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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]

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]

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]

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]

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]

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]

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]

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]

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]

A method for near-optimal real-time on-line operation of urban water distribution system is presented and demonstrated. It uses a reduced model (RM) of the network which reproduces its performance over time with high fidelity with optimization by a genetic algorithm (GA). The RM-GA software uses network data, forecasted demands for an operational planning time-horizon (24 h ahead), field data from a SCADA on the current status of the network, time-of-day energy cost data, and operator-imposed constraints on tank water levels and demand junctions pressures. The GA looks for the near-least-cost operation plan for the whole time horizon, using the reduced network model, and activates the first hour of the plan through the SCADA. At the end of the hour, the status of the network is updated from field data, the time horizon is rolled ahead by 1 h, and the process repeated. The software was developed for and demonstrated on the distribution system of Haifa. Experiments were conducted, in which the operation which simulates the operators' set-point operation is compared with that obtained by the RM-GA, and energy cost savings of 8 and 10% were calculated for a summer and winter month, respectively. [ABSTRACT FROM AUTHOR]

A sequential irrigation schedule that honors user demands of duration and minimizes earliness and tardiness is interpreted as a single-machine schedule with earliness and tardiness costs and a common deadline (or fixed interval). A heuristic solution is presented for this irrigation scheduling problem. Four models are presented to reflect the different methods in which an irrigation system at the tertiary unit level may be operated, the first model permits jobs to be noncontiguous, i.e., idle time between jobs is permitted, whereas the others permit contiguous jobs only. The heuristic is tested extensively and the solution quality is compared with either an optimum solution from an integer program or the best available solution obtained from an integer program within allocated computation time. The heuristic is computationally efficient for all models presented, however for schedules with noncontiguous jobs, or where idle time is inserted before and after a contiguous set of jobs, solution quality deteriorates. The work brings the science of single scheduling from operations research into irrigation scheduling and suggests areas for further development. [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]

Evolutionary algorithms (EAs) have been used extensively to find globally optimal solutions for water distribution system (WDS) optimization problems. However, as these algorithms are being applied to increasingly complex systems, computational efficiency is becoming an issue, and hence approaches that enable near-optimal solutions to be identified within reasonable computational budgets have received increasing attention. One of these approaches is the initialization of EAs in a manner that accounts for domain knowledge of WDS design problems. Although the effectiveness of these initialization approaches has been studied previously, the impact of algorithm searching behavior on the speed with which near-optimal solutions can be found has not yet been examined. To this end, this study aims to investigate the relative impact of different algorithm initialization methods and searching mechanisms on the speed with which near-optimal solutions can be identified for large WDS optimization problems. Fitness function and run-time behavioral statistics are used for this purpose. The results show that both the starting population and algorithm searching mechanism have an impact on the speed with which near-optimal solutions are identified. The fitness function and run-time behavioral statistics indicate that EA parameterizations that favor exploitation over exploration enable near-optimal solutions to be identified earlier in the search, which is due to the "big bowl" shape of the fitness function for all of the WDS problems considered. Using initial populations that are informed by domain knowledge further increases the speed with which near-optimal solutions can be identified. [ABSTRACT FROM AUTHOR]

