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An integrated participatory approach based on Bayesian belief network (BBN) and evolutionary multiobjective optimization is proposed as an efficient decision-making tool in complex management problems. The proposed methodology incorporates all the available evidence and conflicting objectives to evaluate implications of alternative actions in the decision-making process and suggests best decision pathways under uncertainty. A BBN provides a framework within which the contributions of stakeholders can be taken into account. It allows a range of different factors and their probabilistic relationship to be considered simultaneously. It takes into account uncertainty by assigning probability to those variables whose states are not certain. The integration of BBN with evolutionary multiobjective optimization allows the analysis of tradeoff between different objectives and incorporation and acknowledgement of a broader set of decision goals into the search and decision-making process. The proposed methodology can be used as a decision support tool to model decision-making processes for complex problems. It deals with uncertainties in decision making pertaining to human behavior and checks for consistency of the developed BBN structure and the parameters of the probabilistic relationship by uncovering discrepancies in the decision analysis process (e.g., bias in completeness or redundancy of the model based on a utility function). It generates a set of efficient management options (appropriate combinations of interventions) that balances conflicting objectives. The effectiveness of the proposed methodology is discussed through application to a real case study. It is shown that it successfully identifies any inconsistencies in the developed BBN models and generates large numbers of management options that achieve an optimal tradeoff between different objectives., (Copyright © 2011 SETAC.)

The worsening water scarcity has imposed a significant stress on food production in many parts of the world. This stress becomes more critical when countries seek self-sufficiency. A literature review shows that food self-sufficiency has not been assessed as the main factor in determining the optimal cultivation patterns. However, food self-sufficiency is one of the main policies of these countries and requires the most attention and concentration. Previous works have focused on the virtual water trade to meet regional food demand and to calculate trade flows. The potential of the trade network can be exploited to improve the cropping pattern to ensure food and water security. To this end, and based on the research gaps mentioned, this study develops a method to link intra-country trade networks, food security, and total water footprints (WFs) to improve food security. The method is applied in Iran, a water-scarce country. The study shows that 781 × 106 m3 of water could be saved by creating a trade network. Results of the balanced trade network are input to a multi-objective optimization model to improve cropping patterns based on the objectives of achieving food security and preventing water crises. The method provides 400 management scenarios to improve cropping patterns considering 51 main crops in Iran. Results show a range of improvements in food security (19-45%) and a decrease in WFs (2-3%). The selected scenario for Iran would reduce the blue water footprint by 1207 × 106 m3, and reduce the cropland area by 19 × 103 ha. This methodology allows decision makers to develop policies that achieve food security under limited water resources in arid and semi-arid regions.

This paper investigates the application of multiobjective evolutionary algorithms to the identification of the payoff characteristic between total cost and reliability of a water distribution system using the well-known 'Anytown' network as an example. An expanded rehabilitation problem is considered where the design variables are the pipe rehabilitation decisions, tank sizing, tank siting, and pump operation schedules. To provide flexibility, the network is designed and operated under multiple loading conditions. Inclusion of pump operation schedules requires consideration of water system operation over an extended period. The cost of the solution includes the capital costs of pipes and tanks as well as the present value of the energy consumed during a specified period. Optimization tends to reduce costs by reducing the diameter of, or completely eliminating, some pipes, thus leaving the system with insufficient capacity to respond to pipe breaks or demands that exceed design values without violating required performance levels. A resilience index is considered as a second objective to increase the hydraulic reliability and availability of water during pipe failures. Sensitivity analysis of solutions on the payoff curve generated by twin-objective optimization shows poor performance of these networks under random pipe failure or a pump being out of service. The minimum surplus head is added as a third objective to overcome the shortcomings of the resilience index. Results are presented for the payoff characteristics between total cost and reliability for 24 h design and five loading conditions. DOI: 10.1061/(ASCE)0733-9496(2005) 131:3(161) CE Database subject headings: Water distribution: Multiple objective analysis: Water tanks: Pumping: Operation: Rehabilitation: Water pipelines.

Sampling design (SD) for water distribution systems (WDS) is an important issue, previously addressed by various researchers and practitioners. Generally, SD has one of several purposes. The aim of the methodologies developed and presented here is to find the optimal set of network locations for pressure loggers, which will be used to collect data for the calibration of a WDS model. First, existing SD approaches for WDS are reviewed. Then SD is formulated as a multiobjective optimization problem. Two SD models are developed to solve this problem, both using genetic algorithms (GA) as search engines. The first model is based on a single-objective GA (SOGA) approach in which two objectives are combined into one using appropriate weights. The second model uses a multiobjective GA (MOGA) approach based on Pareto ranking. Both SD models are applied to two case studies (literature and real-life problems). The results show several advantages and one disadvantage of the MOGA model when compared to SOGA. A comparison of the MOGA SD model solution to the results of several published SD models shows that the Pareto optimal front obtained using MOGA acts as an envelope to the Pareto fronts obtained using previously published SD models. CE Database subject headings: Sampling; Water distribution; Calibration; Pipe networks; Algorithms.

