Skip to main content
SpringerLink
Log in

Comparison of the Performance of a Surrogate Based Gaussian Process, NSGA2 and PSO Multi-objective Optimization of the Operation and Fuzzy Structural Reliability of Water Distribution System: Case Study for the City of Asmara, Eritrea

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

Optimal scheduling of pumps in water distribution systems (WDSs) entails reducing operational cost while supplying the required water quality and quantity. The combined use of pumps, however, can increase breakage rate of aging pipes due to high internal pressure. Multi-objective optimization (MO) is crucial in the determination of a trade-off between the two objective functions, minimization of the operational cost and maximization of the velocity reliability index. The velocity reliability index is used as a surrogate metric to quantify the structural performance of the pipes. The optimization process requires repetitive hydraulic simulations resulting in high computational cost. This paper proposes a Gaussian-Process (GP) based sequential approaches that efficiently estimate the optimal Pareto front with reduced computational effort. The technique simultaneously optimizes the two objective functions over a box-constrained domain where each GP model is fitted independently through an infill criterion that balances the space exploration (search of new observations) and exploitation (local improvement around existing observations). The reduced computational cost allows running full hydraulic simulations during the optimization process permitting real time decision making for pumps schedule in large complex WDSs. Utility of the proposed technique was applied for Asmara’s WDSs, composed of 9 pumping stations and 12 storage tanks, and showed good performance of the GP based optimization compared to traditional evolutionary optimization techniques (such as NSGA2 and Particle Swarm Optimization). The GP-MO only requires 20 iterations to identify the optimal Pareto front while, even with more than 1000 generations, the NSGA2 is not getting to find a good agreement between the two objective functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability

The authors are ready to respond to any request.

Code Availability

The authors are ready to respond to any request.

References

  • Bagirov AM, Barton A, Mala-Jetmarova H, Al Nuaimat A, Ahmed S, Sultanova N, Yearwood J (2013) An algorithm for minimization of pumping costs in water distribution systems using a novel approach to pump scheduling. Math Comput Model 57(3–4):873–886

    Article  Google Scholar 

  • Balekelayi N, Tesfamariam S (2017) Optimization techniques used in design and operations of water distribution networks: a review and comparative study. Sustain Resilient Infrastruct 2(4):153–168

    Article  Google Scholar 

  • Balekelayi N, Zeraebruk KN, Teklemariam M, Tesfamariam S (2021) Optimization of water distribution system operation with multiple tanks and pumps: Application for Asmara, Eritrea’s water supply system. J Pipeline Syst Eng Pract 12(4):04021037

    Article  Google Scholar 

  • Barlow E, Tanyimboh TT (2014) Multiobjective memetic algorithm applied to the optimisation of water distribution systems. Water Resour Manag 28(8):2229–2242

    Article  Google Scholar 

  • Beygi S, Tabesh M, Liu S (2019) Multi-objective optimization model for design and operation of water transmission systems using a power resilience index for assessing hydraulic reliability. Water Resour Manag 33(10):3433–3447

    Article  Google Scholar 

  • Bi W, Dandy GC (2013) Optimization of water distribution systems using online retrained metamodels. J Water Resour Plan Manag 140(11):04014032

    Article  Google Scholar 

  • Binois M, Picheny V (2019) GPareto: An R package for gaussian-process-based multi-objective optimization and analysis. J Statist Softw 89:1–30

  • Bohórquez J, Saldarriaga J, Vallejo D (2015) Pumping pattern optimization in order to reduce WDS operation costs. Procedia Eng 119:1069–1077

    Article  Google Scholar 

  • Bonvin G, Demassey S, Le Pape C, Maïzi N, Mazauric V, Samperio A (2017) A convex mathematical program for pump scheduling in a class of branched water networks. Appl Energy 185:1702–1711

    Article  Google Scholar 

  • Broad DR, Dandy GC, Maier HR (2005) Water distribution system optimization using metamodels. J Water Resour Plan Manag 131(3):172–180

    Article  Google Scholar 

  • Burnell D, Race J, Evans P (1993) An overview of the trunk scheduling system for the London ring main. Water Sci Technol 28(11–12):99–109

    Article  Google Scholar 

  • Candelieri A, Perego R, Archetti F (2018) Bayesian optimization of pump operations in water distribution systems. J Global Optim 71(1):213–235

    Article  Google Scholar 

  • Chase DV, Ormsbee LE (1993) Computer-generated pumping schedules for satisfying operational objectives. J Am Water Works Ass 85(7):54–61

