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This paper presents a new valve positioning algorithm (VPA) for water network pressure reduction. The proposed algorithm is a graph theory-based algorithm combined with EPANET2.2 to position pressure-reducing valves (PRVs) at the most effective locations, having the most effect on downstream pressure reduction, and then calculates the setpoint for locally controlled valves. Each algorithm solution positions one valve on the edge with the highest-pressure reduction indicator calculated using the depth-first search algorithm. The setpoint is then calculated according to downstream pressure differences to the minimum service pressure to be supplied. The PRV location and setpoint found by the algorithm may be used to install and set locally controlled PRVs or serve as a guide for positioning remote-controlled PRVs. The algorithm is demonstrated on a simple example network using demand-driven analysis (DDA), pressure-driven analysis (PDA), and genetic algorithms (GA) and on a medium and a large example application (DDA). Any number of PRVs may be installed using the algorithm, which returns stable results and very short solution times while maintaining minimum service pressure requirements to the critical consumers. [ABSTRACT FROM AUTHOR]

This paper reports the use of many-objective optimization for water distribution system (WDS) design or rehabilitation problems. The term many-objective optimization refers to optimization with four or more objectives. The increase in the number of objectives brings new challenges for both optimization and visualization. This study uses a multiobjective evolutionary algorithm termed the epsilon Nondominated Sorted Genetic Algorithm II (-NSGAII) and interactive visual analytics to reveal and explore the tradeoffs for the Anytown network problem. The many-objective formulation focuses on a suite of six objectives, as follows: (1) capital cost, (2) operating cost, (3) hydraulic failure, (4) leakage, (5) water age, and (6) fire-fighting capacity. These six objectives are optimized based on decisions related to pipe sizing, tank siting, tank sizing, and pump scheduling under five different loading conditions. Solving the many-objective formulation reveals complex tradeoffs that would not be revealed in a lower-dimensional optimization problem. Visual analytics are used to explore these complex tradeoffs and identify solutions that simultaneously improve the overall WDS performance but with reduced capital and operating costs. This paper demonstrates that a many-objective visual analytics approach has clear advantages and benefits in supporting more informed, transparent decision-making in the WDS design process. [ABSTRACT FROM AUTHOR]

This paper deals with methods aimed at the effective and efficient detection of accidental and/or intentional contaminant intrusion(s) in water distribution systems. The objective of this paper is to present a methodology entitled sensors local optimal transformation system (SLOTS) to address both single-objective and multiobjective sensor layout problems. SLOTS is tested on two benchmark water distribution networks used for the Battle of the Water Sensors Networks challenge (BWSN), held as part of the Water Distribution Systems Analysis Symposium, in Cincinnati in 2006. The objectives considered are detection likelihood and the expected population affected prior to detection. The results obtained demonstrate that SLOTS sensor placements are often near optimal. For both single-objective and multiobjective cases, SLOTS is shown to be capable of identifying placements which are consistently better performing than one of the best BWSN methodologies, the greedy algorithm. [ABSTRACT FROM AUTHOR]

Considerable research has been carried out on the optimization of water distribution systems (WDSs) over the last three decades. In previous research, attention has mainly focused on the minimization of cost, due to the high expenditure associated with the construction and maintenance of such systems. However, the impacts of WDSs on the environment usually have not been considered adequately. The recent increasing awareness of sustainability and climate change, especially global warming, has led to research where greenhouse gas (GHG) emissions are considered. In the study described in this paper a multiobjective genetic algorithm for WDS optimization has been used as an explorative tool to investigate the trade-offs between the traditional economic objective of minimizing costs and an additional environmental objective of minimizing GHG emissions. The impacts of minimizing GHG emissions on the results of WDS optimization have been explored for a case study in this paper. The results indicate that the inclusion of GHG emission minimization as one of the objectives results in significant trade-offs between the economic and environmental objectives. Furthermore, a sensitivity analysis has been conducted by using different discount rates in a present value analysis for computing both ongoing costs and GHG emissions. The results obtained show that the Pareto-optimal front is very sensitive to the discount rates used. As a result, the selection of discount rates has a significant impact on final decision making. [ABSTRACT FROM AUTHOR]

