Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T12:10:25.476Z Has data issue: false hasContentIssue false
  • English
  • Français

Design of Water Distribution Networks via a Novel Fractional Succedaneum Shuffled Frog Leaping Method

Published online by Cambridge University Press:  11 August 2015

K. M. Aghdam ,
I. Mirzaee ,
N. Pourmahmood  and
M. P. Aghababa
K. M. Aghdam
Affiliation:
Mechanical Engineering Department, Urmia University of Technology, Urmia, Iran
I. Mirzaee
Affiliation:
Mechanical Engineering Department, Urmia University of Technology, Urmia, Iran
N. Pourmahmood
Affiliation:
Mechanical Engineering Department, Urmia University, Urmia, Iran
M. P. Aghababa*
Affiliation:
Electrical Engineering Department, Urmia University of Technology, Urmia, Iran
*
* Corresponding author (m.p.aghababa@ee.uut.ac.ir; m.pour13@gmail.com)
Get access

Abstract

It is known that the design problem of water distribution networks (WDNs) is an NP-hard combinatorial problem which cannot be easily solved using traditional mathematical numerical methods. On the other hand, fractional calculus, which is a generalization of the classical integer-order calculus, involves some interesting features such as having memory of past events. Based on the concept of fractional calculus, this paper proposes the use of a new version of heuristic shuffled frog leaping (SFL) algorithm for solving the optimal design problem of WDNs. In order to increase the convergence speed of the original SFL algorithm, a history of past events is added to the SFL updating formula. Moreover, some memeplexes of the original SFL method are altered to increase the diversification property of the SFL which helps the algorithm to avoid trapping in local optima. The new version of the SFL algorithm is called fractional succedaneum momentum shuffled frog leaping (FSSFL) method. The proposed FSSFL is applied for designing WDNs. Four illustrative and examples are presented to show the efficiency and superiority of the introduced FSSFL compared to the other well-known heuristic algorithms.

