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The traditional optimization approach for water distribution mains is that of considering a single design scenario with prefixed nodal demands representing the peak values at the end of the life cycle of the construction. Instead, this paper presents a different approach for the design of water distribution mains aimed at considering the phasing of construction. It makes it possible to identify, on prefixed time steps or intervals (for instance 25 years), the upgrade of the construction rendering the network able to satisfy, during the expected life of the system, growing nodal demands related to the increment in the population served. To show the benefits of this approach in comparison to using a single design flow, an optimization methodology, aimed at introducing new pipes in the network as needed at each time step, was set up and applied to a simple case study, where two different scenarios were considered concerning the growth of the network. Results showed that this approach is able to yield better results when compared with the single flow design, because it enables short-term construction upgrades to be performed while keeping a vision of the expected long term network growth. [ABSTRACT FROM AUTHOR]

Optimization for water resources management typically requires many simplifying assumptions about the definition and characteristics of the policy or design application in order to express decision makers’ criteria as mathematical objectives and constraints. However, real-world applications often involve important subjective information that cannot be reflected in mathematical expressions accurately or completely. This can result in mathematically optimized solutions that are less meaningful or desirable to decision makers. To address this issue, this paper presents the standard interactive genetic algorithm (SIGA) methodology that enables human decision makers to effectively analyze subjective information that is not easily quantifiable and make decisions about the quality of a design based on their preferences. These decisions are used as continuous run-time subjective feedback, along with the mathematically defined objectives and constraints, to search for optimal designs that reflect both quantitative and qualitative objectives. Although this interactive optimization methodology is applicable for any water resources planning and management problems, this paper focuses on exploring the benefits of such an approach within the domain of groundwater monitoring design. Systematic procedures and guidelines for designing a SIGA are presented, along with proposed strategies for improving the performance of SIGA. The SIGA approach is also compared with a noninteractive genetic algorithm strategy for a real-world application, and the advantages and limitations of the interactive strategy are examined. [ABSTRACT FROM AUTHOR]

This paper describes the development of an optimization model for the management and operation of a large-scale, multireservoir water supply distribution system with preemptive priorities. The model considers multiobjectives and hedging rules. During periods of drought, when water supply is insufficient to meet the planned demand, appropriate rationing factors are applied to reduce water supply. In this paper, a water distribution system is formulated as a network and solved by the GAMS modeling system for mathematical programming and optimization. A user-friendly interface is developed to facilitate the manipulation of data and to generate graphs and tables for decision makers. The optimization model and its interface form a decision support system (DSS), which can be used to configure a water distribution system to facilitate capacity expansion and reliability studies. Several examples are presented to demonstrate the utility and versatility of the developed DSS under different supply and demand scenarios, including applications to one of the largest water supply systems in the world, the São Paulo Metropolitan Area Water Supply Distribution System in Brazil. [ABSTRACT FROM AUTHOR]

In maintenance of a water distribution network, the allocation of limited funds for maintenance among a network’s pipes and the decision to repair or replace a single pipe when failure occurs are the most important issues. Although some researchers in the past have addressed these issues, more work is needed to support water authorities in making maintenance decisions. In this research paper, a mathematical model is developed that aims to support the decision to allocate funds among pipes of the network as well as the decision to repair or replace the pipes in the state of failure. The objective function of the model is to maximize the total weighted long-run availability of the whole system. The concept of hydraulic reliability is employed to determine the weight of pipes in the maintenance program. The deterioration behavior of the pipe is depicted by a semi-Markov process, and the Dantzig–Wolfe decomposition algorithm is applied to deal with the large-scale characteristic of the resulting program. [ABSTRACT FROM AUTHOR]

