Journal of Water and Wastewater Science and Engineering

Journal of Water and Wastewater Science and Engineering

Evaluation of Decision Variable Vector Modeling Methods in Multiphase Optimal Design of Water Distribution Networks

Document Type : Original Article

Authors
1 Ph.D. Graduate, Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz, Ahvaz, Iran,
2 Researcher, Department of Urban Water Management, University of Kaiserslautern, Kaiserslautern, Germany.
3 Assistant professor, Dipartimento di Ingegneria Civile e Architettura, Università Degli Studi di Pavia, Pavia, Italy.
4 Professor, Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz, Ahvaz,
5 Professor, Dipartimento di Ingegneria Civile e Architettura, Università Degli Studi di Pavia, Pavia, Italy.
Abstract
Unlike the static design, a traditional method that completes the design step in one phase, the dynamic method divides the design period into various phases. Nowadays, multi-objective optimization algorithms are employed to achieve optimal designs in the dynamic method. This research explains the multiphase design and construction, a sub-method of the dynamic method. Subsequently, two distinct approaches, namely the aggregated model and the disaggregated model, are introduced for modeling the decision variable vector in the multi-objective optimization algorithm. The aggregated model utilizes a single chromosome for each phase, while the disaggregated model employs two separate chromosomes for each phase. Finally, the effects of different approaches of decision variable vectors modelling applied to the dynamic method are investigated. The results demonstrated that the disaggregated model leads to a 10% improvement in the final Pareto front solutions compared to the aggregated model. Furthermore, this model resulted in a 6% increase in the number of final Pareto front solutions and a 2-fold increase in the number of feasible solutions in the initial iterations compared to the aggregated model.
Keywords

 
Alperovits, E., and Shamir, U., (1977), “Design of optimal water distribution systems”, Water Resources Research, 13(6), 885-900, https://doi.org/10.1029/WR013i006p00885.
Bahrami Chegeni, I., Riyahi, M.M., Bakhshipour, A.E., Azizipour, M., and Haghighi, A., (2025), “Developing Machine Learning models for optimal design of water distribution networks using Graph Theory-based features”, Water, 17(11), 1654, https://doi.org/10.3390/w17111654.
Creaco, E., and Franchini, M., (2012), “Fast network multi-objective design algorithm combined with an a posteriori procedure for reliability evaluation under various operational scenarios”, Urban Water Journal, 9(6), 385-399, https://doi.org/10.1080/1573062X.2012.690432.
Creaco, E., Franchini, M., and Walski, T.M., (2014), “Accounting for phasing of construction within the design of water distribution networks”, Journal of Water Resources Planning and Management, 140(5), 598-606, https://doi.org/10.1061/(ASCE)WR.1943-5452.0000358.
Creaco, E., Franchini, M., and Walski, T.M., (2015), “Taking account of uncertainty in demand growth when phasing the construction of a water distribution network”, Journal of Water Resources Planning and Management, 141(2), 04014049, https://doi.org/10.1061/(ASCE)WR.1943-5452.0000441.
Creaco, E., Franchini, M., and Walski, T.M., (2016), “Comparison of various phased approaches for the constrained minimum-cost design of water distribution networks”, Urban Water Journal, 13(3), 270-283, https://doi.org/10.1080/1573062X.2014.991330.
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T.A.M.T., (2002), “A fast and elitist multiobjective genetic algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, 6(2), 182-197, https://dio.org/10.1109/4235.996017.
Dell’Aira, F., Cancelliere, A., Creaco, E., and Pezzinga, G., (2021), “Novel comprehensive approach for phasing design and rehabilitation of water distribution networks”, Journal of Water Resources Planning and Management, 147(3), 04021001, https://doi.org/10.1061/(ASCE)WR.1943-5452.00013.
Engelhardt, M., (1999), “Development of a strategy for the optimum replacement of water mains”, Doctoral Dissertation, Department of Civil and Environmental Engineering, University of Adelaide.
Farmani, R., Walters, G.A., and Savic, D.A., (2005), “Trade-off between total cost and reliability for Anytown water distribution network”, Journal of Water Resources Planning and Management, 131(3), 161-171, https://doi.org/10.2166/hydro.2006.019b.
Farmani, R., Walters, G., and Savic, D., (2006), “Evolutionary multi-objective optimization of the design and operation of water distribution network: total cost vs. reliability vs. water quality”, Journal of Hydroinformatics, 8(3), 165-179, https://doi.org/10.1061/(ASCE)0733-9496(2005)131:3(161).
Haghighi, A., Samani, H.M., and Samani, Z.M., (2011), “GA-ILP method for optimization of water distribution networks”, Water Resources Management, 25(7), 1791-1808, https://doi.org/10.1007/s11269-011-9775-4.
Krapivka, A., and Ostfeld, A., (2009), “Coupled genetic algorithm, linear programming scheme for least-cost pipe sizing of water-distribution systems”, Journal of Water Resources Planning and Management, 135(4), 298-302, https://doi.org/10.1061/(ASCE)0733-9496(2009)135.
Lansey, K.E., Basnet, C., Mays, L.W., and Woodburn, J., (1992), “Optimal maintenance scheduling for water distribution systems”, Civil Engineering Systems, 9(3), 211-226, https://doi.org/10.1080/02630259208970650.
Minaei, A., Haghighi, A., and Ghafouri, H.R., (2019), “Computer-aided decision-making model for multiphase upgrading of aged water distribution mains”, Journal of Water Resources Planning and Management, 145(5), 04019008, https://doi.org/10.1061/(ASCE)WR.1943-5452.0001070.
Minaei, A., Abusamra, S., Hajibabaei, M., Savic, D., Zecchin, A.C., Creaco, E., and Sitzenfrei, R., (2024), “Optimized phased planning for dynamic rehabilitation of integrated municipal infrastructure”, AQUA, Water Infrastructure, Ecosystems and Society, 73(7), 1389-1405, https://doi.org/10.2166/aqua.2024.083.
Poojitha, S.N., and Jothiprakash, V., (2024), 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, 150(12), 04024055, https://doi.org/10.1061/JWRMD5.WRENG-6420.
Riyahi, M.M., Bakhshipour, A.E., and Haghighi, A., (2023), “Probabilistic warm solutions-based multi-objective optimization algorithm, application in optimal design of water distribution networks”, Sustainable Cities and Society, 91, 104424, https://doi.org/10.1016/j.scs.2023.104424.
Riyahi, M.M., Giudicianni, C., Haghighi, A., and Creaco, E., (2024), “Coupled multi-objective optimization of water distribution network design and partitioning: a spectral graph-theory approach”, Urban Water Journal, 21(6), 745-756. https://doi.org/10.1080/1573062X.2024.2352797.
Volume 11, Issue 1
Spring 2026
Pages 47-62

  • Receive Date 12 April 2025
  • Revise Date 22 August 2025
  • Accept Date 24 September 2025