Optimization Of Water Distribution Networks Research Articles

Multi-criteria decision-making methods for optimal design of intermittent water distribution network

Abstract Multi-objective optimization of water distribution networks (WDNs) is crucial for achieving a balance between cost, equity, and reliability. The present study conducts a comparative analysis, evaluating the effectiveness of four multi-objective optimization algorithms implemented within the EPANET framework for the optimal design of three distinct WDNs taken from the literature. The networks were optimized considering three objectives: maximizing network resilience, and uniformity coefficient (CU, a measure of uniformity), alongside minimizing the cost of the network. Further, multi-criteria decision-making (MCDM) analysis is carried out, encompassing various MCDM techniques and weighting methods, to explore the sensitivity of solution rankings. In Network 1, non-dominated sorting genetic algorithm 2 (NSGA-II) produced suboptimal solutions with CU and In values below 0.4, while caRamel, multi-objective particle swarm optimization based on crowding distance (MOPSO-CD), and multi-objective evolutionary algorithm with decomposition (MOEA/D) showcased increasing CU and In values towards 1, paralleled by a rise in network cost. The performance of NSGA-II in Network 3 was unsatisfactory (CU < 0.32), while the other algorithms demonstrated satisfactory values (>0.98) for reliability and (>0.5) for CU. The findings offer valuable insights into cost-effective strategies for achieving equity in water supply without substantial impact on overall network cost. The findings of the study also underscore the sensitivity of ranking outcomes in MCDM analysis to the choice of technique and weighting method.

Circulatory system-based optimization algorithm with dynamic penalty function for optimum design of large-scale water distribution networks

Water distribution networks (WDNs) are a crucial component of urban infrastructure, and their optimization plays a vital role in minimizing construction costs. However, existing heuristic algorithms for WDN optimization often rely on specific parameters, limiting their performance and hindering their applicability to diverse network configurations, particularly in large-scale systems. To address this challenge, a novel method called circulatory system-based optimization (CSBO) is proposed, which minimizes the need for algorithm-specific parameters and achieves optimal designs across WDNs of various scale. The impact of a dynamic penalty function tailored to pressure constraints on the optimal design is also investigated. This study encompasses the optimization of the Goyang and combined gravity networks and the large-scale Balerma irrigation and Kang and Lansey networks under identical conditions. The results of the standard and dynamic CSBO approaches prove that the proposed algorithms have a superior performance, particularly in convergence rate and stability, compared to previous methods.

Correction to: Design Optimization of Water Distribution Networks with Dynamic Search Space Reduction GA

Correction to: Design Optimization of Water Distribution Networks with Dynamic Search Space Reduction GA

Design Optimization of Water Distribution Networks with Dynamic Search Space Reduction GA

Design Optimization of Water Distribution Networks with Dynamic Search Space Reduction GA

Performance optimization of water distribution network using meta-heuristic algorithms from the perspective of leakage control and resiliency factor (case study: Tehran water distribution network, Iran)

In the context of sustainable development and considering water distribution networks (WDNs) as vital infrastructure systems, designing a resilient and efficient network to deliver water demand to consumption nodes while adhering to engineering standards is of utmost importance. This study specifically focused on the complex structure of the north-west Tehran's WDN, encompassing 1124 pipes totaling 92552 m in length, along with four gravity reservoirs and 988 nodes. Genetic Algorithm (GA) and Nonlinear Programming (NLP) were employed as optimization techniques to enhance the WDN by minimizing leakage and improving its resilience. The study involved determining leakage coefficients for nodes using measured data and GA. Subsequently, the WDN was optimized by defining an objective function, constraints, and decision variables using both GA and NLP. The results demonstrated the superiority of GA in terms of pressure reduction, achieving a significant decrease of 23.7%. Additionally, GA outperformed NLP in enhancing the resiliency index, underscoring its effectiveness in optimizing the network's performance and ensuring its robustness against potential disruptions.

Water Distribution Network Optimization Model with Reliability Considerations in Water Flow (Debit)

Water distribution networks (WDNs) are defined as the planning for the development, distribution, and utilization of water resources. The main challenge of WDNs is to preserve limited water resources while providing effective benefits from these resources in accordance with environmental considerations. Water distribution networks use hydraulic components to connect water resources to consumers. The diameter of each pipe, the layout of the pipe network, and the total length of pipes all contribute to the most effective layout for a water distribution system. This study considers the assurance that the flow (discharge) of water is in accordance with what is expected, with such aspects apt to be described as a particular form of reliability. As a result, this study proposes a stochastic optimization model with non-linear probability constraints for overcoming the challenges of water distribution networks while taking water flow reliability into account. The pressure drop equation causes the non-linear shape. The stochastic model of the opportunity constraint is changed to a deterministic multi-objective model using an approach based on integer programming and sample averaging to solve the resulting model. The direct search approach (neighbourhood search) is then applied to tackle the integer part.