Optimal water distribution system (WDS) design including the layout and pipe sizes is invariably complex, even when hydraulic constraints alone are considered. The addition of water quality (WQ) constraints adds to the computational demands. Using conventional WQ models to evaluate the feasibility of the many networks that must be analyzed can extend the optimization process beyond acceptable limits. Artificial neural networks (ANNs) can approximate disinfectant concentrations in a fraction of the time required by deterministic WQ models, and thus have been used for WDS pipe optimization as fast surrogates of these models. This study seeks to improve the performance of ANNs applied to the optimal design of WDSs by comparing their outcomes on the basis of ANN architecture and data used for ANN training, two factors that affect their speed and accuracy. ANNs were trained to forecast the disinfectant concentration at the relevant nodes of two case studies: A simple WDS (common in the literature of WDS pipe optimization) and a complex WDS that supplies an actual community in the city of Maricopa, Arizona. The results obtained for the first case study showed that ANNs estimated disinfectant concentrations with a satisfactory accuracy, regardless of their architecture or data used for their training. Results obtained for the second case study, however, showed that ANNs with a conventional architecture (wherein multiple ANNs are required to forecast the disinfectant concentration at relevant nodes of the WDS) offered advantages in terms of accuracy over two alternative architectures (that each required a single ANN for the same purpose). However, ANNs trained with a conventional random data set showed a poor performance when compared to ANNs trained with an alternative data set that was obtained with the probabilistic approach described in this paper. [ABSTRACT FROM AUTHOR]

A coupled binary linear programming-differential evolution (BLP-DE) approach is proposed in this paper to optimize the design of water distribution systems (WDS). Three stages are involved in the proposed BLP-DE optimization method. In the first stage, the WDS that is being optimized is decomposed into trees and the core using a graph algorithm. Binary linear programming is then used to optimize the design of the trees during the second stage. In the third stage, a differential evolution (DE) algorithm is utilized to deal with the core design while incorporating the optimal solutions for the trees obtained in the second stage, thereby yielding near-optimal solutions for the original whole WDS. The proposed method takes advantage of both the BLP and DE algorithms: BLP is capable of providing a global optimal solution for the trees (no loops involved) with great efficiency, and a DE is able to efficiently generate good quality solutions for the core (loops involved) with a reduced search space compared to the original full network. Two benchmark WDS case studies and one real-world case study (with multiple demand loading cases) with a number of decision variables ranging from 21-96 are used to verify the effectiveness of the proposed BLP-DE optimization approach. Results show that the proposed BLP-DE algorithm significantly outperforms other optimization algorithms in terms of both solution quality and efficiency. [ABSTRACT FROM AUTHOR]

The establishment of an optimal pumping schedule is a cost-free, efficient measure that is easily adopted to reduce energy costs. This paper proposes an optimal pumping scheduling model for complex irrigation water distribution systems (WDS) for the case in which head and efficiency are independent of flow rate. The proposed model utilizes a simplified pumping scheme and a determinist linear programming (LP) optimization algorithm. A robust and versatile software application was also developed that is useful for WDS managers in adopting optimal pumping scheduling decisions for a specific electricity tariff structure and to satisfy all system performance constraints. The model also provides the option of testing and comparing different alternative electricity tariffs and allows managers to select the most cost-effective tariff for their system. The model is applied to a real WDS located in the province of Almería in southeastern Spain. The optimal pumping scheduling during an entire year is obtained for several alternative tariffs using real data on irrigation demands, pumping efficiencies, energy prices, and tariffs for the analyzed year. The most efficient electricity tariff is also obtained for that year. Finally, the actual management strategies in the studied year are compared with the optimal strategies provided by the model. Although the system managers chose an appropriate tariff for their system, the use of this optimization tool would have provided significant savings to their energy bills, exceeding 20% of the total energy costs. [ABSTRACT FROM AUTHOR]

