Design Of Water Distribution Networks Research Articles

Pareto-optimal design of water distribution networks: an improved graph theory-based approach

Abstract One of the main drawbacks of using evolutionary algorithms for the multi-objective design of water distribution networks (WDNs) is their computational inefficiency, particularly for large-scale problems. Recently, graph theory-based approaches (GTAs) have gained attention as they can help with the optimal WDN design (i.e., determining optimal diameters). This study aims to extend a GTA to further improve the quality of design solutions. The GTA design is based on a customized metric called ‘demand edge betweenness centrality’, which spatially distributes nodal demands through the weighted edges of a WDN graph and provides an estimation of water flows. Assigned edge weights can be constant (i.e., static) or modified iteratively (i.e., dynamic) during the design process, leading to different flow estimations and alternative design options. Three hydraulic-inspired dynamic weights are developed in this study to better reproduce hydraulic behavior and, consequently, find better solutions. Additionally, this work proposes a framework for the optimal design of multi-source WDNs and provides guidelines for obtaining near-optimal solutions in such networks. A comparative study between GTAs and evolutionary optimizations confirms the efficiency of the improved GTA in providing optimal/near-optimal solutions, especially for large WDNs, with a runtime reduction of up to seven orders of magnitude.

Multi‐Objective Optimization Models for the Design of Water Distribution Networks by Exploring Scenario‐Based Approaches

AbstractDemand in a water distribution network (WDN) is an aleatory variable, owing to the unpredictable behaviors of water users. Therefore, it is one of the main reasons for uncertainty in the design of this infrastructure. The increasing number of water demand data sets offers opportunities to improve the traditional deterministic design approaches of WDNs by combining statistical and optimization methods. Robust optimization (RO) takes demand uncertainty into account by studying solutions that perform well under any possible demand scenario, that is, any possible realizations of this variable in the lifetime of a WDN. The right choice of scenario is therefore essential to ensure the reliability of the designed network. This paper presents a statistical methodology for generating scenarios to be used to solve a robust design optimization problem. It involves three steps: (a) descriptive analytics of historical data to derive the marginal distributions of peak hour demand in each node of the WDN, (b) generation of a very large number of snapshots by stratified sampling from the correlated marginal distributions of nodal peak demand, (c) generation of the peak demand scenarios by reducing the number of snapshots. Two heuristic techniques are proposed to reduce the number of snapshots, and for each of them, two different numbers of scenarios are derived. Two multi‐objective RO models are solved: the first model includes cost minimization and a mean‐variance Generalized Resilience and Failure index maximization objectives, and the second one additionally considers the minimization of the maximum undelivered demand, formalized using a regret function.

Hybrid Optimization Algorithms of Firefly with GA and PSO for the Optimal Design of Water Distribution Networks

A novel two-hybrid optimization model of particle swarm optimization (FAPSO) and firefly algorithm with genetic algorithm (FAGA) are introduced to improve the performance of the conventional firefly algorithm for the least cost design of water distribution networks. The performance of the models is tested through application to three of the well-known benchmark networks available in the literature and also to the real case study of the El-Mostakbal City network, Ismailia, Egypt. The performance of the different algorithms was determined by evaluating the minimum, maximum, mean and standard deviation of costs, the function evaluation number, the consumed computational time for 1000 evaluations and the success rate calculated using the fuzzy logic concept for different optimal solutions slightly greater than the known optimal solution (by about 1.0% and 2.0%) were utilized for testing the convergence and search capabilities of the models. It was found that the FAGA model is superior to the standard firefly and FAPSO models in exploring the search space, exploiting the promising areas and convergence to the optimal solution and can be considered as a reasonable optimization technique for the management of water distribution networks.

Optimal Design of Water Distribution Network Using Improved Artificial Bee Colony Algorithm

Optimal Design of Water Distribution Network Using Improved Artificial Bee Colony Algorithm

Optimal design and cost analysis of water distribution networks based on pressure-dependent leakage using NSGA-II

Leakage from water distribution networks (WDNs) is inevitable. Therefore, during design a WDN, engineers add a percentage of each nodal water demand as leakage discharge to total node demand. The amount of leakage depends on the pressure, which is not known at the design stage. Considering a constant percentage of node demand in lieu of its leakage makes the problem worse. In this study, the effect of leakage on the optimal WDN design was investigated by developing the matrix form of the gradient algorithm while accounting for leakage using the pressure-dependent model. Non-dominated genetic algorithm version II (NSGA-II) was used as the optimization engine with two objectives which includes minimizing the network construction cost and minimizing the total network pressure deficiency. Two well-known two- and three-loop WDNs in literature were studied. The results indicated that the pressure-dependent leakage varies between 12.9 and 29.44% of the node demand while the network construction cost stays the same if compared with the fixed percentage leakage model, and the construction cost would increase by 17–31%, if leakage is not accounted for. This is expected the optimized diameters and hydraulic characteristics of the networks being affected by the leakage calculation method.