    Article  Google Scholar 

  • Cheung PB, Reis LF, Formiga KT, Chaudhry FH, Ticona WG (2003) Multiobjective evolutionary algorithms applied to the rehabilitation of a water distribution system: a comparative study. In: International Conference on Evolutionary Multi-Criterion Optimization, Springer, pp 662–676

  • De Paola F, Fontana N, Giugni M, Marini G, Pugliese F (2016) An application of the Harmony-Search Multi-Objective (HSMO) optimization algorithm for the solution of pump scheduling problem. Procedia Eng 162:494–502

    Article  Google Scholar 

  • Dini M, Hemmati M, Hashemi S (2022) Optimal operational scheduling of pumps to improve the performance of water distribution networks. Water Resour Manag 36(1):417–432

    Article  Google Scholar 

  • Emmerich MT, Deutz AH, Klinkenberg JW (2011) Hypervolume-based expected improvement: Monotonicity properties and exact computation. In: 2011 IEEE Congress of Evolutionary Computation (CEC), IEEE, pp 2147–2154

  • Farmani R, Savic D, Walters G (2005) Evolutionary multi-objective optimization in water distribution network design. Eng Optim 37(2):167–183

    Article  Google Scholar 

  • Garzón A, Kapelan Z, Langeveld J, Taormina R (2022) Machine learning-based surrogate modelling for urban water networks: Review and future research directions. Water Resour Res e2021WR031808

  • Geem ZW (2015) Multiobjective optimization of water distribution networks using fuzzy theory and harmony search. Water 7(7):3613–3625

    Article  Google Scholar 

  • Ghimire SR, Barkdoll BD (2007) Issues in energy consumption by municipal drinking water distribution systems. In: World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat, pp 1–10

  • Giacomello C, Kapelan Z, Nicolini M (2012) Fast hybrid optimization method for effective pump scheduling. J Water Resour Plan Manag 139(2):175–183

    Article  Google Scholar 

  • Henkenjohann N, Kunert J (2007) An efficient sequential optimization approach based on the multivariate expected improvement criterion. Qual Eng 19(4):267–280

    Article  Google Scholar 

  • JICA (2015) Preparatory survey report on the project for Asmara water supply development in the State of Eritrea. Japan International Cooperation Agency. https://openjicareport.jica.go.jp/pdf/12244778_01.pdf. Accessed 5 Oct 2022

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Global Optim 13(4):455–492

    Article  Google Scholar 

  • Khatavkar P, Mays LW (2017) Model for optimal operation of water distribution pumps with uncertain demand patterns. Water Resour Manag 31(12):3867–3880

    Article  Google Scholar 

  • Mackle G, Savic G, Walters GA (1995) Application of genetic algorithms to pump scheduling for water supply. In: First international conference on genetic algorithms in engineering systems: innovations and applications, IET, pp 400–405

  • Makaremi Y, Haghighi A, Ghafouri HR (2017) Optimization of pump scheduling program in water supply systems using a self-adaptive NSGA-II: a review of theory to real application. Water Resour Manag 31(4):1283–1304

    Article  Google Scholar 

  • Mehzad N, Asghari K, Chamani MR (2020) Application of clustered-NA-ACO in three-objective optimization of water distribution networks. Urban Water J 17(1):1–13

    Article  Google Scholar 

  • Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press

  • Nitivattananon V, Sadowski EC, Quimpo RG (1996) Optimization of water supply system operation. J Water Resour Plan Manag 122(5):374–384

    Article  Google Scholar 

  • Pasha M, Lansey K (2009) Optimal pump scheduling by linear programming. In: World Environmental and Water Resources Congress 2009: Great Rivers, pp 1–10

  • Pecci F, Abraham E, Stoianov I (2017) Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach. Struct Multidiscip Optim 55(3):857–869

    Article  Google Scholar 

  • Picheny V (2015) Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction. Stat Comput 25(6):1265–1280

    Article  Google Scholar 

  • Prasad TD, Park NS (2004) Multiobjective Genetic algorithms for design of water distribution networks. J Water Resour Plan Manag 130(1):73–82

    Article  Google Scholar 

  • Price E, Ostfeld A (2013) Iterative linearization scheme for convex nonlinear equations: Application to optimal operation of water distribution systems. J Water Resour Plan Manag 139(3):299–312

    Article  Google Scholar 

  • Puleo V, Morley M, Freni G, Savić D (2014) Multi-stage linear programming optimization for pump scheduling. Procedia Eng 70:1378–1385