Keywords

Water distribution networkShuffled frog leaping methodFractional calculusPressure head
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 4 , August 2015 , pp. 369 - 380
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Yates, D. F., Templeman, A. B. and Boffey, T. B., “The Computational Complexity of the Problem of Determining Least Capital Cost Designs for Water Supply Networks,” Engineering Optimization, 7, pp. 143–145 (1984).Google Scholar
2.Schaake, J. C. and Lai, D., “Linear Programming and Dynamic Programming Applied to Water Distribution Network Design,” MIT Hydrodynamics Lab Report, 116, (1969).Google Scholar
3.Alperovits, E. and Shamir, U., “Design of Optimal Water Distribution Systems,” Water Resources Research, 13 pp. 885–900 (1977).CrossRefGoogle Scholar
4.Varma, K., Narasimhan, S. and Bhallamudi, S. M., “Optimal Design of Water Distribution Systems Using NLP Method,” Journal of Environmental Engineering, 123, pp. 381–388 (1997).Google Scholar
5.Sherali, H. D., Totlani, R. and Loganathan, G. V., “Enhanced Lower Bounds for the Global Optimization of Water Distribution Networks,” Water Resources Research, 34, pp. 1831–1841 (1998).Google Scholar
6.Prasad, D. T. and Park, N. S., “Multiobjective Genetic Algorithms for Design of Water Distribution Networks,” Journal of Water Resources Planning and Management, 130, pp. 73–82 (2004).Google Scholar
7.Kadu, M. S., Gupta, R. and Bhave, P. R., “Optimal Design of Water Networks Using a Modified Genetic Algorithm with Reduction in Search Space,” Journal of Water Resources Planning and Management, 134, pp. 147–160 (2008).Google Scholar
8.Bolognesi, A., Bragalli, C., Marchi, A. and Artina, S., “Genetic Heritage Evolution by Stochastic Transmission in the Optimal Design of Water Distribution Networks,” Advances in Engineering Software, 41, pp. 792–801 (2010).Google Scholar
9.Banos, R., Gil, C., Reca, J. and Montoya, F. G., “A Memetic Algorithm Applied to the Design of Water Distribution Networks,” Applied Soft Computing, 10, pp. 261–266 (2010).Google Scholar
10.Eusuff, M. M. and Lansey, K. E., “Optimization of Water Distribution Network Design Using the Shuffled Frog Leaping Algorithm,” Journal of Water Resources Planning and Management, 129, pp. 210–225 (2003).Google Scholar
11.Tospornsampan, J., Kita, I., Ishii, M. and Kitamura, Y., “Split-Pipe Design of Water Distribution Network Using Simulated Annealing,” International Journal of Environmental, Ecological, Geological and Mining Engineering, 1, pp. 153–163 (2007).Google Scholar
12.Zecchin, A. C., Maier, H. R., Simpson, A. R., Leonard, M. and Nixon, J. B., “Ant Colony Optimization Applied to Water Distribution System Design: Comparative Study of Five Algorithms,” Journal of Water Resources Planning and Management, 133, pp. 87–92 (2007).Google Scholar
13.Geem, Z. W., “Optimal Cost Design of Water Distribution Networks Using Harmony Search,” Engineering Optimization, 38, pp. 259–280 (2006).Google Scholar
14.Sung, Y. H., Lin, M. D., Lin, Y. H. and Liu, Y. L., “Tabu Search Solution of Water Distribution Network Optimization,” Journal of Environmental Engineering Manage, 17, pp. 177–187 (2007).Google Scholar
15.Montalvo, I., Izquierdo, J., Perez, R. and Tung, M. M., “Particle Swarm Optimization Applied to the Design of Water Supply Systems,” Computers and Mathematics with Applications, 56, pp. 769–776 (2008).CrossRefGoogle Scholar
16.Geem, Z. W., “Particle-Swarm Harmony Search for Water Networks Design,” Engineering Optimization, 41, pp. 297–311 (2009).Google Scholar
17.Montalvo, I., Izquierdo, J., Perez, R. and Herrera, M., “Improved Performance of PSO with Self-Adaptive Parameters for Computing the Optimal Design of Water Supply Systems,” Engineering Applications of Artificial Intelligence, 23, pp. 727–735 (2010).CrossRefGoogle Scholar
18.Chu, C. W., Lin, M. D., Liu, G. F. and Sung, Y. H., “Application of Immune Algorithms on Solving Minimum-Cost Problem of Water Distribution Network,” Mathematical Computer Modeling, 48, pp. 1888–1900 (2008).CrossRefGoogle Scholar
19.Duan, Q. Y., Gupta, V. K. and Sorooshian, S., “Shuffled Complex Evolution Approach for Effective and Efficient Global Minimization,” Journal of Optimization Theory and Applications, 76, pp. 502–521 (1993).Google Scholar
