Design Of Water Distribution Networks Research Articles

Knowledge-based multi-objective genetic algorithms for the design of water distribution networks

Abstract Water system design problems are complex and difficult to optimise. It has been demonstrated that involving engineering expertise is required to tackle real-world problems. This paper presents two engineering inspired hybrid evolutionary algorithms (EAs) for the multi-objective design of water distribution networks. The heuristics are developed from traditional design approaches of practicing engineers and integrated into the mutation operator of a multi-objective EA. The first engineering inspired heuristic is designed to identify hydraulic bottlenecks within the network and eliminate them with a view to speeding up the algorithm's search to the feasible solution space. The second heuristic is based on the notion that pipe diameters smoothly transition from large, at the source, to small at the extremities of the network. The performance of the engineering inspired hybrid EAs is compared with Non-Dominated Sorting Genetic Algorithm II and assessed on three networks of varying complexity, two benchmarks and one real-world network. The experiments presented in this paper demonstrate that the incorporation of engineering expertise can improve EA performance, often producing superior solutions both in terms of mathematical optimality and also engineering feasibility.

Probabilistic and fuzzy approaches for uncertainty consideration in water distribution networks – a review

Abstract The performance of a water distribution system of providing a required flow rate at all the nodes with required pressure heads throughout its design life is affected by uncertainties associated with different parameters such as future water demands, pipe roughness coefficient values, required pressure heads at nodes, etc. The objective of this paper is to present a comprehensive review on the nature of uncertainties (random or fuzzy), various models and methods used for their quantification, and different ways of handling them in the design of water distribution networks. While probabilistic based approaches are used for handling uncertainty of random type, the possibilistic based approach considers uncertainty of fuzzy nature. Some key issues and serious limitations of the existing approaches for modeling uncertain parameters related to water distribution networks are identified. The uncertainty in water demands is due to both their random nature and lack of information about their values. Therefore, a combination of both types of approaches, called the fuzzy random approach, is found to be more effective. The fuzzy random approach can provide optimal design solutions that are not only cost-effective but also has higher reliability to cope with severe future uncertainties.

Dynamical stability of water distribution networks.

Water distribution networks are hydraulic infrastructures that aim to meet water demands at their various nodes. Water flows through pipes in the network create nonlinear dynamics on networks. A desirable feature of water distribution networks is high resistance to failures and other shocks to the system. Such threats would at least transiently change the flow rate in various pipes, potentially undermining the functionality of the whole water distribution system. Here we carry out a linear stability analysis for a nonlinear dynamical system representing the flow rate through pipes that are interconnected through an arbitrary pipe network with reservoirs and consumer nodes. We show that the steady state is always locally stable and develop a method to calculate the eigenvalue that corresponds to the mode that decays the most slowly towards the equilibrium, which we use as an index for resilience of the system. We show that the proposed index is positively correlated with the recovery rate of the pipe network, which was derived from a realistic and industrially popular simulator. The present analytical framework is expected to be useful for deploying tools from nonlinear dynamics and network analysis in the design, resilience management and scenario testing of water distribution networks.

JHawanet: An Open-Source Project for the Implementation and Assessment of Multi-Objective Evolutionary Algorithms on Water Distribution Networks

Efficient design and management of water distribution networks is critical for conservation of water resources and minimization of both energy requirements and maintenance costs. Several computational routines have been proposed for the optimization of operational parameters that govern such networks. In particular, multi-objective evolutionary algorithms have proven to be useful both properly describing a network and optimizing its performance. Despite these computational advances, practical implementation of multi-objective optimization algorithms for water networks is an abstruse subject for researchers and engineers, particularly since efficient coupling between multi-objective algorithms and the hydraulic network model is required. Further, even if the coupling is successfully implemented, selecting the proper set of multi-objective algorithms for a given network, and addressing the quality of the obtained results (i.e., the approximate Pareto frontier) introduces additional complexities that further hinder the practical application of these algorithms. Here, we present an open-source project that couples the EPANET hydraulic network model with the jMetal framework for multi-objective optimization, allowing flexible implementation and comparison of different metaheuristic optimization algorithms through statistical quality assessment. Advantages of this project are discussed by comparing the performance of different multi-objective algorithms (i.e., NSGA-II, SPEA2, SMPSO) on case study water pump networks available in the literature.

