-014-1367-1

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