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17 pages, 2479 KiB

Open AccessArticle

Improving Multi-Objective Optimization Methods of Water Distribution Networks

by Rahel Amare Kidanu, Maria Cunha, Elad Salomons and Avi Ostfeld

Water 2023, 15(14), 2561; https://doi.org/10.3390/w15142561 - 12 Jul 2023

Cited by 3 | Viewed by 1500

Abstract

Water distribution network design is a complex multi-objective optimization problem and multi-objective evolutionary algorithms (MOEAs) such as NSGA II have been widely used to solve this optimization problem. However, as networks get larger, NSGA II struggles to find the diverse and uniform solutions [...] Read more.

Water distribution network design is a complex multi-objective optimization problem and multi-objective evolutionary algorithms (MOEAs) such as NSGA II have been widely used to solve this optimization problem. However, as networks get larger, NSGA II struggles to find the diverse and uniform solutions that are critical in multi-objective optimization. This research proposes an improved version of NSGA II that uses three new-generation methods to target different regions of the Pareto front and thus increase the number of solutions in critical regions. These methods include saving an archive, local search around extreme and uncrowded Pareto front, and local search around the knee area of the Pareto front. The improved NSGA II is tested on benchmark networks of different sizes and compared to the best-known Pareto front of the networks determined by MOEAs. The results show that the proposed algorithm outperforms the original NSGA II in terms of broadening the Pareto front solution range, increasing solution density, and discovering more non-dominated solutions. The improved NSGA II can find solutions that cover all parts of the Pareto front using a single algorithm without increasing computational effort. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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16 pages, 3773 KiB

Open AccessArticle

Robust Optimal Booster Disinfectant Injection in Water Systems under Uncertainty

by Sriman Pankaj Boindala, G. Jaykrishnan and Avi Ostfeld

Water 2023, 15(9), 1777; https://doi.org/10.3390/w15091777 - 05 May 2023

Viewed by 1282

Abstract

Water distribution systems (WDSs) require high-quality water for safe consumption. To achieve this, disinfectants such as chlorine are often added to the water in the system. However, it is important to regulate the levels of chlorine to ensure they fall within acceptable limits. [...] Read more.

Water distribution systems (WDSs) require high-quality water for safe consumption. To achieve this, disinfectants such as chlorine are often added to the water in the system. However, it is important to regulate the levels of chlorine to ensure they fall within acceptable limits. The higher limit is to control disinfection by-products, while the lower limit is established to guarantee that the water is free of organic contaminants. The rate at which chlorine reacts within the pipes is affected by various factors, such as the type of pipe, its age, the pH level of the water, the temperature, and others. This variability makes it challenging to accurately model water quality in WDSs, which can impact the optimal rate of booster injection. To address the uncertainty in the chlorine reaction rate, the current research proposes a robust counterpart reformulation of the booster chlorination scheduling problem, which considers the chlorination reaction rate as uncertain. The proposed reformulation was tested on two benchmark WDSs and analyzed with a thorough sensitivity analysis. The results showed that as the size of the uncertainty set increased, the injection mass also increased. This reformulated approach can be applied to any WDS and provides a way to obtain optimal scheduling within the desired protection levels. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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20 pages, 4640 KiB

Open AccessArticle

Water Distribution Network Partitioning Based on Complex Network Theory: The Udine Case Study

by Federico Spizzo, Giovanni Venaruzzo, Matteo Nicolini and Daniele Goi

Water 2023, 15(8), 1621; https://doi.org/10.3390/w15081621 - 21 Apr 2023

Cited by 1 | Viewed by 1852

Abstract

Water Distribution Network Partitioning (WDNP), which is the partitioning of the existing Water distribution Network (WDN) into smaller and more homogeneous portions called District Metered Areas (DMAs), is an effective strategy that allows water utilities to improve network management through water balance, pressure [...] Read more.

Water Distribution Network Partitioning (WDNP), which is the partitioning of the existing Water distribution Network (WDN) into smaller and more homogeneous portions called District Metered Areas (DMAs), is an effective strategy that allows water utilities to improve network management through water balance, pressure control, water loss detection, and protection from contamination. The partitioning is realized physically, closing the pipes between two different districts, or virtually, installing flow meters which measure the districts inflow and outflow. Pipe closures lead to a considerable network performance worsening, reducing minimum pressure, resilience, and redundancy; on the other hand, flow meters allow us to avoid these issues but involve a higher investing cost. Hence, the DMAs’ definition could become a hard task because both network performance and maximum investing cost must be respected. This paper presents the application of an optimization approach, based on complex network theory, coupled with an optimization technique based on genetic algorithms (GA). The methodology, implemented in Python environment, consists of a clustering phase carried out with two different algorithms (Girvan–Newman and spectral clustering) and a dividing phase which defines whether a gate valve or a flow meter should be installed in a pipe. The last phase is fulfilled with the GA which allows us to optimize one or more objectives in order to minimize the cost and maximize the network performance. The methodology has been applied on the Udine water distribution system, whose hydraulic model has been calibrated with a recent measure campaign. The results produced with the different clustering algorithms and objective functions have been compared to show their pros and cons. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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15 pages, 1658 KiB

Open AccessFeature PaperArticle

Robust Optimal Operation of Water Distribution Systems

by Gal Perelman, Avi Ostfeld and Barak Fishbain

Water 2023, 15(5), 963; https://doi.org/10.3390/w15050963 - 02 Mar 2023

Cited by 3 | Viewed by 1785

Abstract

The operation of water distribution systems (WDS) is an energy-intensive process, which is subject to constraints such as consumer demands, water quality, and pressure domains. As such, tracing an operation policy in which constraints are met while energy costs are minimized, is a [...] Read more.