20.Kennedy, J. and Eberhart, R., “A Discrete Binary Version of the Particle Swarm Algorithm,” Proceedings of the Conference on Systems, Man, and Cybernetics, pp. 4104–4109 (1997).Google Scholar
21.Rossman, L. A., EPANET 2 Users Manual, Reports EPA/600/R-00/057, US Environmental Protection Agency, Cincinnati, Ohio (2000).Google Scholar
22.Aghababa, M. P., “Fractional Modeling and Control of a Complex Nonlinear Energy Supply-Demand System,” Complexity, Doi: 10.1007/s11071-014-1411-4 (2014).Google Scholar
23.Aghababa, M. P. and Borjkhani, M., “Chaotic Fractional-Order Model for Muscular Blood Vessel and Its Control Via Fractional Control Scheme,” Complexity, DOI: 10.1002/cplx.21502 (2014).Google Scholar
24.Aghababa, M. P., “Chaos in a Fractional-Order Micro-Electro-Mechanical Resonator and Its Suppression,” Chinese Physics B, 21, 100505 (2012).Google Scholar
25.Aghababa, M. P., “Chaotic Behavior in Fractional-Order Horizontal Platform Systems and Its Suppression Using a Fractional Finite-Time Control Strategy,” Journal of Mechanical Science and Technology, 28, pp. 1885–1880 (2014).Google Scholar
26.Aghababa, M. P., “Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems Based on Fractional Lyapunov Stability Theory,” ASME Journal of Computational Nonlinear Dynamics, 7, pp. 021010 – 1–5 (2012).Google Scholar
27.Aghababa, M. P., “Robust Stabilization and Synchronization of a Class of Fractional-Order Chaotic Systems Via a Novel Fractional Sliding Mode Controller,” Communications in Nonlinear Science and Numerical Simulation, 17, pp. 2670–2681 (2012).CrossRefGoogle Scholar
28.Aghababa, M. P., “Finite-Time Chaos Control and Synchronization of Fractional-Order Chaotic (Hy-perchaotic) Systems Via Fractional Nonsingular Terminal Sliding Mode Technique,” Nonlinear Dynamics, 69, pp. 247–261 (2012).Google Scholar
29.Podlubny, I., Fractional Differential Equations, Academic Press, New York (1999).Google Scholar
30.Liong, S. Y. and Atiquzzaman, M. D., “Optimal Design of Water Distribution Network Using Shuffled Complex Evolution,” Journal of Institute of Engineers, 44, pp. 93–107 (2004).Google Scholar
31.EPANET Programmer’s Toolkit, Water Supply and Water Resources Division of the U.S. Environmental Protection Agency’s National Risk Management Research Laboratory.Google Scholar
32.Fujiwara, O. and Khang, D. B., “A Two Phase Decomposition Method for Optimal Design of Looped Water Distribution Networks,” Water Resources Research, 26, pp. 539–549 (1990).Google Scholar
33.Reca, J., Martinez, J., Gil, C. and Banos, R., “Application of Several Meta-Heuristic Techniques to the Optimization of Real Looped Water Distribution Networks,” Water Resources Management, 22, pp. 1367–1379 (2007).Google Scholar
34.Zecchin, A. C., Maier, H. R., Simpson, A. R., Leonard, M., Roberts, A. J. and Berrisford, M. J., “Application of Two Ant Colony Optimization Algorithms to Water Distribution System Optimization,” Mathematical and Computer Modelling, 44, pp. 451–468 (2006).Google Scholar
35.Dandy, G. C., Simpson, A. R. and Murphy, L. J., “An Improved Genetic Algorithm for Pipe Network Optimization,” Water Resources Research, 32, pp. 449–458 (1996).Google Scholar
36.Maier, H. R., Simpsom, A. R., Zwcchin, A. C., Foong, W. K., Phang, K. Y., Seah, H. Y. and Tan, C. L., “Ant Colony Optimization for the Design of Water Distribution Systems,” Journal of Water Resources Planning and Management, 129, pp. 200–209 (2003).Google Scholar
37.Kim, J. H., Kim, T. G., Kim, J. H. and Yoon, Y. N., “A Study on the Pipe Network System Design Using Non-Linear Programming,” Journal of Korean Water Resource Association, 27, pp. 59–67 (1994).Google Scholar
38.Dong, X. L., Liu, S. Q., Tao, T., Li, S. P. and Xin, K. L., “A Comparative Study of Differential Evolution and Genetic Algorithms for Optimizing the Design of Water Distribution Systems,” Journal of Zhejiang University — Science A (Applied Physics & Engineering), 13, pp. 674–686 (2012).Google Scholar
39.Lee, S. C.Lee, S. I., “Genetic Algorithms for Optimal Augmentation of Water Distribution Networks,” Journal of Korean Water Resource Association, 34, pp. 567–575 (2001).Google Scholar