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.

Multiobjective design of water distribution networks using modified NSGA-II algorithm

Abstract Optimally designed water distribution networks (WDNs) make engineers’ tasks difficult due to various challenges like non-linearity between head-loss and flow, commercially available distinct diameters, combinatorial, nondeterministic polynomial-time hard problems and a large number of decision variables. This paper develops a new hybrid NSGA-II algorithm augmented with a random multi-point crossover operator and a local search denoted by RLNSGA-II to design the multiobjective WDN. The efficiency of the proposed algorithm (RLNSGA-II) is tested on three benchmark problems, namely New York, Hanoi and Balerma networks. The results obtained are compared with the best-known algorithms available in the literature. The results have shown that the proposed algorithm RLNSGA-II has found better converged and distributed solutions for all three representative benchmark problems considered in the literature consistently and evidently when compared with the best-known approximation of solutions published. Furthermore, as the complexity of the WDN increases, its advantages over other algorithms become more significant.

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.

Parallel evolutionary algorithm for Water Distribution Network Design, using the Masters–Students model in distributed environment

The Water Distribution Networks Design Problem study is widespread in the scientific community due to its practical applicability. In this work, a sequential evolutionary algorithm has been designed, developed, and successfully applied to solve small and medium instances; it has been called the Evolutionary Algorithm for Water Distribution Network Design Problem. This algorithm is executed in centralized environments and can perfectly solve these instances in less than minutes. For large-scale real-world instances, the Evolutionary Algorithm has been adapted to work in distributed environments by using a novel parallel model, also proposed in this work, called the Masters–Students​ model. This model has been used for designing, developing, and implementing the resulting parallel evolutionary algorithm, named PEA-WDND. The Evolutionary Algorithm would last for days in the case of real-world instances, but the parallel algorithm solves them in seconds or, at maximum, in minutes. This study shows that the parallel algorithm yields an execution time lower than the execution time obtained from the evolutionary algorithm for different theoretical and practical instances.

Design Water Supply Network Using Epanet Software

Abstract: This study represents use of EPANET software in the design of water distribution network. EPANET software is a user friendly software. In order to ensure the availability of sufficient quantity of good quality of water to the various section of community in accordance with the demand, many computer tools were developed, out of all the tools available EPANET become most popular and convenient for the effective design of complex pipe networks. This paper highlights only the effective design and distribution of network of pipes using EPANET tool. The residual head at each and every node was found out by having the elevation as input and thereby the corresponding flow quantities were derived like residual head, velocity and nodal demand etc.

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.

Analysis of Water Distribution Network Using Epanet for Normal and Leakage Condition and Its Effect on Pressure

Abstract: Water distribution network is a system of engineered hydrologic and hydraulic component which supplies water from the source to the required area. In the design of water distribution network, it is crucial that the network supplies the forecasted demands with enough residual heads at all nodes of the network during the entire design period. However with the increasing change in future scenario, either the nodal demands change or the water distribution network falls short to meet the increasing demands. Therefore, we require a proper analysis of water networks to strengthen them for future. In situations like this, softwares play a major role in analyzing water distribution network to make it work as per the design. The present study is an effort to analyze the water supply network using available software, it proposes hydraulic simulation model for water distribution network analysis and comparison of results.

Application of Fine-Tuned Krill Herd Algorithm in Design of Water Distribution Networks

Stochastic population-based metaheuristic algorithms have been widely used to design water distribution networks (WDNs). The present study introduces one of its kind, the krill herd algorithm (KHA), a novel swarm intelligence-based metaheuristic. Demonstrating KHA application to WDN design, the study proposes its enhanced version to improve its convergence precision. Consequently, combining the fine-tuned mechanism of KHA with the EPANET 2.2 simulation software, the fine-tuned KHA (FIT-KHA) model is formulated and checked for its efficiency in handling the WDN design problem. Because three benchmark problems (new and rehabilitation WDNs) of different dimensions are considered, the significance of the algorithm control parameters concerning the network size is studied. From sensitivity analysis, the time step factor, number of krill, and maximum iteration size are found to influence the algorithm performance. Their optimal values followed an increasing trend with the network size. The computational results reinforce a superior search exploitation ability of the FIT-KHA. Importantly, the results exhibit a better computational efficiency of KHA over most of the reported metaheuristic algorithms. Then, the performance state of optimally designed WDN under hydraulic (demand, roughness coefficient variations) and mechanical (single- and two-pipe failure) uncertain scenarios is studied. Besides reliability and surrogate measures, multiaspect metrics based on adequacy and equity are evaluated to assess the network’s performance. The WDNs are observed to be more susceptible to demand uncertainties over roughness coefficient variation. At higher states of mechanical (pipe) failure scenarios, especially, the equity of the WDN is disturbed compared to the adequacy, except for rehabilitated WDN. Certainly, the performance study manifests that the reliability measure that truly presents the WDNs performance is the function of network type. While proposing KHA as an effective alternative optimization tool, the study suggests a prior performance study to choose an appropriate metric to formulate a reliability-based multiobjective framework for the robust design of WDNs.