Fairness-guided design of water distribution networks for agricultural lands

Allocating finite resources (utility) among stakeholders in a fair manner is a nontrivial task. In this work, we provide an optimization framework to design water distribution networks that ensure fair allocations to multiple agricultural lands. Our formulation is a mixed integer nonlinear programming model that uses different schemes (social welfare, Rawlsian welfare, and Nash allocation) to guide water allocations to agricultural lands of varying sizes and over different seasonal periods. We demonstrate the applicability of our model by using a case study in the State of Sinaloa, Mexico. We find that the social welfare approach (the most widely used approach for social planning) yields allocations that are not unique and, as a result, the solution is ambiguous. Moreover, this approach fails to properly capture relative sizes of the stakeholders and tends to favor large stakeholders. We also demonstrate that the Rawlsian welfare approach favors smaller stakeholders but at the expense of more expensive designs; moreover, this approach also suffers from ambiguity due to solution multiplicity. Finally, we demonstrate that the Nash approach provides unique solutions that balance the utilities of large and small stakeholders in a more systematic manner.

Geospatial Design of Optimal Water Distribution Network in Ado-Ekiti, Ekiti State, Nigeria

The supply of water to both rural and urban centres of Nigeria is extremely poor with reference to quantity and access. The study investigated water distribution and supply in Ado-Ekiti metropolis applying a geospatial approach, with a view to generating baseline information to optimize water supply and distribution in the metropolis. Materials used included: a map of Ado-Ekiti with a scale of 1:50000 obtained from the Local Government Office, AdoEkiti water distribution facility map (2000) with a scale of 1:30000 obtained from the Ado-Ekiti State Water Corporation and population estimate of Ado-Ekiti from the Bureau of Statistics. Sets of structured questionnaires were used to get information from the residents and the State’s Water Corporation. The study delineated existing water distribution network of the metropolis, provided (i) a map of the service areas, (ii) information on areas with distribution problems and (iii) the per capita demand of the population as inferred from the questionnaires. A lasting solution was also proffered through the design of a water distribution network for the estimated daily water demand for the years 2019 and 2049 irrespective of the variation in water needs of the residents in the area. The Geospatial approach was found to be useful in improving the distribution system through extension of pipelines and identification of various locations for service reservoirs.Keywords: Management, reservoir, distribution problems, served, pipe-borne

A New Optimization Approach for the Least-Cost Design of Water Distribution Networks: Improved Crow Search Algorithm

Due to large number of decision variables and several hydraulic constraints, optimal design of water distribution networks (WDNs) is considered as one of the most complex optimization problems. This paper introduces and applies a new optimization approach, improved crow search algorithm (ICSA), based on the improvement of original crow search algorithm (CSA) by adding an operator parameter. Both approaches (i.e., CSA and ICSA) were applied to two case studies (i.e., Two-Reservoir and Khorramshahr City networks) by linking the hydraulic simulator (e.g., EPANET 2.0). The proposed ICSA saved the total construction cost by 2.16% and 1.79% for the Two-Reservoir and Khorramshahr City networks compared to the original CSA based on optimal network design, respectively. Results revealed that the proposed ICSA provided outstanding design for the both WDNs compared to previous studies and original CSA.

