Abstract
This paper presents the comparison of two hybrid methodologies for the two-objective (cost and resilience) design of water distribution systems. The first method is a low-level hybrid algorithm (LLHA), in which a main controller (the non-dominated sorting genetic algorithm II, NSGA-II) coordinates various subordinate algorithms. The second method is a high-level hybrid algorithm (HLHA), in which various sub-algorithms collaborate in parallel. Applications to four case studies of increasing complexity enable the performances of the hybrid algorithms to be compared with each other and with the performance of the NSGA-II. In the case study featuring low/intermediate complexity, the hybrid algorithms (especially the HLHA) successfully capture a more diversified Pareto front, although the NSGA-II shows the best convergence. When network complexity increases, instead, the hybrid algorithms (especially the LLHA) turn out to be superior in terms of both convergence and diversity. With respect to both the HLHA and the NSGA-II, the LLHA is capable of detecting the final front in a single run with a lower computation burden. In contrast, the HLHA and the NSGA-II, which are more affected by the initial random seed, require numerous runs with an attempt to reach the definitive Pareto front. On the other hand, a drawback of the LLHA lies in its reduced ability to deal with general problem formulations, i.e., those not relating to water distribution optimal design.
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References
Bragalli C, D’Ambrosio C, Lee J, Lodi A, Toth P (2008) Water Network Design by MINLP. Report No. RC24495. IBM Research Report
Cheung PB, Reis LFR, Formiga KTM, Chaudhry FH, Ticona WGC (2003) Multiobjective evolutionary algorithms applied to the rehabilitation of a water distribution system: a comparative study, proceedings of the 2nd international conference on evolutionary multi-criterion optimization. Springer, Faro
Cisty M (2010) Hybrid genetic algorithm and linear programming method for least-cost design of water distribution systems. Water Resour Manag 24(1):1–24
Creaco E, Franchini M (2012) Fast multi-objective design algorithm combined with an a posteriori procedure for reliability evaluation under various operational scenarios. Urban Water J 9(6):385–399
Creaco E, Franchini M (2013) Low level hybrid procedure for the multi-objective design of water distribution networks. 12th International Conference on Computing and Control for the Water Industry, CCWI2013. Elsevier: Italy
Creaco E, Fortunato A, Franchini M, Mazzola R (2013) Comparison between entropy and resilience as indirect measures of reliability in the framework of water distribution network design. 12th International Conference on Computing and Control for the Water Industry, CCWI2013. Elsevier: Italy
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE T Evol Comput 6(2):182–197
di Pierro F, Khu ST, Savic D, Berardi L (2009) Efficient multi-objective optimal design of water distribution networks on a budget of simulations using hybrid algorithms. Environ Model Softw 24(2):202–213
Dumedah G, Berg A, Wineberg M, Collier R (2010) Selecting model parameter sets from a trade-off surface generated from the non-dominated sorting genetic algorithm-II. Water Resour Manage 24(15):4469–4489
Farmani R, Walters GA, Savic DA (2005) Trade-Off between total cost and reliability for anytown water distribution network. J Water Resour Plann Manage 131(3):161–171
Ferreira JC, Fonseca CM, Gaspar-Cunha A (2007) Methodology to select solutions from the Pareto-optimal set: a comparative study. In genetic and evolutionary computation conference. Proceedings of the 9th annual conference on genetic and evolutionary computation. GECCO, London, pp 789–796
Fu G, Kapelan Z, Reed P (2012) Reducing the complexity of multiobjective water distribution system optimization through global sensitivity analysis. J Water Resour Plann Manage 138(3):196–207
Fu G, Kapelan Z, Kasprzyk J, Reed P (2013) Optimal design of water distribution systems using many-objective visual analytics. J Water Resour Plann Manage 139(6):624–633
Haario H, Saksman E, Tamminen J (2001) An adaptive metropolis algorithm. Bernoulli 7(2):223–242
Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufmann Publishers Inc., San Francisco
Kollat JB, Reed PM (2006) Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design. Adv Water Resour 29(6):792–807
Marchi A, Salomons E, Ostfeld A et al (2013) The battle of the water networks II (BWN-II). J Water Resour Plann Manage doi:. doi:10.1061/(ASCE)WR.1943-5452.0000378
Papadimitriou CH, Steiglitz K (1998) Combinatorial optimization: algorithms and complexity. Dover Publications, New York
Prasad TD, Park NS (2004) Multiobjective genetic algorithms for design of water distribution networks. J Water Resour Plann Manage 130(1):73–82
Raad D, Sinske A, van Vuuren J (2009) Robust multi-objective optimization for water distribution system design using a meta-metaheuristic. Int Trans Oper Res 16(5):595–626
Raad DN, Sinske A, van Vuuren JH (2011) Water distribution systems design optimisation using metaheuristics and hyperheuristics. ORiON: J ORSSA 27(1):17–44
Rossman LA (2000) EPANET 2 USERS MANUAL. U.S. Environment Protection Agency, Cincinnati
Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359
Talbi EG (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8:541–564
Todini E (2000) Looped water distribution networks design using a resilience index based heuristic approach. Urban Water J 2(2):115–122
Todini E, Pilati S (1988) A gradient algorithm for the analysis of pipe networks. In: Coulbeck B, Choun-Hou O (eds) Computer application in water supply, vol I—system analysis and simulation. Wiley, London, pp 1–20
Vrugt JA, Robinson BA (2007) Improved evolutionary optimization from genetically adaptive multimethod search. Proc Natl Acad Sci U S A 104(3):708–711
Walski TM (2001) The wrong paradigm, Why water distribution optimization Doesn’t work. J Water Resour Plann Manage 127(4):203–205
Wang Q, Savić DA, Kapelan Z (2014) Hybrid metaheuristics for multi-objective design of water distribution systems. J Hydroinform 16(1):165–177
Acknowledgments
The first author would like to appreciate the financial support given by both the University of Exeter and the China Scholarship Council towards the PhD research. The work of the second and third author was carried out as part of the PRIN 2012 “Devices and Procedures for an Advanced and Substainable management of Water Distribution Systems” and under the framework of Terra&Acqua Tech Laboratory, Axis I activity 1.1 of the POR FESR 2007–2013 project funded by Emilia-Romagna Regional Council (Italy). We also appreciate the comments and suggestions given by anonymous reviewers, which helped improve the quality of this paper substantially.
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Wang, Q., Creaco, E., Franchini, M. et al. Comparing Low and High-Level Hybrid Algorithms on the Two-Objective Optimal Design of Water Distribution Systems. Water Resour Manage 29, 1–16 (2015). https://doi.org/10.1007/s11269-014-0823-8
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DOI: https://doi.org/10.1007/s11269-014-0823-8