Chaotic differential evolution algorithms for optimal design of water distribution networks

ABSTRACT Recently, coupling chaos theory with evolutionary algorithms (EAs) elevated further scope for improving EAs’ performance efficiency. In this view, the present study emphasizes investigating the influence of chaotic force on convergence properties of differential evolution (DE) algorithm in designing water distribution networks (WDNs). To this end, two novel chaos-directed DE models, Chaotic-DE and Chaotic-Fm-DE, are proposed. The Chaotic-DE model is formulated to enhance DE’s searchability and faster convergence by replacing every random phenomenon with a chaotic force. The Chaotic-Fm-DE model with a dynamic, chaotic mutation factor is developed to improve DE’s exploitation behavior. Essentially, these models differ from the previous chaos-directed EA models in how chaos ergodicity is simulated in DE mechanism. A novel scheme of non-sequential approach is used for this purpose. Further, their respective elitist models are formulated to promote the search in promising areas. Importantly, the elitism scheme developed saves the elite trial vectors to pass through the next generations. The results of proposed algorithms validated on five (new and rehabilitated) benchmark WDNs (whose dimensions vary from 8 to 454) demonstrate the enhanced search behavior of the chaotic models with solution precision and remarkable reduction in computational effort over the non-chaotic ones.

A Chaotic Sobol Sequence-based multi-objective evolutionary algorithm for optimal design and expansion of water networks

The design of a water distribution network (WDN) is an optimization problem that is computationally challenging with conflicting objectives. This study offers an enhanced Chaotic Sobol Sequence-based Multi-Objective Self-Adaptive Differential Evolution (CS-MOSADE) algorithm for multi-objective WDN design. The CS-MOSADE algorithm was tested on two benchmark WDNs, and a real WDN. Optimization results indicate that the CS-MOSADE algorithm converged two to three times faster than the MOSADE and NSGA-IIalgorithms and led to better output in terms of even distribution of solutions and convergence towards the true Pareto-optimal front. Smaller spacing metric indicated better uniformity in the obtained solutions; and larger hyper-area and coverage function values depicted better convergence towards the true Pareto-optimal front for the CS-MOSADE algorithm compared to the other algorithms. The CS-MOSADE algorithm was then applied to solve a WDN expansion problem for optimal pump scheduling and minimization of Life Cycle Cost, maximization of reliability and minimization of Green House Gas (GHG) emissions. A significant reduction in GHG emissions of 2.17 x 106 kg was achieved at an additional cost of $0.55 x 107 when optimal pump scheduling was incorporated in the model of the real WDN over service life of 50 years.

Fuzzy cluster analysis and decision-making algorithms for optimal water distribution network design

ABSTRACT Three objectives, maximization of resilience, minimization of cost, and minimization of leakages, were considered in the Water Distribution Network (WDN) framework for a benchmark problem of Hanoi WDN and a real-world problem, Pamapur WDN, Telangana, India. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is employed to generate Non-dominated WDN Strategies (NWDNS). In order to simplify the decision-making process of engineers, Fuzzy Cluster Analysis (FCA) is employed to categorize NWDNS into groups. An optimum number of clusters are based on the Elbow method. Representative NWDNS, i.e. RNWDNS for each sub-cluster, is based on the membership values. Ranking of RNWDNS is performed with two decision-making algorithms, namely, Preference Ranking Organization METHod for Enrichment of Evaluations-2 (PROMETHEE-2) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The additive ranking rule is also applied to obtain ranks in a group decision-making environment to arrive at the optimal WDN. It is observed that 1020 NWDNSH (H represents Hanoi) generated for the Hanoi are optimally classified into 18 clusters based on the Elbow method, and A13 representing RNWDNSH 37 (cost, resilience, and leakages, respectively, are 7.8818 × 106 $, 0.3194, 0.2024 × 10−3 m3/s) is preferable, respectively. Whereas 272 NWDNSP (P represents Pamapur) generated for the Pamapur are classified into 9 clusters where S6 representing RNWDNSP 203 (cost, resilience, and leakages, respectively, are 3.5159 × 106 Rs., 0.8367, 0.5317 × 10−3 m3/s) is preferred, respectively. The present study facilitated seamless integration of NSGA-II (generation of Pareto front), FCA (reducing to manageable set) and MCDM methods (to rank the reduced manageable set) in a robust manner.