A graph theory-based algorithm is demonstrated for optimal pump scheduling of two example application water networks. The hydraulic part of the problem is solved using a dedicated and efficient hydraulic solver. The pump scheduling part of the problem is solved using a skeletonized operational graph, representing only the basic logic operational relations existing in the network required for pump selection: the pumping units (with nominal operating costs), water tanks and clustered demand nodes. The hydraulic solver advances one time step at a time. After each time step advance, the nodes of the model are checked to see if satisfy minimum service pressure and minimum water tank level. For nodes not satisfying the service constraints, the Dijkstra's shortest path algorithm is applied to the skeletonized graph to determine the optimal pumping unit to be activated and then updating the pumps operation pattern in the model. The hydraulic solver is then reinitialized to resolve and recheck the time steps one by one. The algorithm ends when the solver reaches the last time step with all nodes meeting service constraints. The algorithm returns an optimal minimal cost pump-scheduling pattern under greater-than constraints over the examined time period, such as (1) minimal consumer service pressure, and (2) water balance closure at the water tanks. The algorithm returns discrete pump operation scheduling with minimal pump switching and minimal water age in the tanks, demonstrating short solution times (28 s to schedule 11 pumps over a 168-hour period). The algorithm may be applicable for real-time pump scheduling. Future research may include water quality constraints and variable frequency drive pump scheduling. Pump selection is based on the assumption that the optimal pump operation order is not affected by changes in the network's hydraulic conditions, such as water tank levels and location along the pump efficiency curve (assuming constant efficiency). If hydraulic conditions change the optimal activation order, then the pumps' working points must by updated after each time step solution, which is not addressed in the current work. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithms have been successfully used to handle a wide range of water resource optimization problems in recent years. The relative performance of various DE variants has been typically assessed based on the quality of the final solutions for the selected problems within the given computational budget. Such a comparative analysis, however, provides limited under- standing on how various operational mechanisms alter the DE algorithms' searching behavior and what searching properties lead to improved performance. To improve research in this area, this study aims to characterize and compare the searching behavior of four DE variants using a range of measure metrics, mainly focusing on real-time statistics of the algorithm's search quality, search progress, and convergence manner. The utility of the metrics is demonstrated using the four DE variants (SDE, dDE, MdDE, and SADE) applied to three water distribution network (WDN) design problems with significantly increased complexity (scales). The behavioral results offer an appreciably improved understanding of the searching characteristics associated with each DE variant, thereby providing guidance for choosing the most suitable DE algorithm to solve a particular WDN optimization problem as well as offering knowledge to develop new advanced algorithms. For real- world problems, the SDE algorithm is more suitable if a limited computational budget is allowed, whereas the SADE and MdDE variants are respectively more appealing when moderate and large computational budgets are available. A new solution with a cost of $12.62 million for the large-scale problem (1,278 decision variables) is presented. [ABSTRACT FROM AUTHOR]

In order to address the issue of water demand uncertainty due to the effect of climate change and urbanization in the design and management of water distribution systems (WDSs), a flexible methodology that combines sampling techniques (Monte Carlo-MC or Latin Hypercube-LH simulations), decision tree analysis, and genetic algorithm optimization is presented. The methodology gives flexible and optimal decisions as future water demand unfolds. The problem of optimal WDS design under uncertain future water demand is formulated here as a multiobjective optimization problem. The two objectives are as follows: (1) minimisation of total intervention cost; and (2) maximization of WDS end resilience. The decision variables are the conventional design interventions (e.g., pipe duplication and/or replacement of existing pipes with new ones, addition of tanks and pumps, etc.) and the water demand threshold values. The output from the nondominated sorting genetic algorithm (NSGA2) optimisation process is the Pareto front containing staged (developmental) design solutions represented in a decision tree form with an optimal water demand threshold value that results due to the trade-off in terms of the two objectives analyzed over the planning horizon. This methodology was applied on the New York Tunnels and the Anytown network problems. The results show that there is value achieved by building flexibility in design when compared to the deterministic approach in the long-term planning of WDSs under uncertainty. [ABSTRACT FROM AUTHOR]

Surge vessels provide efficient protection against low and high transient pressures in water distribution systems. However, they can be quite expensive, and any reduction in surge vessel size can significantly reduce surge protection costs. Graphical and other heuristic methods reported in literature are limited to sizing surge vessels for simple rising mains. Attempts to use more structured optimization techniques have been largely unsuccessful because of their impractical computational requirements. This article proposes a robust framework for developing surge protection design tools and demonstrates the usefulness of the framework through an example surge vessel sizing tool. The essence of the proposed framework is in the identification of key transient response parameters that influence surge vessel characteristics from seemingly unmanageable transient response data. This parameterization helps the sizing tool to exploit the similarity between transient responses of small pipe networks and subsections of large pipe networks. The framework employs a knowledge-base of transient pressures and flows derived from several small network models and corresponding optimal surge vessel sizes obtained from genetic algorithm (GA) optimizers. Key transient response parameters were identified from this knowledge-base and used as input variables for a neural network model along with the associated surge vessel characteristics as output variables. The trained neural network model was successfully applied for complex pipe networks to obtain optimal surge vessel sizes for transient protection. Neural network model predictions were compared with optimal surge vessel characteristics, and their performance was evaluated by transient simulation models to assess the efficiency of the proposed framework and sizing tool. Application of this framework has the advantage of developing surge protection sizing tools independent of network system schematics and boundary conditions. [ABSTRACT FROM AUTHOR]

