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A least-cost optimization of a water distribution system (WDS) results in a branched network if some system reliability measures are not considered. Using an explicit level of system redundancy is one way to enhance reliability in the WDS network. This approach consists of first dividing the network into subsystems. Then, during the optimization stage, the subsystems are optimized simultaneously by demanding each one to maintain some level of service. Which pair of subsystems is ultimately selected determines the outcome of the optimization problem. However, there is little if no literature on the optimization of the selection of a pair of subsystems. This study addresses both subsystem and component sizing optimization in designing a level-1 redundant network. Candidate subsystems are enumerated using graph theory where st-numbering for the network is assigned first, and then the backups are generated following the decrement and increment orders of the node's st-numbering. [ABSTRACT FROM AUTHOR]

The optimal design of WDS has been extensively researched for centuries, but most of these studies have employed deterministic optimization models, which are premised on the assumption that the parameters of the design are perfectly known. Given the inherently uncertain nature of many of the WDS design parameters, the results derived from such models may be infeasible or suboptimal when they are implemented in reality due to parameter values that differ from those assumed in the model. Consequently, it is necessary to introduce some uncertainty in the design parameters and find more robust solutions. Robust counterpart optimization is one of the methods used to deal with optimization under uncertainty. In this method, a deterministic data set is derived from an uncertain problem, and a solution is computed such that it remains viable for any data realization within the uncertainty bound. This study adopts the newly emerging robust optimization technique to account for the uncertainty associated with nodal demand in designing water distribution systems using the subsystem-based two-stage approach. Two uncertainty data models with ellipsoidal uncertainty set in consumer demand are examined. The first case, referred to as the uncorrelated problem, considers the assumption that demand uncertainty only affects the mass balance constraint, while the second case, referred to as the correlated case, assumes uncertainty in demand and also propagates to the energy balance constraint. [ABSTRACT FROM AUTHOR]

The multi-objective design optimization of water distribution systems (WDS) is to find the Pareto front of optimal designs of WDS for two or more conflicting design objectives. The most popular conflicting objectives considered for the design of WDS are minimization of cost and maximization of resilience index which are considered for the current study. Robust multi-objective optimization is to find the optimal set of the Pareto front considering demand is uncertain. The robustness is controlled by a single parameter that defines the size of the uncertainty set it can vary. The study explores ellipsoidal uncertainty set with different sizes and co-variance matrices. A combined simulation–optimization framework with a combination of self-adaptive multi-objective cuckoo search (SAMOCSA) and the fmincon optimization algorithm is proposed to solve the robust multi-objective design problem. The proposed algorithm is applied to medium and large WDS. The main contribution of this paper is to study the effect of demand uncertainty and the correlation on the WDS designs in a multi-objective framework. The study shows that the inclusion of correlation into the multi-objective design framework can significantly affect the optimal designs. [ABSTRACT FROM AUTHOR]

Least-cost operation of water distribution systems (WDS) is a well-known problem in water distribution systems optimization. The formulation of the problem started with deterministic modeling, and the problem was subsequently handled with more sophisticated stochastic models that incorporate uncertainties related to the problem’s parameters. This work applied a recently developed algorithm entitled limited multistage stochastic programming (LMSP) to deal with the stochastic formulation of the least-cost operation of WDS and serves merely as a proof of concept on an illustrative network. The demand is considered as the uncertain parameter in the problem formulation. This algorithm reduces the complexity of the classical multistage stochastic programming (MSP) by adding constraints which result in a linear growth of the problem, as opposed to an exponential growth in the MSP problem. This is accomplished by clustering decision variables based on a postanalysis of the implicit stochastic program of the problem. The clusters allow reduction of the number of decision variables, thus reducing the complexity of the optimization problem. The LMSP is expected to increase the cost because of the additional constraints imposed on the problem; however, a trade-off exists between the computational complexity and the optimality of the objective value to the number of clusters considered. An illustrative example application is provided for demonstrating the suggested methodology abilities. [ABSTRACT FROM AUTHOR]