Application of the Harmony Search Algorithm for Optimization of WDN and Assessment of Pipe Deterioration

The relevance of the optimal design of water distribution networks lies in its applicability. Thus, the design must be as efficient and affordable as possible, meaning that it achieves a minimum level of serviceability using an appropriate amount of resources. In this context, an ideal water network requires the use of minimum-size elements to reach the minimum head pressure required for each node of the system with the lowest energy consumption. For this purpose, a relatively new meta-heuristic algorithm, called Harmony Search, was used in this study to optimize the water distribution network of Cheongna International City, Korea, in terms of the pipe diameter. Furthermore, using the same algorithm under a different approach, an assessment of the deterioration of conduits over time was conducted by analyzing the optimal roughness coefficient for the original pipe material, which provides a useful tool for decision making. Other heuristic and meta-heuristic algorithms have been applied to this type of problem; however, Harmony Search provides a convenient implementation at a reasonable computational cost. In this study, Harmony Search is demonstrated to be a valuable tool for water distribution network optimization as well as for pipe aging assessment.

Chaos-directed genetic algorithms for water distribution network design: an enhanced search method

The design of a water distribution network (WDN) is an ever-challenging problem. The formulation and application of optimization techniques for WDN design have been an important area of research. Recently, the introduction of chaos theory-based evolutionary algorithms (EAs), in addition to traditional random-based ones, has elevated the scope for further improving the performance of EAs. The present study proposes a chaos-directed genetic algorithm (CDGA) by incorporating chaos ergodicity in GA mechanics for the optimal design of WDNs by introducing two novel frameworks, namely non-sequential approach and sequential approach. In improving the search efficacy of GA, the influence of chaotic systems with high-dimensionality maps is also explored when compared to the low-dimensionality maps. Considering four widely studied WDN benchmark problems ranging from 8 to 454 dimensions, the performance of the proposed GA and CDGA models is evaluated. The results show that the CDGA models outperform GA with better search efficacy, requiring fewer function evaluations to locate the optimal solution. In addition, the CDGA models are found to outperform other optimization techniques reported previously to handle these benchmark problems. Based on the results obtained, the study suggests the use of the chaotic system with other bio-inspired techniques to further improve their searchability and, thus, their computational efficiency.

Optimization of Water Distribution Networks Using Genetic Algorithm Based SOP–WDN Program

Water distribution networks are vital hydraulic infrastructures, essential for providing consumers with sufficient water of appropriate quality. The cost of construction, operation, and maintenance of such networks is extremely large. The problem of optimization of a water distribution network is governed by the type of water distribution network and the size of pipelines placed in the distribution network. This problem of optimal diameter allocation of pipes in a distribution network has been heavily researched over the past few decades. This study describes the development of an algorithm, ‘Smart Optimization Program for Water Distribution Networks’ (SOP–WDN), which applies genetic algorithm to the problem of the least-cost design of water distribution networks. SOP–WDN demonstrates the application of an evolutionary optimization technique, i.e., genetic algorithm, linked with a hydraulic simulation solver EPANET, for the optimal design of water distribution networks. The developed algorithm was applied to three benchmark water distribution network optimization problems and produced consistently good results. SOP–WDN can be utilized as a tool for guiding engineers during the design and rehabilitation of water distribution pipelines.

Improved MOSADE algorithm incorporating Sobol sequences for multi-objective design of Water Distribution Networks

Design of Water Distribution Networks (WDNs) is a tremendously hard optimization problem, and consideration of reliability further adds to the complexity, which may involve huge computational effort. As several past studies stressed that Evolutionary Algorithms (EAs) could be efficient tools for WDN design, so this study, presents an effective methodology, Multi-Objective Self Adaptive Differential Evolution (MOSADE) algorithm using Sobol sequences for random number generation, termed as (S-MOSADE) for WDN design. The efficacy of the S-MOSADE framework is evaluated by application on a few benchmark WDNs, by considering cost minimization and mechanical reliability maximization and comparing the results with that of NSGA-II algorithm. The results illustrated that S-MOSADE algorithm leads to a better Pareto-optimal front than NSGA-II with respect to uniformly spaced and wide range of non-dominated solutions, and converges faster as compared to other algorithms. To further reduce the computational burden, minimizing the cost and maximizing the network resilience is carried out to generate the initial population for S-MOSADE algorithm. This has reduced the computational burden by almost three times as compared to random initialization of population, thus saving a lot of computational time. The study concludes that the proposed S-MOSADE algorithm with the strategy of solutions initialized with minimum cost and maximum network resilience could be used effectively for speeding-up the multi-objective design of WDNs.