Optimal pipe dimensioning in water distribution networks using Gravitational Search Algorithm

ABSTRACT An effective method for optimal design of water distribution network (WDN) can significantly benefit to develop commercial software for component sizing. This research investigates Gravitational Search Algorithm (GSA) for pipe cost optimization model problems. GSA is a meta-heuristic (MH) algorithm which makes ease of its applicability to the design of WDNs due to its minimum number of algorithm parameters and requiring least effort in fine-tuning the parameters. Three well-known benchmark networks (Hanoi network, Two-Reservoir network and New York tunnels network) and a real-world WDN located Khorramshahr city in Iran were used. The GSA results were compared with the solutions obtained through various Evolutionary Algorithms. Experimental results show success of GSA in arriving minimum cost solution. GSA achieved to the best so far solution reported for one case (Hanoi network), and it could find the least cost for three other networks compared to the best results of other optimization algorithms. In addition, for two case studies (Hanoi network and Khorramshahr city network) number of function evaluations were less than other algorithms. Further, the study reveals that GSA achieved the maximum number of times the best so far solution and confirming rapid convergence without struck up at local optimum.

Minimizing the variance of flow series using a genetic algorithm for reliability-based design of looped water distribution networks

ABSTRACTA network design based on the flow uniformity in various pipes improves the reliability of the network. One way to obtain such a flow distribution is by minimizing the variance of pipe flows. The available analytical method is critically studied, and observed to fail in providing global minimum variance of flow series. The analytical method accounts for the flow directions, while a variance evaluation requires that only the magnitude of flows is considered. A general nonlinear programming approach is tried, and it is observed that it requires correct knowledge of the flow direction. This article presents a genetic algorithm-based method to avoid this limitation. A linear programming-based algorithm is then suggested for selecting the optimal pipe sizes considering reliability. The proposed method is found to provide better design solutions than those obtained using some of the methodologies previously suggested for expansion of a water main system.

Graph-Theoretic Surrogate Measure to Analyze Reliability of Water Distribution System Using Bayesian Belief Network–Based Data Fusion Technique

AbstractReliability assessment is an integral component of the decision-making process in the planning, design, and operations of water distribution networks (WDNs). Two different approaches are us...

Water distribution networks optimization considering unknown flow directions and pipe diameters

Water Distribution Networks (WDN) are present in a large number of industrial processes and urban centers. Reservoirs, pipes, nodes, loops, and pumps compose WDN and their design can be formulated as an optimization problem. The main objective is the minimization of the network cost, which depends on the pipe diameters and flow directions known a priori. However, in the design of new WDN in real industrial problems, flow directions are unknown. In the present paper, a disjunctive Mixed Integer NonLinear Programming (MINLP) model is proposed for the synthesis of WDN considering unknown flow directions. Two case studies are employed to test the model and global optimization techniques are used in its solution. Results show that the global optima WDN cost with the correct flow directions is obtained for the studied cases without the necessity of using additional software to calculate pressure drops and velocities in the pipes.

Testing evolutionary algorithms for optimization of water distribution networks

Water distribution networks (WDNs) are one of the most important elements of urban infrastructure and require large investment for construction. Design of WDNs is classified as a large combinatorial discrete nonlinear optimization problem. The main concerns associated with the optimization of such networks are the nonlinearity of the discharge-head loss relationships for pipes and the discrete nature of pipe sizes. Due to these issues, this problem is widely considered to be a benchmark problem for testing and evaluating the performance of nonlinear and heuristic optimization algorithms. This paper compares different techniques, all based on evolutionary algorithms (EAs), which yield optimal solutions for least-cost design of WDNs. All of these algorithms search for the global optimum starting from populations of solutions, rather than from a single solution, as in Newton-based search methods. They use different operators to improve the performance of many solutions over repeated iterations. Ten EAs, four of them for the first time, are applied to the design of three networks and their performance in terms of the least cost, under different stopping criteria, are evaluated. Statistical information for 20 executions of the ten algorithms is summarized, and Friedman tests are conducted. Results show that, for the two-loop benchmark network, the particle swarm optimization gravitational search and biology and bioinformatics global optimization algorithms efficiently converge to the global optimum, but perform poorly for large networks. In contrast, given a sufficient number of function evaluations, the covariance matrix adaptation evolution strategy and soccer league competition algorithm consistently converge to the global optimum, for large networks.