Application of Strength Pareto Evolutionary Algorithm II in Multi-Objective Water Supply Optimization Model Design for Mountainous Complex Terrain

Water distribution networks (WDN) model optimization is an important part of smart water systems to achieve optimal strategies. WDN optimization focuses on the nonlinearity of the discharge head loss equation, the availability of discrete properties of pipe sizes, and the conservation of constraints. Multi-objective evolutionary algorithms (MOEAs) have been proposed and successfully applied in the field of WDN design optimization. Previous studies have focused on comparing the optimization effects of algorithms in water distribution networks, ignoring the problems of unbalanced pressure distribution and water hammer at the nodes of the pipe network caused by the complex terrain in mountainous areas. In this paper, a multi-objective water supply optimization model that integrated cost, reliability, and water quality was established for a mountainous WDN in real engineering. The method of traversing the nodes to solve the water age was introduced to find a more scientific and practical water age solution model, with setting the weight function to evaluate the water age of the water supply model comprehensively. Strength Pareto Evolutionary Algorithm II (SPEA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) were adopted to optimize the WDN design model in the mountainous complex terrain. The significance levels of the number of Pareto solutions (NOPS) and running time are 0.029 and 0.001, respectively, indicating that the two algorithms have significant differences. Compared to NSGA-II, SPEA-II has a better convergence rate and running time in multi-objective water supply optimization design. The solution set distribution of SPEA-II is more concentrated than that of NSGA-II, also the numerical value is better. The number of SPEA-II optimization schemes is larger and the scheme is more effective. Among them, the Pareto solution set of SPEA-II can obtain more desirable optimization results on cost, reliability index (RI) and water age. In summary, the study provides valuable information for decision makers in WDN with complex terrain.

Pengoptimalan Jaringan Pipa Primer PDAM Tirtanadi Cabang Tuasan Dengan Menggunakan Algoritma Kruskal

Kruskal's algorithm in searching for minimum spanning trees can be applied to pipelines installed at the location of PDAM Tirtanadi Tuasan where problem identification starts with the water discharge reaching the consumer is small but the discharge flowing from the reservoir is sufficient, so this research is used as a solution to this problem and also as an optimization of the clean water distribution network in the Tirtanadi Regional Drinking Water Company (PDAM) of the Tuasan Branch with the intention of cutting the direction of the pipe flow to overcome this problem. The data obtained from PDAM Tirtanadi Tuasan Branch is in the form of a floor plan and formed into a weighted graph. After the data is obtained, then it is calculated manually that the length of the installed water pipe is 32,645 m with 86 vertices and 100 edges, then the pipe length is represented as a set of paths and the pipe connection ends are represented as nodes. The pipe length obtained using Kruskal's algorithm and inspection of iterations using the QM for windows software is 22,095 m, with 86 vertices and 85 edges. So, using the Kruskal Algorithm and the help of the QM for windows software, the difference in pipe length obtained is 10,610 m.

Advances in Assessing the Reliability of Water Distribution Networks: A Bibliometric Analysis and Scoping Review

The reliability of Water Distribution Networks (WDNs) is a critical topic that has been explored by many researchers over the last few decades. Nevertheless, this research domain has gained momentum in the last decade. WDN reliability was addressed in the literature using different approaches and techniques. This study presents a bibliometric analysis and scoping review of the progress and gaps in research on WDN reliability. The analysis was performed on a total of 347 articles from 2000 to 2022, which were retrieved from the SCOPUS database. The bibliometric analysis identified trends and gaps by focusing on articles output, citation network of articles, co-authorship and collaboration analysis, co-citation, and clustering analysis. In addition, coupling keywords analysis with thematic maps analysis helped identify basic, niche, emerging, and declining research themes in the field of WDN reliability. Three major research themes were found: WDN optimization, reliability assessment, and consideration of GHG emissions and energy-cost for WDN expansion. Reliability surrogate measures (RSMs) were found to be one of the most widely researched topics in this field. Performance assessment of various RSMs, as well as the consideration of energy and cost for WDN design and expansion stood out as the emerging trends for future research in the field of WDN reliability.

A Two-Stage Swarm Optimizer With Local Search for Water Distribution Network Optimization.

Evolutionary computation (EC) algorithms have been successfully applied to the small-scale water distribution network (WDN) optimization problem. However, due to the city expansion, the network scale grows at a fast speed so that the efficacy of many current EC algorithms degrades rapidly. To solve the large-scale WDN optimization problem effectively, a two-stage swarm optimizer with local search (TSOL) is proposed in this article. To address the issues caused by the large-scale and multimodal characteristics of the problem, the proposed algorithm divides the optimization process into an exploration stage and an exploitation stage. It first finds a promising region of the search space in the exploration stage. Then, it searches thoroughly in the promising region to obtain the final solution in the exploitation stage. To search effectively the huge search space, we propose an improved level-based learning optimizer and use it in both the exploration and exploitation stages. Two new local search algorithms are proposed to further improve the quality of the solution. Experiments on both synthetic benchmark networks and a real-world network show that the proposed algorithm has outperformed the state-of-the-art metaheuristic algorithms.