The operation of water distribution systems (WDS) is an energy-intensive process, which is subject to constraints such as consumer demands, water quality, and pressure domains. As such, tracing an operation policy in which constraints are met while energy costs are minimized, is a foremost objective for water utilities. Given the inherent uncertainties in WDS operation and the importance of supply continuity, it is essential to find an operational strategy that is robust against a wide range of circumstances. One promising approach for optimization under uncertainty is robust optimization (RO), which assures a robust (feasible) solution to realizations of the uncertain parameters, within predefined bounds. This study presents an RO-based method for optimizing pump scheduling under uncertainties of consumer demands and pumping costs. The method can capture various types of correlations between the uncertain parameters, thus better reflecting the uncertain nature of WDS operation. The developed methodology is demonstrated in two case studies with different levels of complexity. The impacts of uncertainty levels and correlation coefficients are analyzed to demonstrate their implications on operation policy. The results show the advantages of using RO with tradeoffs between costs and constraints satisfaction. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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14 pages, 2491 KiB

Open AccessFeature PaperArticle

Optimization of Water Network Topology and Pipe Sizing to Aid Water Utilities in Deciding on a Design Philosophy: A Real Case Study in Belgium

by Ina Vertommen, Djordje Mitrović, Karel van Laarhoven, Pieter Piens and Maarten Torbeyns

Water 2022, 14(23), 3973; https://doi.org/10.3390/w14233973 - 06 Dec 2022

Cited by 4 | Viewed by 3152

Abstract

Numerical optimization is gradually finding its way into drinking water practice. For successful introduction of optimization into the sector, it is important that researchers and utility experts work together on the problem formulation with the water utility experts. Water utilities heed the solutions [...] Read more.

Numerical optimization is gradually finding its way into drinking water practice. For successful introduction of optimization into the sector, it is important that researchers and utility experts work together on the problem formulation with the water utility experts. Water utilities heed the solutions provided by optimization techniques only when the underlying approach and performance criteria match their specific goals. In this contribution, we demonstrate the application of numerical optimization on a real-life problem. The Belgian utility De Watergroep is looking to not only reinforce its distribution networks but to also structurally modify the network’s topology to enhance the quality of water delivered in the future. To help the utility explore the possibilities of these far-reaching changes in the most flexible way possible, an optimization problem was formulated to optimize topology and pipe sizing simultaneously for the distribution network of a Belgian city. The objective of the problem is to minimize the volume of the looped network and thereby work towards a situation where most of the customers are fed by branched extremities of the network. This objective is constrained by pressure and fire flow requirements and thresholds on the number of customers on the branched sections. The requirements for continuity of supply under failure scenarios are guaranteed by these constraints, as verified in the final solution. The results of the optimization process show that it is possible to design a network which is 18.5% cheaper than the currently existing network. Moreover, it turns out the—previously completely meshed—topology can be restructured so that 67% of the network length is turned into branched clusters, with a meshed superstructure of 33% of the length remaining. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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22 pages, 5114 KiB

Open AccessArticle

On the Evolution of the Optimal Design of WDS: Shifting towards the Use of a Fractal Criterion

by Juan Saldarriaga, Camilo Salcedo, María Alejandra González, Catalina Ortiz, Federico Wiesner and Santiago Gómez

Water 2022, 14(23), 3795; https://doi.org/10.3390/w14233795 - 22 Nov 2022

Cited by 1 | Viewed by 1994

Abstract

Several researchers have proposed methodologies for addressing the problem of designing optimal water distribution systems. Metaheuristic approximations are studied the most due to the vast solution space. In search of reducing computational time, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) has been tested [...] Read more.

Several researchers have proposed methodologies for addressing the problem of designing optimal water distribution systems. Metaheuristic approximations are studied the most due to the vast solution space. In search of reducing computational time, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) has been tested with retrofitting from the Optimal Power Use Surface (OPUS) methodology. A previous study demonstrates how OPUS significantly improves the results since it seeks to reduce energy losses in the network, in order to approximate minimum-cost designs using fewer hydraulic executions. However, more research is still needed to determine applicable hydraulic criteria that allow an enhanced comprehension of optimal designs. Therefore, this paper aims to understand the characteristics of near-optimal solutions using designs from the retrofitted OPUS/NSGA-II Pareto fronts of four distinct networks (Hanoi, Balerma, Fossolo, and Modena). Moreover, fractal characteristics of the networks’ energy dissipation, flow, and diameter distribution have been analyzed for this purpose. In this way, outcomes suggest that the hydraulic gradient line box dimension in optimal designs approaches a value of two, demonstrating that objects resemble a single-plane surface. These promising results propose fractal analysis as a practical design criterion due to its hydraulic significance and low computational cost. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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14 pages, 2430 KiB

