Achieving sustainable water distribution through penalty‐free multi‐objective evolutionary design optimization
Authors: Kambalame Emily , Ndiritu John 
Published: December 2024

AbstractWater distribution networks are costly long‐term investments, prompting researchers to seek cost reduction and efficient design solutions using optimization techniques. In this context, the Penalty‐Free Multi‐Objective Evolutionary Algorithm (PFMOEA) is employed alongside pressure‐dependent analysis (PDA) to optimize water distribution systems (WDSs). This integrated approach facilitates a multi‐objective evolutionary search, leading to improved WDS designs. The research aimed to improve the computational efficiency of PFMOEA by using real coding, where decision variables are represented as real numbers rather than integers or binary formats. Additionally, it adjusted the allocation of feasible and infeasible solutions near the Pareto front (the boundary of optimal or least‐cost solutions) during the elitism step of the optimization process. A feasible solution was regarded as the one that meets all the pressure and flow rate requirements while an infeasible solution fails to meet these requirements. These adjustments were labeled as PFMOEA‐A, PFMOEA‐B, and PFMOEA‐C, with allocation percentages of 15% feasible and 15% infeasible solutions, 20% feasible and 10% infeasible solutions, and 30% feasible and 0% infeasible solutions, respectively. The study utilized two benchmark network problems, the two‐looped and Hanoi networks, for analysis. A comparative assessment was then conducted to evaluate the performance of the real‐coded PFMOEA in comparison to other approaches documented in the literature. The algorithm demonstrated competitive performance for the two benchmark networks by implementing real coding. The real‐coded PFMOEA achieved the novel best‐known solutions ($419,000 and $6.081 million) and a zero‐pressure deficit for the two networks, requiring fewer function evaluations than the binary‐coded PFMOEA. Additionally, by replacing 15% of the feasible solutions with infeasible ones that are close to the Pareto front with minimal pressure deficit violations, the computational efficiency of the PFMOEA was enhanced. This led to a 20% and 17% reduction in the number of function evaluations required to identify the optimal solutions for the Two‐looped network and the Hanoi network, respectively. The findings of this study aim to contribute to a more equitable and resilient water management framework. Ultimately, the insights gained will not only support the optimization of existing water distribution networks but also inform policy decisions that prioritize sustainability and resource conservation. This holistic approach will facilitate improved water security and support the overarching goal of achieving sustainable water management against the growing challenges related to climate change and urbanization.HIGHLIGHTS
PFMOEA eliminates the need for penalties through the adoption of a pressure‐dependent analysis within a multi‐objective optimization search.
Employing real coding in PFMOEA instead of binary coding enhances the computational efficiency of PFMOEA.
Retaining a small percentage of infeasible solutions near the boundary of optimal solutions during optimization also improves the computational performance of PFMOEA.