Optimisation of water distribution system design is a well-established research field, which has been extremely productive since the end of the 1980s. Its primary focus is to minimise the cost of a proposed pipe network infrastructure. This paper reviews in a systematic manner articles published over the past three decades, which are relevant to the design of new water distribution systems, and the strengthening, expansion and rehabilitation of existing water distribution systems, inclusive of design timing, parameter uncertainty, water quality, and operational considerations. It identifies trends and limits in the field, and provides future research directions. Exclusively, this review paper also contains comprehensive information from over one hundred and twenty publications in a tabular form, including optimisation model formulations, solution methodologies used, and other important details. [ABSTRACT FROM AUTHOR]

Nowadays, the unprecedented computing power of desktop personal computers and efficient computational methodologies such as the global gradient algorithm (GGA) make large water-distribution-system modeling feasible. However, many network analysis applications, such as optimization models, require running numerous hydraulic simulations with modified input parameters. Therefore, a methodology that can reduce the computational burden of network analysis and still provide the required model accuracy is needed. This paper presents a matrix transformation approach to convert the classic GGA, which is implemented within the widely available freeware EPANET 2, into a more computationally efficient enhanced global gradient algorithm (EGGA). The latter achieves improved efficiency by reducing the size of the mathematical problem through the transformed topological representation of the original network model. By removing serial nodes and serial pipe sections from the original topological representation while preserving those elements in both energy and mass balance equations, EGGA significantly improves the model's computational efficiency without forfeiting its hydraulic accuracy. The computational efficiency and effectiveness of the EGGA approach are demonstrated on four real-life networks. Results show that the computational burden of the EGGA model is significantly lower than that of its GGA counterpart, particularly as the size of the network and/or number of service connections increases. [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]

During the last two decades, the water resources planning and management profession has seen a dramatic increase in the development and application of various types of evolutionary algorithms (EAs). This observation is especially true for application of genetic algorithms, arguably the most popular of the several types of EAs. Generally speaking, EAs repeatedly prove to be flexible and powerful tools in solving an array of complex water resources problems. This paper provides a comprehensive review of state-of-the-art methods and their applications in the field of water resources planning and management. A primary goal in this ASCE Task Committee effort is to identify in an organized fashion some of the seminal contributions of EAs in the areas of water distribution systems, urban drainage and sewer systems, water supply and wastewater treatment, hydrologic and fluvial modeling, groundwater systems, and parameter identification. The paper also identifies major challenges and opportunities for the future, including a call to address larger-scale problems that are wrought with uncertainty and an expanded need for cross fertilization and collaboration among our field’s subdisciplines. Evolutionary computation will continue to evolve in the future as we encounter increased problem complexities and uncertainty and as the societal pressure for more innovative and efficient solutions rises. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology for assessing an isolation valve system and the portions of a water distribution network (segments) directly isolated by valve closure. Planned (e.g. regular maintenance) and unplanned interruptions (e.g. pipe burst) occur regularly in water distribution networks, making it necessary to isolate pipes. To isolate a pipe in the network, it is necessary to close a subset of valves which directly separate a small portion of the network, i.e., causing minimum possible disruption. This is not always straightforward to achieve as the valve system is not normally designed to isolate each pipe separately (i.e. having two valves at the end of each pipe). Therefore, for management purposes, it is important to identify the association between each subset of valves and the segments directly isolated by closing them. Furthermore, it is also important to improve the design of the isolation valve system in order to increase network reliability. Thus, this paper describes an algorithm for identifying the association between valves and isolated segments. The approach is based on the use of topological matrices of a network whose topology is modified in order to account for the existence of the valve system. The algorithm is demonstrated on a simple network and tested on an Apulian network where the isolation valve system is designed using a classical multi-objective optimisation using genetic algorithms. [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]

Planned (e.g., regular maintenance) and unplanned (e.g. pipe burst) interruptions occur regularly in water distribution systems leading to their reduced performance. This paper presents an extended period simulation model capable of assessing system’s performance under these conditions. The extended period simulation model is based on the recently developed steady-state pressure driven hydraulic model and is capable of calculating pressures, flows, and hence actual water demands delivered under modified network topology conditions (caused by the use of isolation valves). The model is accompanied by several reliability indicators which can be used to assess system’s performance under interruptions. The above-mentioned methodology is demonstrated on a real-life case study in Italy. The role of isolation valve design and uncertainty in valve operability is analyzed and discussed. The case study results obtained demonstrate that the least cost design/rehabilitation of water distribution systems is likely to result in unreliable systems if the actual network configurations obtained by closing isolation valves in abnormal working conditions are not taken into account. [ABSTRACT FROM AUTHOR]