A Dynamic Adaptive Approach for Water Distribution Network Design

In the face of a highly uncertain future, there is a need for water utilities to develop structured approaches for the long-term strategic design of water distribution networks (WDNs). A new conceptual framework for developing an integrative approach based on a multicriteria decision analysis (MCDA), embracing an optimization model to size flexible alternatives, is proposed. The flexible solutions are evaluated through MCDA for all the criteria (investment costs, carbon emissions, resilience, and reliability of WDNs) across all the scenarios generated for the sake of robustness and will help to adapt WDNs to changing conditions over a long planning horizon, divided into phases. The alternatives are ranked through two different MCDA methods, Preference Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), so that decision makers will have more comprehensive information for analyzing highly ranked design solutions and after the first phase, solutions for the other phases can be reassessed by the same dynamic adaptive framework.

Combined flow and pressure deficit-based penalty in GA for optimal design of water distribution network

ABSTRACT The optimal design of water distribution networks involves minimizing the cost of the network subject to the constraints of satisfying the pressure requirements at all the nodes. In genetic algorithm (GA)-based optimal design, such constrained problems are generally converted to unconstrained ones using penalty methods. The penalty is applied for not meeting the pressure constraints. Researchers observed previously that the optimal solutions lie on the boundary of feasible and infeasible solutions. They suggested self-organizing penalty based on pressure heads for increasing the computational efficiency and obtaining better solutions. Usually, a flow-dependent analysis is carried out to obtain pressure deficiency at different nodes with the assumption that all nodal demands are satisfied. The assumption of demand satisfaction at all nodes for infeasible solutions results in higher pressure deficiency at different nodes, resulting in higher penalty costs than actually required. This may delay the convergence. Herein, a novel flow-based penalty approach is suggested in which the penalty is obtained based on the shortfalls in the pressures and flows at different nodes using pressure-dependent analysis. The methodology is illustrated with results from benchmark networks. The modified GA method is found to be converging faster as compared to other methods of penalty application.

Design of Water Distribution Network by Heuristic Approach

Optimization of Water Distribution Network (WDN) is a NP hard type and extremely complex problem due to non-linear relationship between Flow and Head loss and discrete pipe diameters. Benchmark problem Hanoi Network is solved herewith by Heuristic methodology using Velocity as Implicit Function by using Candidate diameters obtained from Critical Path Concept. The simulation is performed using EPANET Software. The results obtained are compared with other meta-heuristic methods like Genetic Algorithm, Simulated Annealing and GA-ILP method. The present study concludes that the results are close to optimal values reported in literature in minimum number of iterations.

Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP

Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goals of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in the building are allowed. We propose a branch-and-bound algorithm for solving the corresponding mixed-integer nonlinear program, which exploits problem specific structure and outperforms state-of-the-art solvers. A further desirable feature is that the system is K-resilient, i.e., still able to operate under K pump failures during the use phase. Using a characterization of resilient solutions via a system of inequalities, the branch-and-bound scheme is extended by a separation algorithm to produce cost optimal resilient solutions. This implicitly solves a multilevel optimization problem which contains the computation of worst-case failures. Moreover, using a large set of test instances, the increased energy-efficiency of decentralized networks for the supply of building is shown and properties of resilient layouts are discussed.

Evaluación experimental de correlaciones para el cálculo del factor de fricción para flujo turbulento en tuberías cilíndricas

The hydraulic systems that distribute water to users have an important role in their quality of life. For this reason, the precise determination of the friction factor in pipes is of great importance in the design of water distribution networks because it directly influences the calculation of pressure drop (head losses) in hydraulic systems. The objective of the present work was to evaluate in an experimental manner different correlations that describe, in an explicit form, the friction factor in a pipe under turbulent flow and the implicit Colebrook-White correlation. This was done by comparing the numerical values predicted by the correlations in regard to the experimental value, finding that the Colebrook-White correlation predicts the friction factor with the lowest error percentage among the 27 correlations studied. For the solution of the Colebrook-White equation the Newton-Raphson method was used, given that it presents a recurrent structure that can be taken to algorithms and quickly solved by computer programs. In this work, a tool was developed in the C ++ programming language to solve the Colebrook-White equation.