Least-cost design of water distribution system is a well-known problem in the literature. The formulation of the least-cost design problem started by deterministic modeling and later by more sophisticated stochastic models that incorporate uncertainties related to the problem's parameters. Recently, a new nonprobabilistic modeling, titled the robust counterpart (RC) approach, has been developed for the least-cost design problem to incorporate the uncertainty without the need for full stochastic information. These nonprobabilistic methods, developed in the field of robust optimization, were shown to be advantageous over classical stochastic methods in the following aspects: tractability and computation time, nonnecessity of full probabilistic information, and the ability to integrate correlation of uncertain parameters aspects without adding complexity. Former studies have considered the RC approach for a special case of the least-cost problem with a single load demand uncertainty, and single gravitational source to simplify the problem formulation and facilitate the use of the method. This special case does not handle the joint temporal and spatial correlations between the problem uncertainties and does not include components such as pumping stations and storage facilities. These new components require trading off capital and operation (i.e., energy) costs in the objective function, as the design cost is explicitly influenced by the demand uncertainty, unlike the situation where only capital cost is considered. In this study, the RC approach is expanded to cover the general least-cost design problem, including (1) multiload patterns, (2) pumping stations, and (3) storage facilities. The unknowns are the pipe diameters, pump and tank capacities, and the heads added by the pumping stations. The problem is solved using the cross-entropy method for several possible protection levels, which are defined by the size of the uncertainty set. The results are demonstrated on two examples to show the trade-off between cost and reliability and test the network's ability to cope with unexpected scenarios. [ABSTRACT FROM AUTHOR]

The battle of background leakage assessment for water networks (BBLAWN) challenge was approached using successive linear programming. A linear representation was solved successively for the nonlinear constraints of headloss, leakage, pump energy consumption, and pipe sizing. The optimization model returned minimal cost pump scheduling and pipe sizing while minimizing leakage and maintaining minimum service pressures to the consumers. Pressure reducing valves, pump, and water tank sizing were performed manually and their effect was examined using the optimization model. Parallel pipes were added along the main supply pipes from the pumping stations to the water tanks, to allow for minimum service pressures. Pressure reducing valves were added to pipes branching from the main supply pipes to lower excess pressures to the secondary supply pipes. [ABSTRACT FROM AUTHOR]

Abstract: This study describes a decision support system, alerts for contamination events in water distribution systems. The developed model comprises a weighted support vector machine (SVM) for the detection of outliers, and a following sequence analysis for the classification of contamination events. The contribution of this study is an improvement of contamination events detection ability and a multi-dimensional analysis of the data, differing from the parallel one-dimensional analysis conducted so far. The multivariate analysis examines the relationships between water quality parameters and detects changes in their mutual patterns. The weights of the SVM model accomplish two goals: blurring the difference between sizes of the two classes' data sets (as there are much more normal/regular than event time measurements), and adhering the time factor attribute by a time decay coefficient, ascribing higher importance to recent observations when classifying a time step measurement. All model parameters were determined by data driven optimization so the calibration of the model was completely autonomic. The model was trained and tested on a real water distribution system (WDS) data set with randomly simulated events superimposed on the original measurements. The model is prominent in its ability to detect events that were only partly expressed in the data (i.e., affecting only some of the measured parameters). The model showed high accuracy and better detection ability as compared to previous modeling attempts of contamination event detection. [Copyright &y& Elsevier]

Abstract: Decision-making processes often involve uncertainty. A common approach for modeling uncertain scenario-based decision-making progressions is through multi-stage stochastic programming. The size of optimization problems derived from multi-stage stochastic programs is frequently too large to be addressed by a direct solution technique. This is due to the size of the optimization problems, which grows exponentially as the number of scenarios and stages increases. To cope up with this computational difficulty, solution schemes turn to decomposition methods for defining smaller and easier to solve equivalent sub-problems, or through using scenario-reduction techniques. In our study a new methodology is proposed, titled Limited Multi-stage Stochastic Programming (LMSP), in which the number of decision variables at each stage remains constant and thus the total number of decision variables increases only linearly as the number of scenarios and stages grows. The LMSP employs a decision-clustering framework, which utilizes the optimal decisions obtained by solving a set of deterministic optimization problems to identify decision nodes, which have similar decisions. These nodes are clustered into a preselected number of clusters, where decisions are made for each cluster instead of for each individual decision node. The methodology is demonstrated on a multi-stage water supply system operation problem, which is optimized for flow and salinity decisions. LMSP performance is compared to that of classical multi-stage stochastic programming (MSP) method. [Copyright &y& Elsevier]

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]

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]

Abstract: A computerized learning algorithm was developed for assessing the extent of biofouling formations on the inner surfaces of water supply pipelines. Four identical pipeline experimental systems with four different types of inlet waters were set up as part of a large cooperative project between academia and industry in Israel on biofouling modeling, prediction, and prevention in pipeline systems. Samples were taken periodically for hydraulic, chemical, and biological analyses. Biofilm sampling was done using Robbins devices, carrying stainless steel coupons. An MT–GA, a hybrid model combining model trees (MTs) and genetic algorithms (GAs) in which the sampled input data are selected by the proposed methodology, was developed. The method outcome is a set of empirical linear rules which form a model tree, iteratively optimized by a GA and verified using the dataset resulting from the empirical field studies. Good correlations were achieved between modeled and observed cell coverage area within the biofilm. Sensitivity analysis was conducted by testing the model’s response to changes in: (1) the biofilm measure used as output (target) variable; (2) variability of GA parameters; and (3) input attributes. The proposed methodology provides a new tool for biofouling assessment in pipelines. [Copyright &y& Elsevier]

