Hybrid Differential Evolution and Krill Herd Algorithm for the Optimal Design of Water Distribution Networks
Publication: Journal of Computing in Civil Engineering
Volume 36, Issue 1
Abstract
For optimally designing water distribution networks (WDNs), the nondeterministic polynomial hard problem, a novel hybrid model, is introduced with the combined features of evolutionary and swarm intelligence techniques. An evolutionary algorithm with better exploration properties, differential evolution (DE), and the swarm intelligence technique with better exploitation properties, namely the krill herd algorithm (KHA), is considered for this purpose. Because exploration and exploitation are the essential features of the metaheuristic algorithms, the hybrid algorithm with a combination of the DE and KHA features, the DE-KHA, resulted in a balanced search methodology. The results on the application of the proposed model on well-studied benchmark problems have demonstrated its enhanced search behavior, converging faster to the promising results with considerable robustness. Moreover, compared with other competing algorithms reported for optimally designing the WDNs, the DE-KHA outperforms with better computational efficiency. Additionally, considering the few control parameters that have to be calibrated for their optimal values, the computational burden will be less for performing the sensitivity analysis. As a result, considering the solution precision, quick convergence ability, and robustness of DE-KHA, the study suggests the algorithm for efficiently handling real-life case studies.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The data for the benchmark problems considered in the present study are taken from the Centre for Water Systems, Benchmark Problems, University of Exeter (emps.exeter.ac.uk/engineering/research/cws/resources/benchmarks/pareto/) and could also be found in Geem (2006).
All the models or codes that support the findings of this study are available from the corresponding author (written in MATLAB software and compiled with the simulation software EPANET using the MATLAB-EPANET toolkit).
References
Babu, K. S. J., and D. P. Vijayalakshmi. 2013. “Self-adaptive PSO-GA hybrid model for combinatorial water distribution network design.” J. Pipeline Syst. Eng. Pract. 4 (1): 57–67. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000113.
Blum, C., and A. Roli. 2003. “Metaheuristics in combinatorial optimization: Overview and conceptual comparison.” ACM Comput. Surv. 35 (3): 268–308. https://doi.org/10.1145/937503.937505.
Bolaji, A. L., M. A. Al-Betar, M. A. Awadallah, A. T. Khader, and L. M. Abualigah. 2016. “A comprehensive review: Krill herd algorithm (KH) and its applications.” Appl. Soft Comput. 49 (2016): 437–446. https://doi.org/10.1016/j.asoc.2016.08.041.
Das, S., A. Konar, and U. K. Chakraborty. 2005. “Two improved differential evolution schemes for faster global search.” In Proc., ACMSIGEVO GECCO, 991–998. New York: Association for Computing Machinery.
Eusuff, M. M., and K. E. Lansey. 2003. “Optimization of water distribution network design using the shuffled frog leaping algorithm.” J. Water Resour. Plann. Manage. 129 (3): 210–225. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(210).
Ezzeldin, R., B. Djebedjian, and T. Saafan. 2014. “Integer discrete particle swarm optimization of water distribution networks.” J. Pipeline Syst. Eng. Pract. 5 (1): 04013013. https://doi.org/10.1061/(ASCE)PS.1949-1204.0000154.
Fallah, H., O. Kisi, S. Kim, and M. Rezaie-Balf. 2019. “A new optimization approach for the least-cost design of water distribution networks: Improved crow search algorithm.” Water Resour. Manage. 33 (10): 3595–3613. https://doi.org/10.1007/s11269-019-02322-8.
Flierl, G., D. Grunbaum, S. Levin, and D. Olson. 1999. “From individuals to aggregations: The interplay between behaviour and physics.” J. Theor. Biol. 196 (4): 397–454. https://doi.org/10.1006/jtbi.1998.0842.
Gandomi, A. H., and A. H. Alavi. 2012. “Krill herd: A new bio-inspired optimization algorithm.” Commun. Nonlinear Sci. Numer. Simul. 17 (12): 4831–4845. https://doi.org/10.1016/j.cnsns.2012.05.010.
Geem, Z. W. 2006. “Optimal cost design of water distribution networks using harmony search.” Eng. Optim. 38 (3): 259–277. https://doi.org/10.1080/03052150500467430.
Hofmann, E. E., A. G. E. Haskell, J. M. Klinck, and C. M. Lascara. 2004. “Lagrangian modelling studies of Antarctic krill (Euphausia superba) swarm formation.” ICES J. Mar. Sci. 61 (4): 617–631. https://doi.org/10.1016/j.icesjms.2004.03.028.
Kadu, M. S., R. Gupta, and P. R. Bhave. 2008. “Optimal design of water networks using a modified genetic algorithm with reduction in search space.” J. Water Resour. Plann. Manage. 134 (2): 147–160. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:2(147).
Kim, J. H., T. G. Kim, J. H. Kim, and Y. N. Yoon. 1994. “A study on the pipe network system design using non-linear programming.” J. Korean Water Resour. Assoc. 27 (4): 59–67.
Krapivka, A., and A. Ostfeld. 2009. “Coupled genetic algorithm-linear programming scheme for least-cost pipe sizing of water-distribution systems.” J. Water Resour. Plann. Manage. 135 (4): 298–302. https://doi.org/10.1061/(ASCE)0733-9496(2009)135:4(298).
Liong, S. Y., and M. Atiquzzaman. 2004. “Optimal design of water distribution network using shuffled complex evolution.” J. Inst. Eng. 44 (1): 93–107.