The problem of deploying sensors in a large water distribution network is considered, in order to detect the malicious introduction of contaminants. It is shown that a large class of realistic objective functions—such as reduction of detection time and the population protected from consuming contaminated water—exhibits an important diminishing returns effect called submodularity. The submodularity of these objectives is exploited in order to design efficient placement algorithms with provable performance guarantees. The algorithms presented in this paper do not rely on mixed integer programming, and scale well to networks of arbitrary size. The problem instances considered in the approach presented in this paper are orders of magnitude (a factor of 72) larger than the largest problems solved in the literature. It is shown how the method presented here can be extended to multicriteria optimization, selecting placements robust to sensor failures and optimizing minimax criteria. Extensive empirical evidence on the effectiveness of the method presented in this paper on two benchmark distribution networks, and an actual drinking water distribution system of greater than 21,000 nodes, is presented. [ABSTRACT FROM AUTHOR]

The design of a water distribution network (WDN) is conceptually a multiobjective problem characterized by stringent constraints. Even in its most simple formulation, which requires only the maintenance of minimum pressures, it is difficult to solve, and the simplifications introduced often impair the practicality of the solutions. The paper aims at integrating an engineering approach to the optimization problem by generating pseudofronts in the hydraulically feasible region of the search space. The optimization algorithms provide an entirely feasible trade-off between cost and considered constraints, which may be directly used by a hypothetical decision maker. This engineering approach requires a fast tool to search for feasible solutions: the recently developed genetic heritage by stochastic evolution transmission (GHEST) algorithm, used herein, has proved to be effective and efficient in solving the optimal design problem of WDNs. Tests are carried out on two large-size water distribution networks (Balerma and Modena), using the GHEST algorithm, modified to account for several objectives. [ABSTRACT FROM AUTHOR]

In recent years, a number of evolutionary algorithms have been proposed for optimizing the design and operation of water distribution systems (WDSs). These evolutionary algorithms include genetic algorithms, ant colony optimization, particle swarm optimization, the shuffled leaping frog algorithm, and differential evolution. Although there have been some comparisons made of the performance of the various algorithms, very few of these comparisons have been carried out in a completely rigorous manner. The main aim of this paper is to introduce a methodology for the rigorous comparison of various algorithms for the optimum design of water distribution systems. The methodology involves comparing the various algorithms in terms of (1) the best solution obtained; (2) the speed of convergence; and (3) the spread and consistency of the solutions obtained over a number of random starting seeds and numbers of evaluations. As a demonstration of the methodology, the techniques of genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE) are applied to two frequently used WDS case studies, namely the New York Tunnels and Hanoi water networks. In addition, the techniques are applied to a real-size water distribution system consisting of 476 pipes. The results obtained show that the algorithm performances depend on the specific problem and the number of function evaluations allowed. Moreover, it is shown that correct calibration is an essential phase for a fair comparison of evolutionary algorithms. In fact, the best parameters are a function of the problem characteristics, of the objective function and of the variants in the algorithm operators. Therefore the adoption of configurations tested on slightly different versions of the algorithms can lead to quite different results. [ABSTRACT FROM AUTHOR]

The ability to monitor the flow and how water transforms throughout water networks would greatly improve the management of those distribution systems. The sensor placement problem attempts to find the locations of monitoring devices that would optimally observe water quality and protect consumers from accidents and intrusions of contaminants. In some related critical scenarios, the absence of information about possible contamination events, including knowledge of the injection sources, contaminant types or mass, time of pollution, and the variability of water network input parameters, such as the nodal demands and the pipe roughness coefficients, raises several challenges that must be addressed by the sensor network design process. In this paper, the authors describe a stochastic parameterization and analysis of uncertainty for the design of sensor networks aimed at maximizing the probability of detection of accidents and intrusions in water distribution networks. A challenge with such an approach, in particular, when applied to large urban water networks is the size of the ensuing computational model and the associated numerical optimization problem. This problem is compounded in the presence of uncertainty, where the need to deal with a large number of statistically plausible scenarios underscores the need for efficient yet credible algorithms for addressing the sensor placement issue. In addition to modeling aspects, the authors also address a challenge associated with the computational feasibility and performance of relevant numerical algorithms. Specifically, and through the use of submodular cost functions, the authors are able to solve the optimization problem with a greedy algorithm, yielding sufficient computational performance that allows for the description of stochastic water demands in the context of Monte Carlo simulations. Imperfect sensors are further accounted for while maintaining submodularity. The results show that the optimal sensor network layout is highly dependent on whether uncertainty in the stochastic parameters has been introduced and whether individual sensors can fail or not. [ABSTRACT FROM AUTHOR]