Open AccessArticle

Reliability of a Contamination-Detection Sensor Network in Water Distribution Systems during a Cyber-Physical Attack

by Gopinathan R. Abhijith, Elad Salomons and Avi Ostfeld

Water 2022, 14(22), 3669; https://doi.org/10.3390/w14223669 - 14 Nov 2022

Cited by 1 | Viewed by 1501

Abstract

The vastness of water distribution systems (WDS) makes them vulnerable to exposure to different types of accidental/intentional contamination. Although most such contamination events that occurred in the recent past were accidental, criminal intent was involved in a few. Considering the accessibility of WDS [...] Read more.

The vastness of water distribution systems (WDS) makes them vulnerable to exposure to different types of accidental/intentional contamination. Although most such contamination events that occurred in the recent past were accidental, criminal intent was involved in a few. Considering the accessibility of WDS and the potentially harmful outcomes of drinking-water contamination, online water-quality monitoring sensors are typically positioned in selected locations throughout WDS as a preventive strategy. These sensors, once positioned, communicate over a cyber-infrastructure layer and are liable to cyber-physical attacks—the sensor and/or its communication system becoming compromised or the sensor network becoming malfunctioned such that part of its components is deactivated. However, the sensor network placement state-of-the-art has thus far overlooked these cyber-physical attack scenarios. The current study attempts to overcome this limitation in the state-of-the-art by developing and demonstrating a methodology for evaluating the impact of a cyber-physical attack on a sensor network, compromising its functionality partially. Our proof-of-concept, using a simple network and a straightforward cyber-physical attack scenario, has revealed the vast potential of examining the performance of sensor networks under accidental/intentional malfunctioning and providing valuable information for decision makers in water utilities and regulators. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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20 pages, 2370 KiB

Open AccessArticle

Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems

by Qi Zhao, Wenyan Wu, Angus R. Simpson and Ailsa Willis

Water 2022, 14(20), 3276; https://doi.org/10.3390/w14203276 - 17 Oct 2022

Cited by 5 | Viewed by 2179

Abstract

Hydraulic models of water distribution systems (WDSs) need to be calibrated, so they can be used to help to make informed decisions. Usually, hydraulic model calibration follows an iterative process of comparing the simulation results from the model with field observations and making [...] Read more.

Hydraulic models of water distribution systems (WDSs) need to be calibrated, so they can be used to help to make informed decisions. Usually, hydraulic model calibration follows an iterative process of comparing the simulation results from the model with field observations and making adjustments to model parameters to make sure an acceptable level of agreement between predicted and measured values (e.g., water pressure) has been achieved. However, the manual process can be time-consuming, and the termination criterion relies on the modeler’s judgment. Therefore, various optimization-based calibration methods have been developed. In this study, three different optimization methods, i.e., Sequential Least Squares Programming (SLSQP), a Genetic Algorithm (GA) and Differential Evolution (DE), are compared for calibrating the pipe roughness of WDS models. Their performance is investigated over four different decision variable set formulations with different levels of discretization of the search space. Results obtained from a real-world case study demonstrate that compared to traditional engineering practice, optimization is effective for hydraulic model calibration. However, a finer search space discretization does not necessarily guarantee better results; and when multiple methods lead to similar performance, a simpler method is better. This study provides guidance on method and formulation selection for calibrating WDS models. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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Review

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17 pages, 912 KiB

Open AccessReview

A Review of Sources of Uncertainty in Optimization Objectives of Water Distribution Systems

by Graeme Dandy, Wenyan Wu, Angus Simpson and Michael Leonard

Water 2023, 15(1), 136; https://doi.org/10.3390/w15010136 - 30 Dec 2022

Cited by 6 | Viewed by 2387

Abstract

Many studies have applied optimization to the planning, design, rehabilitation or operation of water distribution systems. Recent reviews of the research literature in this area have identified hundreds of papers that address these topics. The objectives considered include variables measuring direct impact of [...] Read more.

Many studies have applied optimization to the planning, design, rehabilitation or operation of water distribution systems. Recent reviews of the research literature in this area have identified hundreds of papers that address these topics. The objectives considered include variables measuring direct impact of the system such as cost, energy, greenhouse gas emissions, as well as performance variables such as pressure deficit and system reliability. Very few of these studies have considered the effects of the various sources of uncertainty on the objectives considered. The sources of uncertainty include model related uncertainty such as uncertainty in model structure and parameters (e.g., pipe roughness and chemical reaction rates for water quality studies), data related uncertainty such as uncertainty in water demand due to natural variability in the short-term or population growth and/or climate change in the long-term, and human related uncertainty such as lack of knowledge about the physical network as well as modelling errors. This paper is aimed at reviewing the relative importance of these various sources of uncertainty on the key optimization objectives. It also summarizes the key literature in this area and identifies areas where there have been few publications. Full article

(This article belongs to the Special Issue Optimization Studies for Water Distribution Systems)

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