Increasingly, water loss via leakage is acknowledged as one of the main challenges facing water distribution system operations. The consideration of water loss over time, as systems age, physical networks grow, and consumption patterns mature, should form an integral part of effective asset management, rendering any simulation model capable of quantifying pressure-driven leakage indispensable. To this end, a novel steady-state network simulation model that fully integrates into a classical hydraulic representation, pressure-driven demand and leakage at the pipe level is developed and presented here. After presenting a brief literature review about leakage modeling, the importance of a more realistic simulation model allowing for leakage analysis is demonstrated. The algorithm is then tested from a numerical standpoint and subjected to a convergence analysis. These analyses are performed on a case study involving two networks derived from real systems. Experimentally observed convergence/error statistics demonstrate the high robustness of the proposed pressure-driven demand and leakage simulation model. [ABSTRACT FROM AUTHOR]

Topological and pressure-driven analyses are an integral part of reliability/risk considerations for a water distribution system. For example, it is often necessary to identify which parts of the distribution network are isolated from water sources after the valves have been closed in response to a mechanical pipe failure. Pressure-driven analysis is then necessary to ascertain the consequences of pipe failures in terms of the performance of the functioning subsystem while pipe breaks are being fixed in the isolated area. Therefore, it is extremely useful to have an algorithm for the automatic identification of nodes/pipes disconnected from the water source(s). However, this is a complex problem because valves sometimes significantly modify the network topology. Furthermore, the use of isolation valves can cause a demand shortage to some customers (due to pressure reduction) during the abnormal operating conditions in the system. Thus, pressure-driven simulation of the network behavior is required. For these reasons, a novel algorithm capable of automatic detection of topological network changes is coupled with a robust pressure-driven simulation model. This algorithm is tested on two case studies involving a small artificial water distribution system and a larger, real-life network. The results obtained clearly demonstrate the robustness of the algorithm developed. [ABSTRACT FROM AUTHOR]

The problem of stochastic ( i.e . robust) water distribution system (WDS) design is formulated and solved here as an optimization problem under uncertainty. The objective is to minimize total design costs subject to a target level of system robustness. System robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. The sources of uncertainty analysed here are future water consumption and pipe roughnesses. All uncertain model input variables are assumed to be independent random variables following some pre-specified probability density function (PDF). Two new methods are developed to solve the aforementioned problem. In the Integration method, the stochastic problem formulation is replaced by a deterministic one. After some simplifications, a fast numerical integration method is used to quantify the uncertainties. The optimization problem is solved using a standard genetic algorithm (GA). The Sampling method solves the stochastic optimization problem directly by using the newly developed robust chance constrained GA. In this approach, a small number of Latin Hypercube (LH) samples are used to evaluate each solution’s fitness. The fitness values obtained this way are then averaged over the chromosome age. Both robust design methods are applied to a New York Tunnels rehabilitation case study. The results obtained lead to the following main conclusions: (i) neglecting demand uncertainty in WDS design may lead to serious under-design of such systems; (ii) both methods shown here are capable of identifying (near) optimal robust least cost designs achieving significant computational savings. [ABSTRACT FROM AUTHOR]

Due to inherent variability in instantaneous water consumption levels, values of demands at nodes in a water distribution system remain one of the major sources of uncertainty in the network design process. Uncertainty in demand leads to uncertainty in head at the nodes, which, in turn, affects the system performance and has to be taken into account when designing new water distribution systems or extending/rehabilitating existing ones. One approach to dealing with this difficulty is to formulate and solve the stochastic optimization problem providing a robust, cost-effective solution. However, stochastic formulation usually requires Monte Carlo simulation, which involves calculation of a large number of state estimates, even for relatively simple networks. This renders the approach intractable when combined with heuristic adaptive search techniques, such as genetic algorithms (GAs) or simulated annealing. These methodologies require the fitness function to be evaluated for thousands of possible network configurations in the course of the search process. In this paper a new approach to quantifying the influence of demand uncertainty on nodal heads is proposed. The original stochastic model is reformulated as a deterministic one, which uses standard deviation as a natural measure of variability. Such an approach allows the use of effective numerical methods to quantify the influence of uncertainty on the robustness of water distribution system solutions. The deterministic equivalent is then coupled with an efficient GA solver to find robust and economic solutions. The proposed methodology was tested on the New York tunnels and Anytown problems. A number of low cost network solutions were found for different levels of reliability and different forms of probability distribution function for demands. The robustness of the solutions found was compared to known solutions for deterministic formulations, whose results were postprocessed using full Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