This paper describes and demonstrates an efficient method for online hydraulic state estimation in urban water networks. The proposed method employs an online predictor-corrector (PC) procedure for forecasting future water demands. A statistical data-driven algorithm (M5 Model-Trees algorithm) is applied to estimate future water demands, and an evolutionary optimization technique (genetic algorithms) is used to correct these predictions with online monitoring data. The calibration problem is solved using a modified least-squares (LS) fit method (Huber function) in which the objective function is the minimization of the residuals between predicted and measured pressure at several system locations, with the decision variables being the hourly variations in water demands. To meet the computational efficiency requirements of real-time hydraulic state estimation for prototype urban networks that typically comprise tens of thousands of links and nodes, a reduced model is introduced using a water system-aggregation technique. The reduced model achieves a high-fidelity representation for the hydraulic performance of the complete network, but greatly simplifies the computation of the PC loop and facilitates the implementation of the online model. The proposed methodology is demonstrated on a prototypical municipal water-distribution system. [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]

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]

Developed and demonstrated in this paper is an ant colony methodology extending previous work on ant colony optimization for least-cost design of gravitational water distribution systems with a single loading case, to the conjunctive least-cost design and operation of multiple loading pumping water distribution systems. Ant colony optimization is a relatively new meta-heuristic stochastic combinatorial computational discipline inspired by the behavior of ant colonies: ants deposit a certain amount of pheromone while moving, with each ant probabilistically following a direction rich in pheromone. This behavior has been used to explain how ants can find the shortest path between their nest and a food source, and inspired the development of ant colony optimization. The optimization problem solved herein is through linking an ant colony scheme with EPANET for the minimization of the systems design and operation costs, while delivering the consumers required water quantities at acceptable pressures. The decision variables for the design are the pipe diameters, the pumping stations maximum power, and the tanks storage, while for the operation—the pumping stations pressure heads and the water levels at the tanks for each of the loadings. The constraints are domain pressures at the consumer nodes, maximum allowable amounts of water withdrawals from the sources, and tanks storage closure. The proposed scheme is explored through base runs and sensitivity analysis using two pumping water distribution systems examples. [ABSTRACT FROM AUTHOR]

A simple, straightforward, modified genetic algorithm scheme for contaminant source characterization using imperfect sensors is presented and demonstrated in this study. Previous work on this subject concentrated on developing source-inversion models using sensors that provide accurate, unbiased, contamination concentration measurements. The developed contamination source-detection model is implemented using three sensor types: (1) perfect sensors providing accurate, unbiased, contamination concentration measurements; (2) sensors transmitting fuzzy measured information (i.e., high, medium, and low contamination); and (3) '0-1' (Boolean) sensors indicating only a contamination presence. A comparison between the three sensor types is explored taking into consideration thesystem's response time (i.e., the time elapsed between a contaminant detection and a decision-maker's response action). The methodology capabilities are demonstrated using two example applications of increasing complexity, showing the trade-offs between the sensor types and the model abilities to receive a unique solution to the source-detection problem. [ABSTRACT FROM AUTHOR]

The optimal design problem of a water distribution system is to find the water distribution system component characteristics (e.g. pipe diameters, pump heads and maximum power, reservoir storage volumes, etc.) which minimize the system's capital and operational costs such that the system hydraulic laws are maintained (i.e. Kirchhoff's first and second laws), and constraints on quantities and pressures at the consumer nodes are fulfilled. In this study, an adaptive stochastic algorithm for water distribution systems optimal design based on the heuristic cross-entropy method for combinatorial optimization is presented. The algorithm is demonstrated using two well-known benchmark examples from the water distribution systems research literature for single loading gravitational systems, and an example of multiple loadings, pumping, and storage. The results show the cross-entropy dominance over previously published methods. [ABSTRACT FROM AUTHOR]