This study introduces a new search method for box-constrained optimization problems called the search method for box optimization (SMBO). SMBO is a population heuristic-based search methodology that solves global optimization problems. SMBO represents the population as a probability density function (PDF) inside the problem bounds. The PDF shape is dynamically adapted during the process to guide to a 'good' search domain. The applicability and the efficiency of the method are demonstrated using two benchmark sets, which include unimodal, multimodal, expanded, and hybrid composition functions. The performance of SMBO is compared with several genetic algorithms (GAs); the first benchmark compares it with nine codes of traditional/classic GAs, and the second compares SMBO with two recent variants of genetic algorithms. The results show that SMBO performs as well as or better than the GAs in both comparisons. The method is demonstrated on a nonlinear model for management of a water supply system (WSS), and the results are compared with the commercial GA toolbox of matrix laboratory (MATLAB). [ABSTRACT FROM AUTHOR]

The design of sensor networks for monitoring contaminants in water distribution systems is currently an active area of research. Much of the effort has been directed at the contamination detection problem and the expression of public health protection objectives. Monitoring networks once they are in place, however, are likely to be used to gather monitoring data for source inversion as well. Thus, the design of these networks with the unique objectives associated with source inversion problems in mind is a necessity. Source inversion problems in water distribution systems are inherently underdetermined and exhibit solution nonuniqueness; and moreover, the structure of the errors associated with a solution are a function of monitoring observations. Optimal inverse experiment design is investigated as an approach for improving solution quality. The approach involves the selection of monitoring locations that are best suited to the generation of a well-conditioned source identification inverse problem. The monitoring design problem is formulated as a nonlinear combinatorial optimization problem and solved using a genetic algorithm. The monitoring designs generated exhibit an optimal substructure that may be exploited to develop more efficient methods of solution. An analysis is conducted to evaluate the source inversion performance of an optimized monitoring network relative to networks designed using different methods. The results of the analysis demonstrate that when the source identification problem is underdetermined, the number of monitoring sensors installed in the network is more important than the method used to locate them. [ABSTRACT FROM AUTHOR]

Maintaining a disinfectant residual in water distribution systems (WDSs) is generally considered paramount to ensuring a safe drinking water supply. This objective can be assisted by the use of booster stations to increase disinfectant concentrations throughout the network. However, identifying the appropriate dose at each station is an optimization problem. The aim is to minimize the total mass of disinfectant dosed and reduce the cost of disinfection along with potential taste, odor, or by-product problems, while maintaining a certain minimum residual in the network. The residual present in the water at any location is not only dependent on the amount of disinfectant added to the water, but also the hydraulics of the system and the resulting detention times. A number of previous studies have tackled this optimization problem, however, a review of current literature suggests that in many cases the hydraulics of the system have been held constant, or the WDSs considered were hypothetical systems with relatively few constraints. This study considers the booster disinfection dosing problem, including daily pump scheduling, for a real system in Sydney, Australia. Before the system can be optimized, a representative model is required to ensure useful results, and the many constraints on the daily operation system must be accounted for in the fitness function considered. The results from the optimization study indicate it is necessary to consider the hydraulics as well as the dosing regime in the optimization process, as cycling reservoir levels minimizes detention times, and hence, disinfectant residuals are maintained at the extremities of the network. Also, significant energy cost savings of up to 30% can be made by scheduling the pumping in the system in line with the off-peak electricity costs. [ABSTRACT FROM AUTHOR]

In recent years, drinking water distribution systems security has become a major concern. To protect public health and minimize the effected community by a contaminant intrusion, water quality needs to be continuously monitored and analyzed. Contamination warning systems are being designed to detect and characterize contaminant intrusions into water distribution systems. Since contamination injections can occur at any node at any time the theoretical number of possible injection events, even for a medium-size network, is huge and grows substantially with system size. As a result of that contamination warning systems are designed based on a subset of contamination events, which is not necessarily the most critical. To cope with this difficulty a method derived from cross entropy, which originates from rare event simulations, is proposed. The suggested algorithm is able to sample efficiently a rare subset (i.e., a subset of events with a small probability to occur, but with an extreme impact) of the entire set of possible contamination events. The suggested methodology is demonstrated using an illustrative example and two water distribution systems example applications. [ABSTRACT FROM AUTHOR]