Comparison of evolutionary multi objective optimization algorithms in optimum design of water distribution network

Abstract In this paper, the application of three well-known multi-objective optimization algorithms to water distribution network (WDN) optimum design has been considered. Non-dominated sorting genetic algorithm II (NSGA-II), Multi-objective differential evolution (MODE) and Multi-objective particle swarm optimization (MOPSO) algorithms are applied to benchmark mathematical test function problems for evaluating the performance of these algorithms. The Accuracy and computational runtime are the two indicators used for the comparison of these three algorithms. The optimization results of mathematical test functions show that all three algorithms were able to accurately produce Pareto Front, but the computational time of MODE algorithm to achieve the optimal solutions is lower than the two other algorithms. Then, the discussed algorithms have been used to optimize the WDN design problem. Comparison of the generated solutions on the Pareto Front for WDN design shows that the obtained Pareto Front of MODE is more accurate and faster.

Multicriterial water distribution networks design

O dimensionamento de redes de distribuição de água (RDAs) é feito para que as restrições operacionais de velo- cidade e pressão se mantenham dentro de limites que garantam a eficiência operacional. Assim, buscam-se as tubulações de menor custo para que essas condições sejam satisfeitas. Entretanto, ao adotar essa prática, ou- tras características da rede podem ser afetadas negativamente, como sua resiliência e capacidade de expansão. Dessa forma, este trabalho apresenta um estudo de caso em que a análise multicriterial é utilizada para realizar o dimensionamento de uma RDA. Primeiramente, um mapa cognitivo é feito para identificar os principais cri- térios a serem considerados na solução do problema. Em seguida, o método Delphi é usado em conjunto com o Analytic Hierarchy Process (AHP) para determinar os pesos relativos de cada critério. Por fim, três diferentes métodos de análise multicritérios são utilizados para a solução do problema: AHP, Electre e Promethee. Palavras-chave: Rede de distribuição. Otimização. Análise multicritério. Abstract The design of water distribution networks (WDNs) is made to match velocity and pressure constraints that guaran- tee operational efficiency. Thus, pipes with lower cost are selected to attend these conditions. However, this proce- dure can harm other characteristics of the network, as for example its resilience and expansion capacity. Therefore, this paper presents a case study in which the multicriterial analysis is used to design a WDN. First, a cognitive map is built to identify the main criteria to be considered during the design process. Then, the Delphi method is used jointly with the Analytic Hierarchy Process (AHP) to define the relative weights of each criteria. Finally, three different methods for multicriterial analysis are used to solve the problem: AHP, Electre and Promethee. Keywords: Water distribution network. Optimization. Multicriterial analysis.

A robust possibilistic programming model for water allocation problem

Over the past few years, water allocation problem has increasingly spotlighted by governments, researchers and practitioners. As water plays an important role in people’s life and business environment, the problem of water allocation should be considered carefully to properly satisfy demand of water consumers. In the real world applications, problems like water allocation are uncertain owing to long-term planning horizon of such problems. Therefore, employing efficient methods for tackling uncertainty of parameters should be regarded by field researchers. In this regard, this paper proposes a bi-objective mathematical programming model for water distribution network design. The extended model maximizes total profit of water distribution as well as maximizing priority of water transferring among water customer zones. Then, to cope effectively with uncertainty of parameters, a novel robust possibilistic programming method is applied. Then, fuzzy and robust fuzzy programming models are compared against each other and output results confirm superiority and effective performance of the robust fuzzy model in the water allocation problem. Also, output results of the extended model show its accurate performance that results in applicability of the model as a strong planning tool in real world cases.