This article extends previous work on optimal booster chlorination injection design and operation in water distribution systems by solving the scheduling problem of pumping units in conjunction with the design and operation problem of booster chlorination stations. Two models are formulated and solved using a genetic algorithm scheme tailor-made to EPANET: Min Cost—for minimizing the costs of pumping and the chlorine booster design and operation, and Max Protection—for maximizing the system protection by maximizing the injected chlorine dose. An example application is explored through a base run and sensitivity analysis showing that the algorithm proposed is robust and reliable, and that the pump and chlorine injection scheduling are mutually connected. [ABSTRACT FROM AUTHOR]

The events of September 11, 2001 in the United States have brought to the fore the problem of drinking water distribution systems security. As a water distribution system is spatially diverse, limiting physical access to all components is practically impossible. Deliberate intrusions of contaminants directly into tanks, treatment plants, or through connecting devices is considered one of the most serious terrorist threats. An effective means of reducing this threat is online contamination monitoring. This paper extends previous work of the writers for optimal allocation of monitoring stations to secure drinking water distribution systems against deliberate contamination intrusions. The current methodology takes explicitly into account the randomness of the flow rate of the injected pollutants, the randomness in consumer’s demands, and the detection sensitivity and response time of the monitoring stations. The objective is to determine the optimal location of a set of monitoring stations aimed at detecting deliberate external terrorist hazard intrusions through water distribution system nodes: sources, tanks, treatment plant intakes, consumers—subject to extended period hydraulic demands and water quality conditions, and a maximum volume of polluted water exposure to the public at a concentration higher than a minimum hazard level. The methodology is implemented in a noncommercial program entitled optiMQ-S and demonstrated on EPANET Example 3. [ABSTRACT FROM AUTHOR]

A method incorporating a genetic algorithm tailored to EPANET for the conjunctive optimal design and operation of multiquality water distribution systems under unsteady hydraulics is presented and demonstrated. The objective is to minimize the total cost of designing and operating the system for a selected operational time horizon while delivering to consumers the required quantities at acceptable qualities and pressures. The decision variables for the design are the pipe diameters, tank maximum storage, maximum pumping unit power, and maximum removal ratios at the treatment facilities. For the operation phase, the decision variables are set for each time step of the total operational time horizon. These decisions include the scheduling of the pumping units and the treatment removal ratios at the treatment facilities. The constraints are domain heads and concentrations at consumer nodes, maximum removal ratios at the treatment facilities, maximum allowable amounts of water withdrawals at the sources, and return at the end of the operational time horizon to a prescribed total storage in the water distribution system tanks. The model is explored through two example applications. [ABSTRACT FROM AUTHOR]

This paper describes the methodology and application of a genetic algorithm scheme tailor-made to EPANET, for optimizing the operation of a water distribution system under unsteady water quality conditions. The water distribution system consists of sources of different qualities, treatment facilities, tanks, pipes, control valves, and pumping stations. The objective is to minimize the total cost of pumping and treating the water for a selected operational time horizon, while delivering the consumers the required quantities at acceptable qualities and pressures. The decision variables for each of the time steps that encompass the total operational time horizon include: the scheduling of the pumping units, settings of the control valves, and treatment removal ratios at the treatment facilities. The constraints are: head and concentrations at the consumer nodes, maximum removal ratios at the treatment facilities, maximum allowable amounts of water withdrawals at the sources, and returning at the end of the operational time horizon to a prescribed total volume in the tanks. The model is explored through two example applications. [ABSTRACT FROM AUTHOR]

This study aims to develop and solve a multi-objective water distribution systems optimization problem incorporating pumps' optimal scheduling and leakage minimization. An iterative optimization model was presented for calibrating and computing leakages in water distribution systems to recognize the critical impact of leakage control on system operation. The multi-dimensional and nonlinear optimization model, incorporating pump control, consumer demands, storage, and other water distribution systems' components, was constructed and was minimized using a multi-objective genetic algorithm coupled with hydraulic simulations. The model was demonstrated on two example applications with increasing complexity through base runs and sensitivity analyses. Results showed that leakage minimization competes against pumping, mainly when significant differences occur between demands during low and high energy tariffs. Pumping during the periods with high electricity tariffs (when the demands are high) generated pressure distribution that decreased the overall leakage related to pump scheduling that replicated the natural inclination to pump as much as possible at low tariffs (when the demands are low). The optimal fronts were found to be very sensitive to the leakage exponent value, and changing its value indeed contradicted the balance between minimizing the leakage and the energy cost significantly. Altogether, the idea presented in this paper was found capable of facilitating the decision-makers to conveniently select between the energy-efficient pump scheduling and pump scheduling reflecting minimum leakage based on the system operator's preferences. The research also paves the way to rebuild the optimization model by incorporating water distribution reliability and water quality that, in some cases, may also contradict the choice between energy cost and leakage minimization. [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]