Water distribution networks (WDN) are traditionally designed without integrating tanks in the optimization process, despite the numerous benefits tanks bring to network operation. Since 2004, a number of efforts have been made to integrate tanks, and especially consideration of tank sizing, in optimization models for WDN, but important limitations in these models have impeded their adoption. This paper reviews different approaches to including tank consideration in WDN optimization, and examines the gap between proposed models and current engineering practice. It then analyzes the strengths and weaknesses of these models and suggests a procedure for selecting the most suitable approach to real-world WDN optimization projects. Further research is proposed to improve the validity and applicability of models to decision makers and policymakers. [ABSTRACT FROM AUTHOR]

Calibration is a process of comparing model results with field data and making the appropriate adjustments so that both results agree. Calibration methods can involve formal optimization methods or manual methods in which the modeler informally examines alternative model parameters. The development of a calibration framework typically involves the following: (1) definition of the model variables, coefficients, and equations; (2) selection of an objective function to measure the quality of the calibration; (3) selection of the set of data to be used for the calibration process; and (4) selection of an optimization/manual scheme for altering the coefficient values in the direction of reducing the objective function. Hydraulic calibration usually involves the modification of system demands, fine-tuning the roughness values of pipes, altering pump operation characteristics, and adjusting other model attributes that affect simulation results, in particular those that have significant uncertainty associated with their values. From the previous steps, it is clear that model calibration is neither unique nor a straightforward technical task. The success of a calibration process depends on the modeler's experience and intuition, as well as on the mathematical model and procedures adopted for the calibration process. This paper provides a summary of the Battle of the Water Calibration Networks (BWCN), the goal of which was to objectively compare the solutions of different approaches to the calibration of water distribution systems through application to a real water distribution system. Fourteen teams from academia, water utilities, and private consultants participated. The BWCN outcomes were presented and assessed at the 12th Water Distribution Systems Analysis conference in Tucson, Arizona, in September 2010. This manuscript summarizes the BWCN exercise and suggests future research directions for the calibration of water distribution systems. [ABSTRACT FROM AUTHOR]

The paper describes the development of a DENET computer model that involves the application of an evolutionary optimization technique, differential evolution, linked to the hydraulic simulation solver, EPANET, for optimal design of water distribution networks. A model is formulated with the objective of minimizing cost and this formulation is applied to two benchmark water distribution system optimization problems—New York water supply system and Hanoi water distribution network. The study yielded promising results as compared with earlier studies in the literature and encouraged to reformulate the model for a new objective of maximizing network resilience. The results of the analysis demonstrate that DENET can be considered as a potential alternative tool for economical and reliable water distribution network planning and management. [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]

Reservoir operations play an important role in water resources planning and management. During periods of drought, when inflows to the reservoir are low, it may not be possible to satisfy the target delivery (planned demand), and shortage occurs. Reservoir hedging rules, which include a set of rule curves and rationing factors, are used to guide the operation under such a situation. In particular, hedging rules are employed to balance the current shortage in supply with future storage to avoid severe water shortages in the future. In general, hedging rules are determined at the planning stage, or at the early stage of a reservoir’s operating life. However, after years of operation, the reservoir system, as well as the demand characteristics, may change. Hence, it becomes necessary to reevaluate and update the existing hedging rules to incorporate changes that have taken place. The purpose of this paper is to devise new hedging rules for an existing multireservoir system. An original mixed-integer nonlinear programming model is transformed to a mixed-integer quadratic programming model. A multireservoir system in southern Taiwan is used as a case study to demonstrate the utility of the model. The results show that the optimized new hedging rules improve the efficiency of reservoir operations of the water distribution system. [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]

Water supply is energy intensive, resulting in large amounts of greenhouse gas emissions and increased electricity bills for water service providers (WSPs). In recent years, the incorporation of microhydropower (MHP) turbines within water supply networks (WSN) has been shown to be a viable option for pressure reduction and improved water supply sustainability. An option for optimal pressure management of a WSN is presented through the installation of MHP turbines. The optimization objective was to find optimal locations in a WSN to install turbines for maximized power generation. For comparison, a nonlinear programming approach, a mixed integer nonlinear programming (MINLP) approach, and an evolutionary optimization approach, using a genetic algorithm, were employed. The performance and suitability of each method was initially demonstrated on a theoretical five-node WSN. MINLP was found to be the most suitable technique. Further analyses were undertaken of a benchmark 25-node network. It was recommended that WSPs adopt this hydropower optimization approach in the decision-making process to reduce carbon footprint, increase revenue, and reduce the operational costs of water supply. [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 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]