    Article  Google Scholar 

  • Sakawa M, Nishizaki I, Katagiri H (2011) Fuzzy stochastic multiobjective programming, vol 159. Springer Science & Business Media

  • Salomons E, Goryashko A, Shamir U, Rao Z, Alvisi S (2007) Optimizing the operation of the Haifa-A water-distribution network. J Hydroinf 9(1):51–64

    Article  Google Scholar 

  • Scanlan M, Filion YR (2015) Application of energy use indicators to evaluate energy dynamics in Canadian water distribution systems. Procedia Eng 119:1039–1048

    Article  Google Scholar 

  • Shamir U, Salomons E (2008) Optimal real-time operation of urban water distribution systems using reduced models. J Water Resour Plan Manag 134(2):181–185

    Article  Google Scholar 

  • Shirzad A, Tabesh M, Atayikia B (2017) Multiobjective optimization of pressure dependent dynamic design for water distribution networks. Water Resour Manag 31(9):2561–2578

    Article  Google Scholar 

  • Statistics Canada (2019) Operation and maintenance costs of drinking water plants by production volume and main source water type. URL: https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3810026901

  • Tanyimboh TT, Czajkowska AM (2018) Joint entropy based multi-objective evolutionary optimization of water distribution networks. Water Resour Manag 32(8):2569–2584

    Article  Google Scholar 

  • Tanyimboh TT, Templeman AB (2000) A quantified assessment of the relationship between the reliability and entropy of water distribution systems. Eng Optim 33(2):179–199

    Article  Google Scholar 

  • Todini E (2000) Looped water distribution networks design using a resilience index based heuristic approach. Urban Water 2(2):115–122

    Article  Google Scholar 

  • Van Zyl JE, Savic DA, Walters GA (2004) Operational optimization of water distribution systems using a hybrid genetic algorithm. J Water Resour Plan Manag 130(2):160–170

    Article  Google Scholar 

  • Xu Q, Wehrle E, Baier H (2012) Adaptive surrogate-based design optimization with expected improvement used as infill criterion. Optimization 61(6):661–684

    Article  Google Scholar 

  • Yu G, Powell R, Sterling M (1994) Optimized pump scheduling in water distribution systems. J Optim Theory Appl 83(3):463–488

    Article  Google Scholar 

  • Zeraebruk KN (2017) Development of decision support tools for sustainable water development and management in urban areas: Case study of Asmara water supply system, Eritrea. PhD thesis, COETEC, Jomo Kenyatta University of Agriculture and Technology

  • Zhang Q, Liu W, Tsang E, Virginas B (2009) Expensive multiobjective optimization by MOEA/D with Gaussian process model. IEEE Trans Evol Comput 14(3):456–474

    Article  Google Scholar 

  • Zhang Y, Li H, Bao E, Zhang L, Yu A (2019) A hybrid global optimization algorithm based on particle swarm optimization and Gaussian process. Int J Comput Intell Syst 12(2):1270–1281

    Article  Google Scholar 

  • Zhou Q, Jiang P, Huang X, Zhang F, Zhou T (2018) A multi-objective robust optimization approach based on Gaussian process model. Struct Multidiscip Optim 57(1):213–233

    Article  Google Scholar 

Download references

Acknowledgements

The third author acknowledges the financial support through Natural Sciences an Engineering Research Council of Canada under the Discovery Grant programs (RGPIN-2019-05584).

Author information

Authors and Affiliations

  1. School of Engineering, The University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Ngandu Balekelayi, Haile Woldesellasse & Solomon Tesfamariam

Authors
  1. Ngandu Balekelayi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haile Woldesellasse
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Solomon Tesfamariam
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Solomon Tesfamariam and Ngandu Balekelayi contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ngandu Balekelayi and Solomon Tesfamariam. Haile Woldesellasse contributed in the literature review of the paper. The first draft of the manuscript was written by all authors.

Corresponding author

Correspondence to Solomon Tesfamariam.

Ethics declarations

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent to Publication

Not applicable.

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Balekelayi, N., Woldesellasse, H. & Tesfamariam, S. Comparison of the Performance of a Surrogate Based Gaussian Process, NSGA2 and PSO Multi-objective Optimization of the Operation and Fuzzy Structural Reliability of Water Distribution System: Case Study for the City of Asmara, Eritrea. Water Resour Manage 36, 6169–6185 (2022). https://doi.org/10.1007/s11269-022-03347-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-022-03347-2

Keywords

Search

Navigation