Probabilistic warm solutions-based multi-objective optimization algorithm, application in optimal design of water distribution networks

Single objective optimization of water distribution networks (WDNs) based on construction costs reduces system resiliency. Thus, researchers have developed various optimization frameworks to maximize system resilience while minimizing construction costs during the last decade. They generally utilized population-based meta-heuristic algorithms. These algorithms start with random populations (initial cold solutions), so they need high computational time to converge to the optimal solutions. This paper aims to reduce search space by introducing prebaked initial or warm solutions based on the hydraulic properties of WDNs which are discharge variance and dissipated power function. After generating initial warm solutions, several probabilistic models are used to bring them closer to the global optimal Pareto front and increase their diversity. The proposed approach is used to optimize the design of two well-known benchmarks, Alprovits and Hanoi, and a real-world large-scale WDN. Results show that using warm solutions as the initial population reduces time, the number of iterations, and fitness evaluations to reach a certain accuracy level, more than two times on average for the benchmarks. Also, results show that the proposed method reduces the average construction costs by 45% compared to the traditional optimization method in the same execution time for real-world WDN.

Isolation Valve Placement Optimization of Water Distribution Networks to Reduce Vulnerability

Due to the growing pace of urbanization and the rapid expansion of the population, the utilities nowadays are facing a more challenging task than ever before, to maintain the functionality of their massive Water Distribution Networks. In this paper, three different techniques are presented for the maximization of network robustness against random pipe-bursts. This paper analyses the vulnerability of segments of WDNs from the viewpoint of the consumers that is the product of the failure rate and the relative demand loss. Topological parameters could approximate the vulnerability. During the investigation, 27 real-life WDNs were analyzed from the region of Western Hungary. In two networks, a complete isolation valve replacement optimization is presented using these low-cost topological parameters as fitness functions. It is proved that by rearranging the isolation valves of the WDN, using a standard genetic algorithm and a fast-evaluated fitness function, the nature of the vulnerability distribution can be changed to a more favorable one. This means that it is possible to increase the robustness of a WDN even without using a calibrated hydraulic model; since these topological parameters can be extracted from simple databases.

Seismic and Economic Optimization of Water Distribution Networks Using Entropy and Ant Colony Algorithm

Seismic and Economic Optimization of Water Distribution Networks Using Entropy and Ant Colony Algorithm

Optimization of water distribution networks using hybrid BBO-IWO algorithm

ABSTRACT Due to the increasing population and the pollution of existing water resources because of various factors, the need for water in the world is increasing. This requires building additional water distribution systems along with rehabilitation of existing systems. The cost of transmission and distribution constitutes more than half of the total cost of water supply systems. For this reason, by the optimum design of pipeline systems, the cost of water supply can be reduced. In this study, the optimization of pipe diameters in three networks, Two- Loop, Hanoi and GoYang, was carried out by a combination of two metaheuristic algorithms, namely Biogeography based optimization (BBO) and invasive weed optimization (IWO) under the same constraints. In addition, the Combined Gravity Network was successfully optimized with the current method for the first time in the literature.

A new multi-objective evolutionary algorithm for the optimization of water distribution networks

Abstract This work introduces a new bi-objective optimization model for the design of a water distribution network (WDN). Reliability and design cost are two contradicting objectives that are optimized. The evolutionary technique multi-objective (MO) Jaya, hereafter referred as MO-JAYANET, is developed for the optimal design of WDN. EPANET is used as a hydraulic network solver in this study. The concept of constraint violation, dominance, non-dominance and crowding distance is used to develop MO-JAYANET. As the Jaya algorithm is a parameter-less technique, and with the concept of constraint dominance involved in the MO model, the penalty parameter required to penalize the non-feasible solution is also dropped. This makes MO-JAYANET a completely parameter-less technique, requiring no tuning at all. MO-JAYANET is applied on two benchmark networks from the literature using three different reliability indices that are Resilience Index, Network Resilience Index, and Modified Resilience Index. MO-JAYANET is found to be very easy and efficient for WDN optimization. The present work obtains a smooth Pareto Front (PF) that overlaps the best-known PF. The maximum reliability diameters obtained by the MO-JAYANET for the three indices are also simulated for both hydraulic and mechanical failures under different scenarios to identify a better-performing index.

Multi-objective optimization of water distribution networks based on non-dominated sequencing genetic algorithm.