Following the identification of a contaminant in a water distribution network, a variety of response actions must be examined in order to implement the most beneficial consequence management strategy. Optimization techniques can be employed to determine the cost/benefit of reducing impacts to the network from contamination by isolating and/or flushing the system. In this current effort, we employ a genetic algorithm to minimize contaminant concentrations in a network while minimizing the cost of demand alteration. Application of this technique to two relatively simple networks demonstrates the usefulness of this optimization method as a consequence management strategy to reduce contaminant concentration. For the EPANET Example 1 network, the optimal response solution included closure of two pipes and alteration of the demand at one node, reducing the total network concentration by 95%, with a 73% increase in total network demand. For the Anytown network, the optimal response solution included altering the demand at four nodes, which resulted in a 12% increase in total network demand, while closing four pipes reduced the total network concentration by 54%. [ABSTRACT FROM AUTHOR]

Control and design problems of water distribution systems rely on simulation models for predicting the system behavior under dynamic boundary conditions. A detailed network model may result in thousands to tens of thousands of pipelines and nodes, making the system hydraulics and water quality analysis a complicated task. In this manuscript a methodology and application of a conjunctive hydraulic and water quality model for water distribution systems aggregation is presented. The model outcome provides a reduced network with fewer nodes and links which resembles the original system performance in both the hydraulics (i.e., quantities and pressures) and water quality (i.e., concentrations) at high accuracy. The proposed methodology is demonstrated using the three example applications of EPANET. [ABSTRACT FROM AUTHOR]

A water distribution system was analyzed for optimal sensor placement based on different intrusion scenarios and optimization criteria. The spatial distributions of the selected sensor networks were analyzed and compared using a geographic information system to determine spatial trends in sensor placement. Frequency, average nearest neighbor, and spatial autocorrelation analyses indicated the different intrusion scenarios and optimization criteria created networks with sensors in similar locations and with the same placement order, particularly for the first few sensors placed. Thus, sensor networks based on different optimization criteria and attack scenarios are expected to offer similar protection to the water distribution system. The relationship between sensor location and water demand was also analyzed using a geographic information system and a chi-square analysis. Sensor locations selected by minimizing the volume of consumed contaminated water or minimizing the population affected are likely to coincide with network nodes with a high reachable average demand. Alternatively, sensor locations selected by maximizing the detection likelihood are likely to coincide with network nodes with a low reachable average demand. [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]

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]

A new two-stage iterative methodology is presented for upgrading of single-source water distribution networks to achieve redundancy. In the first stage, the existing network is strengthened using linear programming (LP) for a fixed flow distribution obtained using a model that maximizes flow uniformity by minimizing variance of flows in the distribution network. In the second stage, the performance of the network is assessed under single-pipe failure conditions using a node-flow analysis, and the most critical pipe-failure condition having the maximum deficiency in meeting nodal demands is noted. To also make the network satisfactory during the failure of a critical pipe, a new flow distribution is obtained by removing the critical pipe. Constraints for this new flow distribution along with previous flow distribution are then simultaneously considered in a new LP problem. An improved design of the network is obtained by repeating the first stage. This two-stage methodology is continued until the network becomes capable of meeting demands at all nodes during any single link failure. The proposed methodology is illustrated by upgrading a water main system for redundancy. The results of the application demonstrate that the new methodology is more efficient and less computationally demanding as compared to other methodologies used for upgrading of the illustrative water main system. [ABSTRACT FROM AUTHOR]