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A noncrossover dither creeping mutation-based genetic algorithm (CMBGA) for pipe network optimization has been developed and is analyzed in this paper. This CMBGA differs from the classic genetic algorithm (GA) optimization in that it does not utilize the crossover operator; instead, it only uses selection and a proposed dither creeping mutation operator. The creeping mutation rate in the proposed dither creeping mutation operator is randomly generated in a range throughout a GA run, rather than being set to a fixed value. In addition, the dither mutation rate is applied at an individual chromosome level rather than at the generation level. The dither creeping mutation probability is set to take values from a small range that is centered about (where = number of decision variables of the optimization problem being considered). This is motivated by the fact that a mutation probability of approximately previously has been demonstrated to be an effective value and is commonly used for the GA. Two case studies are used to investigate the effectiveness of the proposed CMBGA. An objective of this paper is to compare the performance of the proposed CMBGA with four other GA variants and other published results. The results show that the proposed CMBGA exhibits considerable improvement over the considered GA variants, and comparable performance with respect to other previously published results. Two big advantages of the CMBGA are its simplicity and the fact that it requires the tuning of fewer parameters compared with other GA variants. [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]

Contamination emergency in water distribution systems is a complex situation where optimal operation becomes important for public health. In case of emergency corrective operational actions for flushing the pollutant out of the network are needed, which have to be fast and accurate. Under such a stressful situation, trial-and-error simulation experiments with the hydrodynamic and water quality models cannot be applied since significant number of model evaluations may be required to identify the optimal solution. This paper presents a methodology for finding sets of operational interventions in a supply network for flushing a contaminant by minimizing the impact on the population. The situation is treated as both single- and multiobjective optimization problem, which is solved by using evolutionary optimization approaches, in combination with the EPANET solver engine. The methodology is tested on a simple imaginary network configuration, as well as on a real case study for the city of Villavicencio in Colombia. The results prove the usefulness of the approach for advising the operators and decision makers. [ABSTRACT FROM AUTHOR]

The area of systematic identification of contamination sources in water distribution systems is in its infancy and is rapidly growing. The real water distribution network problem poses many challenges that current methods usually assume away to facilitate manageable method development and testing. Current methods may not readily and efficiently address issues, such as multiple sources, unknown contamination types with different reaction kinetics, use of different types of sensors with varying degree of resolution, dynamically varying demand and sensor information, and uncertainty and errors in the data and measurements. With the aim of addressing these imminent challenges, this paper reports the findings of an ongoing research investigation that develops and tests an evolutionary algorithm-based flexible and generic procedure, which is structured within a simulation-optimization paradigm. This paper describes the specific implementation of the method using evolution strategies (ESs), a population-based heuristic global search algorithm. A key component of designing this source characterization method is to define a compact, but comprehensive, solution encoding structure. The new method is constructed using a tree-based encoding design to enable the representation of variable-length decision vectors and a set of associated genetic operators that enable an efficient search. This algorithm is successfully tested and demonstrated to have consistently good performance for several instances of an illustrative water distribution contamination case study. As the ES-based algorithm conducts a probabilistic search, its robustness is tested using multiple random trials, and the method is shown to exhibit a robust behavior. [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]

Cost-effective reduction of water loss is a compelling but challenging task for water utilities. This paper presents a model-based optimization method for leakage detection of water distribution systems. Leakage hotspots are assumed to exist at the model nodes identified. Leakage is represented as pressure-dependent demand simulated as emitter flows at selected model nodes. The leakage detection method is formulated to optimize the leakage node locations and their associated emitter coefficients such that the differences between the model predicted and the field observed values for pressure and flow are minimized. The optimization problem is solved by using a competent genetic algorithm. The leakage detection method is developed as an add-on feature of the optimization-based model calibration tool. This enables engineers to undertake leakage hotspot optimization as an independent task or combine the task with hydraulic model calibration, subject to suitably varied field data. Two case studies are discussed in this paper including an example from literature and a district water system in the United Kingdom. The results obtained illustrate that the optimization model for predicting leakage hotspots can be effective despite the recognized challenges of model calibration and the physical measurement limitations from the pressure and flow surveys also referred to as field tests. It is found that the method is effective at being applied for hydraulic conditions that occur in the early hours of the morning, often on water networks with excess design capacity and where hydraulic gradients are slack and loggers may sometimes be working close to their limits of accuracy. [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 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]