This work presents a postoptimization methodology for refining the solutions found by adaptive search algorithms used in the design of large water distribution networks. The approach uses two heuristics to search for an optimal combination of pipes that, after a reduction of their diameters, will maximize cost savings while continuing to meet design constraints. Adaptive search methods are often used to design urban water distribution networks when the number of pipes in the network is insignificant. For complex, real-world networks, however, such methods are computationally demanding, and they have difficulty finding near-global optima. To identify a solution as close to the global optimum (and in which no pipe can be reduced without violating pressure constraint), requires a high-speed computer potentially running for a long time and also probably some good fortune. The postoptimization approach presented in this paper is shown to be an efficient complement to heuristic search algorithms used in the design of real-world networks. In a network created with the aid of a genetic algorithm, the proposed heuristics found that 4.37% of the pipes with a diameter greater than the minimum could be further reduced without causing hydraulic failure. [ABSTRACT FROM AUTHOR]

The suitability of genetic algorithms (GAs) for the optimization of water distribution systems (WDSs) has been demonstrated extensively. However, despite many years of application in many different fields, the selection of the GA parameters remains a difficult and time consuming task. In this paper, two methodologies that do not require trial-and-error GA parameter calibration have been tested on a WDS optimization problem to determine their suitability for application in the water resources field and to assess their ability in locating near-optimal solutions. The results indicate that both approaches located solutions that were significantly better than a GA using typical parameter values, while the methodology based on convergence of the GA population located the best solutions overall. This method can be easily applied to assist GA users in identifying suitable GA parameters without requiring a time consuming trial-and-error approach. [ABSTRACT FROM AUTHOR]

Water distribution network that includes supply reservoirs, overhead tanks, consumer demand nodes, interconnecting pipes, lifting pumps, and control valves is the main mode of water supply for majority of the communities especially in urban areas. Supply of required quantity of water and at right time is the primary objective of water distribution network analysis. The analysis of water distribution networks can be broadly classified into design and operation problems and both problems have been the focus of many researchers over the past three decades. In the water distribution network design problems, the target is attaining the cost effective configuration that satisfies the minimum hydraulic head requirement at the demand nodes. In this paper, a new algorithm for design of water distribution network namely “heuristics-based algorithm” which completely utilizes the implicit information associated with the water distribution network to be designed has been proposed and validated with two water distribution networks. It is found that the proposed algorithm performs well for the least-cost design of water distribution networks. [ABSTRACT FROM AUTHOR]

The efficient and effective search for the optimum design solution of a water distribution network using genetic algorithms (GAs) is governed by several factors such as representation scheme, population size, hydraulic simulation model, fitness function, penalty method, GA operators, number of generations, and more importantly the size of the search space. This paper proposes a modified GA that uses basic operators along with their derivatives randomly. Further, a methodology based on critical path method is suggested to reduce the search space. A software tool, GA-WAT, based on the proposed methodology is developed and first tested and verified for its efficiency and effectiveness on two previously published single source networks. Later, it is applied to the optimal design of a larger, two-source hypothetical network. The results obtained indicate that the modified GA with reduction in search space proposed herein is more effective, especially for large practical networks. [ABSTRACT FROM AUTHOR]

Water distribution systems (WDSs) are costly infrastructure, and much attention has been given to the application of optimization methods to minimize design costs. In previous studies, ant colony optimization (ACO) has been found to perform extremely competitively for WDS optimization. In this paper, five ACO algorithms are tested: one basic algorithm (ant system) and four more advanced algorithms [ant colony system, elitist ant system, elitist-rank ant system (ASrank), and max-min ant system (MMAS)]. Experiments are carried out to determine their performance on four WDS case studies, three of which have been considered widely in the literature. The findings of the study show that some ACO algorithms are very successful for WDS design, as two of the ACO algorithms (MMAS and ASrank) outperform all other algorithms applied to these case studies in the literature. [ABSTRACT FROM AUTHOR]