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

Sampling design (SD) for water distribution systems (WDS) is undoubtedly an important issue, and has been addressed in the past by a number of scientists and practitioners. The aim of the SD methodology developed here is to find a set of optimal network locations at which to place measurement devices. Optimal locations are determined with the aim of collecting data that will be used later on in the calibration of the analyzed WDS hydraulic model. First, existing calibration and SD approaches in the case of WDS are reviewed. After that, SD is formulated as a two-objective optimization problem. The objectives are maximization of the calibrated model accuracy by minimization of the relevant uncertainties, and minimization of total SD costs. The optimal SD problem is then solved using a multiobjective genetic algorithm based on Pareto ranking, niching, and restricted mating. The methodology developed is applied and verified on a case study. At the end, a summary is made and relevant conclusions are drawn. [ABSTRACT FROM AUTHOR]

A new software tool, GACOMP, for the optimal design of general and symmetric/balanced laminates (or sandwich panels) with specified mechanical properties has been developed. The approach taken relies on the analysis of a given laminate, of known materials and stacking sequence, and on an efficient genetic algorithm-based optimization procedure to come up with the best design with respect to single or multiple objectives and constraints. Required engineering constants or their ratios, weight, strength, anisotropy, isotropy, or twist, considered individually or in any combination, can be used as optimization objectives. Several improvements to the genetic algorithms were introduced to provide faster convergence and the ability to identify multiple optima in a single run. Two practical examples are presented to show the effective performance of GACOMP The first tackles the design of a composite laminate with specified in-plane and flexural engineering constants, while the second deals with the design of a laminate with specified stiffness ratios, minimum twisting under the load considered, and maximum strength. [ABSTRACT FROM AUTHOR]

The article discusses the study "Optimum Design and Management of Pressurized Branched Irrigation Networks." The study explores the disadvantages of using a simple genetic algorithm in looking for a global optimum for branched networks. The authors explain that the created modified genetic algorithm has one operator responsible for considering the combinatorial nature of the problem.

Various multiobjective evolutionary algorithms (MOEAs) have been applied to solve the optimal design problems of a water distribution system (WDS). Such methods are able to find the near-optimal trade-off between cost and performance benefit in a single run. Previously published work used a number of small benchmark networks and/or a few large, real-world networks to test MOEAs on design problems of WDS. A few studies also focused on the comparison of different MOEAs given a limited computational budget. However, no consistent attempt has been made before to investigate and report the best-known approximation of the true Pareto front (PF) for a set of benchmark problems, and thus there is not a single point of reference. This paper applied 5 state-of-the-art MOEAs, with minimum time invested in parameterization (i.e., using the recommended settings), to 12 design problems collected from the literature. Three different population sizes were implemented for each MOEA with respect to the scale of each problem. The true PFs for small problems and the best-known PFs for the other problems were obtained. Five MOEAs were complementary to each other on various problems, which implies that no one method was completely superior to the others. The nondominated sorting genetic algorithm-II (NSGA-II), with minimum parameters tuning, remains a good choice as it showed generally the best achievements across all the problems. In addition, a small population size can be used for small and medium problems (in terms of the number of decision variables). However, for intermediate and large problems, different sizes and random seeds are recommended to ensure a wider PF. The publicly available best-known PFs obtained from this work are a good starting point for researchers to test new algorithms and methodologies for WDS analysis. [ABSTRACT FROM AUTHOR]

Abstract: An integrated methodology, based on Bayesian belief network (BBN) and evolutionary multi-objective optimization (EMO), is proposed for combining available evidence to help water managers evaluate implications, including costs and benefits of alternative actions, and suggest best decision pathways under uncertainty. A Bayesian belief network is a probabilistic graphical model that represents a set of variables and their probabilistic relationships, which also captures historical information about these dependencies. In complex applications where the task of defining the network could be difficult, the proposed methodology can be used in validation of the network structure and the parameters of the probabilistic relationship. Furthermore, in decision problems where it is difficult to choose appropriate combinations of interventions, the states of key variables under the full range of management options cannot be analyzed using a Bayesian belief network alone as a decision support tool. The proposed optimization method is used to deal with complexity in learning about actions and probabilities and also to perform inference. The optimization algorithm generates the state variable values which are fed into the Bayesian belief network. It is possible then to calculate the probabilities for all nodes in the network (belief propagation). Once the probabilities of all the linked nodes have been updated, the objective function values are returned to the optimization tool and the process is repeated. The proposed integrated methodology can help in dealing with uncertainties in decision making pertaining to human behavior. It also eliminates the shortcoming of Bayesian belief networks in introducing boundary constraints on probability of state values of the variables. The effectiveness of the proposed methodology is examined in optimum management of groundwater contamination risks for a well field capture zone outside Copenhagen city. [Copyright &y& Elsevier]