The paper presents a method for the design of water distribution networks with various network elements such as pipes, pumps, and tanks. A steady-state genetic algorithm is used to solve the proposed single objective model. Minimization of total cost, which includes capital cost and energy cost, is considered as the objective. A new approach for tank sizing is proposed, which does not require explicit consideration of some of the operational constraints, such as the limits on maximum and minimum tank levels. Unlike other methods, the one proposed here conducts extended period simulation for every trial solution in the optimization process. To demonstrate the efficacy of the model, a well-known design example, namely the “Anytown” water distribution network is solved. Designs obtained, using the present method, are cheaper than those proposed by other researchers under similar performance conditions but with different tank sizing methods. Comparison of the results obtained with those published in the literature shows the advantage of using the proposed model in obtaining optimal/near optimal solutions. [ABSTRACT FROM AUTHOR]

Following the events of September 11, 2001, in the United States, world public awareness for possible terrorist attacks on water supply systems has increased dramatically. Among the different threats for a water distribution system, the most difficult to address is a deliberate chemical or biological contaminant injection, due to both the uncertainty of the type of injected contaminant and its consequences, and the uncertainty of the time and location of the injection. An online contaminant monitoring system is considered as a major opportunity to protect against the impacts of a deliberate contaminant intrusion. However, although optimization models and solution algorithms have been developed for locating sensors, little is known about how these design algorithms compare to the efforts of human designers, and thus, the advantages they propose for practical design of sensor networks. To explore these issues, the Battle of the Water Sensor Networks (BWSN) was undertaken as part of the 8th Annual Water Distribution Systems Analysis Symposium, Cincinnati, Ohio, August 27–29, 2006. This paper summarizes the outcome of the BWSN effort and suggests future directions for water sensor networks research and implementation. [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]

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]

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]

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]

In this study we provide a methodology for the optimal design of water sensor placement in water distribution networks. The optimization algorithm used is based on a simulation-optimization and a single-objective function approach which incorporates multiple factors used in the design of the system. In this sense the proposed model mimics a multiobjective approach and yields the final design without explicitly specifying a preference among the multiple objectives of the problem. A reliability constraint concept is also introduced into the optimization model such that the minimum number of sensors and their optimal placement can be identified in order to satisfy a prespecified reliability criterion for the network. Progressive genetic algorithm approach is used for the solution of the model. The algorithm works on a subset of the complete set of junctions present in the system and the final solution is obtained through the evolution of subdomain sets. The proposed algorithm is applied to the two test networks to assess the selected design. The results of the proposed solution are discussed comparatively with the outcome of other solutions that were submitted to a water distribution systems analysis symposium. These comparisons indicate that the algorithm proposed here is an effective approach in solving this problem. [ABSTRACT FROM AUTHOR]

Water-distribution systems least-cost pipe sizing/design is probably the most explored problem in water-distribution systems optimization. Attracted numerous studies over the last 4 decades, two main approaches were employed: decomposition in which an “inner” linear programming problem is solved for a fixed set of flows/heads, while the flows/heads are altered at an “outer” problem using a gradient or a subgradient type technique; and the employment of a general evolutionary optimization algorithm. In 1995 Loganathan and his colleagues proposed to couple these two approaches into one framework, thus overcoming the limitations of each. This study employs this framework with two modifications: (1) application of a genetic algorithm for the “outer” optimization search instead of simulated annealing; and (2) constraining the sought solution to the lowest cost spanning tree layout with the spanning tree chords kept at their minimum permissible pipe diameters. A comparison of the methodology to a genetic algorithm application without the refinement of using a spanning tree with minimal chord diameters was explored, showing the proposed methodology dominance. The suggested method is limited to one loading gravitational systems, and is demonstrated using a simple example application. [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]

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]