This paper develops a multicommodity flow model to optimize water distribution and water quality in a regional water supply system. Waters from different sources with different qualities are considered as distinct commodities that concurrently share a single water distribution system. The model can accommodate two-way flow pipes, represented by undirected arcs, and the perfect mixing condition. Additionally, blending requirements are specified at certain control nodes within the system to ensure that downstream users receive the desired water quality. The optimization model is highly nonlinear and solved by a hybrid genetic algorithm (GA). The GA is first used to globally search for the directions of all undirected arcs. Then a generalized reduced gradient (GRG) algorithm embedded in the GA is used to optimize the objective function for fitness evaluation. The proposed methodology was first tested and verified on a hypothetical system and then applied to the regional water distribution system of the Metropolitan Water District of Southern California. The results obtained indicate that the proposed hybrid GA is a viable way of converting an undirected network to a directed network by separating the complicating variables, and that the resulting directed network model can be solved iteratively and efficiently by a gradient-based algorithm. [ABSTRACT FROM AUTHOR]

In design of water distribution networks, there are several constraints that need to be satisfied; supplying water at an adequate pressure being the main one. In this paper, a self-adaptive fitness formulation is presented for solving constrained optimization of water distribution networks. The method has been formulated to ensure that slightly infeasible solutions with a low objective function value remain fit. This is seen as a benefit in solving highly constrained problems that have solutions on one or more of the constraint bounds. In contrast, solutions well outside the constraint bounds are seen as containing little genetic information that is of use and are therefore penalized. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to infeasible solutions. The performance of the method has been examined by its application to two water distribution networks from literature. The results have been compared with previously published results. It is shown that the method is able to find optimum solutions with less computational effort. The proposed method is easy to implement, requires no parameter tuning, and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution, this being an advantage in real-world applications having many optimization variables. [ABSTRACT FROM AUTHOR]

This paper shows how pipe replacements and control valve installations can be optimized in water distribution networks to reduce leakage, under minimum nodal pressure constraints. To this end, a hybrid multiobjective algorithm, which has pipe diameters and valve positions and settings as decisional variables, was set up. The algorithm also enables identification of the isolation valves that have to be closed in order to improve effectiveness of the control valves installed. The algorithm is initially applied to the optimal valve location problem, where it explores the trade-off between the number of installed control valves and the daily leakage volume. In this context, the analysis of the results proves the new algorithm more effective than a multiobjective genetic algorithm widely adopted in the scientific literature. Furthermore, it shows that if some isolation valves identified ad hoc are closed in the network, the installation of control valves determines larger leakage volume reductions. In a second application of the algorithm, pipe replacements and control valve installations are simultaneously performed. In this case, a Pareto front of trade-off solutions between installation costs and daily leakage volume is obtained. For the choice of the final solution within the front, an economic criterion based on the long-term convenience analysis is also illustrated. [ABSTRACT FROM AUTHOR]

Control valves are commonly used for the operation of water distribution systems. Modeling these devices typically requires that their operating states are known, or that a computationally expensive search is undertaken over all possible operating states. This paper presents a novel method of modeling control valves (including flow control, pressure sustaining, pressure reducing and check valves) in extended-period simulations of water distribution systems. Instead of the normal discrete control problem formulation, it is approached with the Karush-Kuhn-Tucker equations for an optimization problem with constraints. The proposed method does not prerequire the operating state (open, closed, active) of each valve to be determined, as this is done implicitly. Pipe and valve flow rates and nodal heads are determined by: (1) minimizing deviations from targets at control valves, and (2) satisfy the state equations (conservation of mass and energy) by solving a constrained least-squares problem. Sensitivity equations with respect to the control variables (valve settings) are derived from the state equations, and the control variables are updated using Levenberg-Marquardt iterations. The results of simple problems and case studies are presented to demonstrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]