The goal of calibrating a water distribution model is to establish a numerical model that represents the real system. Given the uncertainty in field data, recent studies have examined model parameter and predictive uncertainties and how those uncertainties can guide future data collection experiments. However, a model is to be used in some decision making process and those decisions can be influenced by the model uncertainty. Therefore, a methodology is presented here to evaluate the impact of uncertainty in pipe roughness values on decisions that are made using the model for a system expansion design using a steady state hydraulic model. To complete the analysis, model parameter uncertainty is evaluated using a first order second moment (FOSM) analysis of uncertainty. Parameter uncertainties are then propagated to model prediction uncertainties through a second FOSM for a defined set of demand conditions. Finally, model prediction uncertainties are embedded in an optimal design model to assess the effect of the uncertainties on model-based decisions. If uncertainty levels are large, the monetary benefits of reducing uncertainties from additional data collection can be addressed directly by examining the change in the design cost with additional data. For demonstration, the methodology is applied to a small literature network. Results suggest that the cost reductions are related to the convergence of the mean parameter estimates and the reduction of parameter variances. The impact of each factor changes during the calibration process as the parameters become more precise and the design is modified. Identification of the cause of cost changes, however, is not always obvious. [ABSTRACT FROM AUTHOR]

Cost of effective design or rehabilitation of the pipe networks depends largely on the available budget and satisfying pressures expected at the demand nodes. With the available market pipe sizes, one or more solutions of the same cost, the least cost, and simultaneously meeting the pressure constraints can be obtained from EPANET, a water distribution network simulation model, coupled with an optimization algorithm. Often, however, the least cost may be prohibitive from the overall budget consideration especially in developing countries and a less optimal solution is therefore the only option. The study shows a scheme in which solution selection is made, among solutions, which (1) is within allowable budget; and (2) yields acceptable total pressure deficit distributed more equally at several nodes instead of loaded on one or a few nodes only. A multiobjective optimization algorithm (NSGA-II) is coupled with water distribution network simulation software (EPANET) to provide the much needed Pareto front of the cost and nodal pressure deficit. A two-looped simple network is used to demonstrate the application of the scheme. [ABSTRACT FROM AUTHOR]

We formulate and solve an estimation problem for identifying both the time and location of contamination sources in municipal water networks using concentration measurements from a sparse sensor grid. Previous work showed that the direct sequential approach was insufficient to solve the time-dependent problem. Instead, a direct simultaneous approach is used, converging the network model and optimization problems simultaneously. An origin tracking algorithm is presented to reformulate the pipe expressions and characterize the time delays associated with network pipes. This algorithm removes the need to discretize along the length of the pipes and is efficient for large networks with many source and output nodes. The solution of the resulting nonlinear program provides the complete time-dependent injection profiles, identifying both the time and location of potential contamination sources. The effectiveness of this formulation is demonstrated on a network model for a real municipal water network. [ABSTRACT FROM AUTHOR]

A new approach for reliability-based optimization of water distribution networks is presented. The approach links a genetic algorithm (GA) as the optimization tool with the first-order reliability method (FORM) for estimating network capacity reliability. Network capacity reliability in this case study refers to the probability of meeting minimum allowable pressure constraints across the network under uncertain nodal demands and uncertain pipe roughness conditions. The critical node capacity reliability approximation for network capacity reliability is closely examined and new methods for estimating the critical nodal and overall network capacity reliability using FORM are presented. FORM approximates Monte Carlo simulation reliabilities accurately and efficiently. In addition, FORM can be used to automatically determine the critical node location and corresponding capacity reliability. Network capacity reliability approximations using FORM are improved by considering two failure modes. This research demonstrates the novel combination of a GA with FORM as an effective approach for reliability-based optimization of water distribution networks. Correlations between random variables are shown to significantly increase optimal network costs. [ABSTRACT FROM AUTHOR]

The multiobjective optimization model described in this study is aimed at exploring the tradeoff between cost and resiliency for water distribution systems optimal design. Many have dealt previously with minimizing cost where reliability was quantified as a constraint. Fewer considered both cost and reliability as objectives. This work suggests a methodology for least cost versus reliability (quantified as resiliency) optimal design, introducing the following contributions: (1) a genetic algorithm multiobjective formulation integrating a previous theoretical result of a possible maximum of two adjacent discrete pipe diameters for a single pipe; (2) comparable results to previous best least-cost design solutions for the two-looped and Hanoi networks; (3) a real life-sized example application analysis for pipes reinforcement; and (4) an interpretation of resiliency through its comparison to two explicit reliability measures involving demands increase and pipes failure, reconfirming that resiliency improvement does not necessarily imply a reliability increase. Three example applications are explored through base runs and sensitivity analyses for demonstrating the study findings. [ABSTRACT FROM AUTHOR]