Evaluation of decision variable vector modeling methods in multiphase optimal design of water distribution networks

Riyahi, Mohammad Mehdi; E. Bakhshipour, Amin; Giudicianni, Carlo; Haghighi, Ali; Creaco, Enrico

doi:10.22112/jwwse.2025.515624.1450

Evaluation of decision variable vector modeling methods in multiphase optimal design of water distribution networks

Articles in Press

Authors

Mohammad Mehdi Riyahi ¹

Amin E. Bakhshipour ²

Carlo Giudicianni ³

Ali Haghighi ²

Enrico Creaco ³

¹ Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz, Ahvaz 61357-83151, Iran

² Department of Urban Water Management, University of Kaiserslautern, Paul-Ehrlich-Straße 14, Kaiserslautern D- 67663, Germany

³ Dipartimento di Ingegneria Civile e Architettura, Università Degli Studi di Pavia, 27100 Pavia, Italy

10.22112/jwwse.2025.515624.1450

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 demonstrate that the disaggregated model leads to a 10% improvement in the final Pareto front solutions compared to the aggregated model. Furthermore, this model results 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

Water distribution networks

multi-objective optimization

static and dynamic design methods

multi-phase method