Maier, H. R., A. R. Simpson, A. C. Zecchin, W. K. Foong, K. Y. Phang, H. Y. Seah, and C. L. Tan. 2003. “Ant colony optimization for design of water distribution systems.” J. Water Resour. Plann. Manage. 129 (3): 200–209. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:3(200).
Michalewicz, Z., and M. Schoenauer. 1996. “Evolutionary algorithms for constrained parameter optimization problems.” Evol. Comput. 4 (1): 1–32. https://doi.org/10.1162/evco.1996.4.1.1.
Moosavian, N., and B. Lence. 2019. “Fittest individual referenced differential evolution algorithms for optimization of water distribution networks.” J. Comput. Civ. Eng. 33 (6): 04019036. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000849.
Poojitha, S. N., G. Singh, and V. Jothiprakash. 2020. “Improving the optimal solution of Goyang network—Using genetic algorithm and differential evolution.” Water Supply 20 (1): 95–102. https://doi.org/10.2166/ws.2019.139.
Reca, J., and J. Martinez. 2006. “Genetic algorithms for the design of looped irrigation water distribution networks.” Water Resour. Res. 42 (5): W05416. https://doi.org/10.1029/2005WR004383.
Rossman L. A. 2000. EPANET 2 users manual. Washington, DC: USEPA.
Sedki, A., and D. Ouazar. 2012. “Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems.” Adv. Eng. Inf. 26 (3): 582–591. https://doi.org/10.1016/j.aei.2012.03.007.
Sheikholeslami, R., and S. Talatahari. 2016. “Developed swarm optimizer: A new method for sizing optimization of water distribution systems.” J. Comput. Civ. Eng. 30 (5): 04016005. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000552.
Storn R., and K. Price. 1995. Differential evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley, CA: International Computer Science Institute.
Suribabu, C. R. 2010. “Differential evolution algorithm for optimal design of water distribution networks.” J. Hydroinf. 12 (1): 66–82. https://doi.org/10.2166/hydro.2010.014.
Suribabu, C. R., and T. R. Neelakantan. 2006. “Design of water distribution networks using particle swarm optimization.” Urban Water J. 3 (2): 111–120. https://doi.org/10.1080/15730620600855928.
Vairavamoorthy, K., and M. Ali. 2000. “Optimal design of water distribution systems using genetic algorithms.” Comput.-Aided Civ. Infrastruct. Eng. 15 (5): 374–382. https://doi.org/10.1111/0885-9507.00201.
Wang, G. G., A. H. Gandomi, A. H. Alavi, and D. Gong. 2019. “A comprehensive review of krill herd algorithm: Variants, hybrids and applications.” Artif. Intell. Rev. 51: 119–148. https://doi.org/10.1007/s10462-017-9559-1.
Wang, Q., S. Liu, H. Wang, and D. A. Savic. 2012. “Multi-objective cuckoo search for the optimal design of water distribution systems.” In Proc., Int. Conf. on Civil Engineering and Urban Planning, 402–405. Reston, VA: ASCE. https://doi.org/10.1061/9780784412435.072.
Wu, Z. Y., and A. R. Simpson. 2001. “Competent genetic-evolutionary optimization of water distribution systems.” J. Comput. Civ. Eng. 15 (2): 89–101. https://doi.org/10.1061/(ASCE)0887-3801(2001)15:2(89).
Zecchin, A. C., A. R. Simpson, H. R. Maier, A. Marchi, and J. B. Nixon. 2012. “Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem.” Water Resour. Res. 48 (9): W09505. https://doi.org/10.1029/2011WR011652.
Zheng, F., A. R. Simpson, and A. C. Zecchin. 2011. “A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems.” Water Resour. Res. 47 (8): W08531. https://doi.org/10.1029/2011WR010394.
Zheng, F., A. R. Simpson, and A. C. Zecchin. 2014. “Coupled binary linear programming-differential evolution algorithm approach for water distribution system optimization.” J. Water Resour. Plann. Manage. 140 (5): 585–597. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000367.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jan 15, 2021
Accepted: Aug 26, 2021
Published online: Oct 8, 2021
Published in print: Jan 1, 2022
Discussion open until: Mar 8, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Jui-Sheng Chou, Chi-Yun Liu, Optimized Lightweight Edge Computing Platform for UAV-Assisted Detection of Concrete Deterioration beneath Bridge Decks, Journal of Computing in Civil Engineering, 10.1061/JCCEE5.CPENG-5905, 39, 1, (2025).
- S. N. Poojitha, V. Jothiprakash, Robust and Reliable Design Alternatives to Water Distribution Networks: Introducing a Penalty-Free Hybrid Metaheuristic Multiobjective Algorithm with a Posterior Performance Investigation Model, Journal of Water Resources Planning and Management, 10.1061/JWRMD5.WRENG-6420, 150, 12, (2024).
- Seelam Naga poojitha, Jothiprakash V, Chaotic differential evolution algorithms for optimal design of water distribution networks, ISH Journal of Hydraulic Engineering, 10.1080/09715010.2022.2138585, (1-15), (2022).
- S. N. Poojitha, V. Jothiprakash, Application of Fine-Tuned Krill Herd Algorithm in Design of Water Distribution Networks, Journal of Pipeline Systems Engineering and Practice, 10.1061/(ASCE)PS.1949-1204.0000684, 13, 4, (2022).
- Hongyou Cao, Huiyang Li, Mingyang Wang, Bin Huang, Yuan Sun, A structural reanalysis assisted harmony search for the optimal design of structures, Computers & Structures, 10.1016/j.compstruc.2022.106844, 270, (106844), (2022).