Due to the conflict between reducing cost and improving water supply performance, how to select the appropriate pipe diameter is a current challenge. In this paper, the problem is transformed into a multi-objective optimization problem, and the evolutionary genetic optimization algorithm is used to solve the problem to determine the optimal selection of pipe diameter in the pipe network. To solve this problem, the evolutionary genetic algorithm was coupled with EPANET hydraulic simulation software in Python environment. The results show that NSGA-II and NSGA-III perform better in two typical case tests. Moreover, the increase of the objective functions will lead to an increase in the amount of data in the optimal solution set, and will affect the optimal value of each objective function. That shows that the balance between the economy and reliability of water supply can be successfully found by coupling the hydraulic model and the multi-objective optimization algorithm, which can provide an auxiliary decision for enterprises.

Cost Optimization of Water Distribution Networks without Storage Tanks

Cost Optimization of Water Distribution Networks without Storage Tanks

Principal Component Based Sampling for the Continuous Maintenance of Hydraulic Models

The calibration and continuous maintenance of hydraulic models is essential for the optimisation, planning and management of water distribution networks (WDNs). This process requires model fitting against multiple hydraulic states. However, when extended time series of hydraulic data are considered, it is essential to know which hydraulic states to use for model fitting as too many become computationally impractical. This paper presents a novel principal component analysis (PCA) based sampling method, which evaluates the significance of newly observed hydraulic data to be included in the model calibration and maintenance. A framework is presented, which allows for different sized batches of hydraulic data to be utilised. This enables both model calibration on extended time series of data, or model calibration and maintenance with continuous data. An extensive experimental program was conducted to investigate the performance of the proposed framework with different sampling methods compared to other conventional approaches. The results demonstrate that the presented sampling methods can maintain and improve model prediction accuracy both for retrospective and concurrent implementations when used with extended time series data, which capture different hydraulic states. The hydraulic model of the operational WDN used in this study and the acquired hydraulic data are provided as supplementary data to facilitate reproducible research.

Improvement of the performance of NSGA-II and MOPSO algorithms in multi-objective optimization of urban water distribution networks based on modification of decision space

Water distribution networks require huge investment for construction. Involved people, especially researchers, are always seeking to find a way for decreasing costs and achieving an efficient design. One of the main factors of the network design is the selection of proper diameters based on costs and deficit of flow pressure and velocity in the network. The reduction in construction costs is accomplished by minimizing the diameter of network pipes which leads to the pressure drop in the network. Supplying proper pressure in nodes is one of the important design principles, and low pressure will not provide a complete water supply at the consumption site. Therefore, in this research, the problem of optimization in several sample networks was defined with the objectives of cost minimization and minimization of pressure deficit in the whole network. The EPANET software was used for hydraulic analysis of sample networks, and the multi-objective optimization process was performed by coding NSGA-II and MOPSO algorithms in the MATLAB software environment and linking them to EPANET. The cost function was initially defined only by considering the relationship between cost and diameter and the length of pipes, and in the next definition, the cost resulted by violation of the allowable pressure range was added to this function In both cases, the schedule for achieving the optimal answer was executed. The results showed that these algorithms have a high ability to find optimal solutions and are able to optimize the network in terms of cost and pressure by finding the appropriate pipe diameter. The time for reaching convergence was reduced by considering the cost of violation of the allowable pressure limits significantly and the optimal answer is obtained in a small number of repetitions. In NSGA-II and MOPSO algorithms in two-looped network with 20 and 30 iterations and run time of 0.66 and 0.8 s, respectively, and in Lansey network with 150 and 250 iterations and run time of 5.7 and 9.5 s, the optimal solutions were obtained.

Resilience-based post-earthquake recovery optimization of water distribution networks

This paper proposes a resilience-based pipe optimal recovery model of water distribution networks (WDNs). First, the time-dependent consumer demands are simulated to reflect the real hydraulic status of WDNs during post-earthquake recovery. Herein, three kinds of consumers are incorporated, including shelter, hospital, and ordinary users. Second, to reflect the asynchronous supply plans of crew and equipment, the phased supply plan of the two types of recovery resources are modeled respectively. Third, the ground motion filed is constructed by the attenuation law, by which the damage conditions of WDN can be descript in detail. By the comprehensive consideration of hydraulic analysis, pipe damage, pipe recovery, and ground motion field, the recovery strategies of critical and general pipes are optimized by heuristic genetic algorithm. This framework is demonstrated taking the Mianzhu WDN as an example. Results show the system satisfaction degree curve has multi-stage characteristics caused by the time-dependent consumer demands and recovery resources supply schedules. The effectiveness of the methodology is validated by comparing different recovery strategies. Meantime, different recovery resource supply schedules are analyzed to reveal the impacts on seismic resilience of WDNs.