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A method for optimizing sensor locations to effectively and efficiently detect contamination in a water distribution network is presented here. The problem is formulated and solved as a twin-objective optimization problem with the objectives being the minimization of the number of sensors and minimization of the risk of contamination. Unlike past approaches, the risk of contamination is explicitly evaluated as the product of the likelihood that a set of sensors fails to detect contaminant intrusion and the consequence of that failure (expressed as volume of polluted water consumed prior to detection). A novel importance-based sampling method is developed and used to effectively determine the relative importance of contamination events, thus reducing the overall computation time. The above problem is solved by using the nondominated sorting genetic algorithm II. The methodology is tested on a case study involving the water distribution system of Almelo (The Netherlands) and the potential intrusion of E. coli bacteria. The results obtained show that the algorithm is capable of efficiently solving the above problem. The estimated Pareto front suggests that a reasonable level of contaminant protection can be achieved using a small number of strategically located sensors. [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]

The scarcity of water resources is the driving force behind modernizing irrigation systems in order to guarantee equal rights to all beneficiaries and to save water. Traditional distribution systems have the common shortcoming that water must be distributed through some rotational criteria. This type of distribution is necessary to spread the benefits of scarce resources. Irrigation systems based on on-demand delivery scheduling offer flexibility to farmers and greater potential profit than other types of irrigation schedules. However, in this type of irrigation system, the network design has to be adequate for delivering the demand during the peak period whilst satisfying minimum pressure constraints along with minimum and maximum velocity constraints at the farm delivery points (hydrants) and in the pipes, respectively. In this paper, optimum design and management of pressurized irrigation systems are considered to be based on rotation and on-demand delivery scheduling using a genetic algorithm. Comparison is made between the two scheduling techniques by application to two real irrigation systems. Performance criteria are formulated for the optimum design of a new irrigation system and better management of an existing irrigation system. The design and management problems are highly constrained optimization problems. Special operators are developed for handling the large number of constraints in the representation and fitness evaluation stages of the genetic algorithm. The performance of the developed genetic algorithm is assessed in comparison to traditional optimization techniques. It is shown that the methodology developed performs better than the linear programming method and that solutions generated by the modified genetic algorithm show an improvement in capital cost. The method is also shown to perform better in satisfying the constraints. Comparison between on-demand and rotation delivery scheduling shows that a greater than 50% saving can be achieved in total cost at the cost of reducing flexibility in the irrigation time. Finally, it is shown that minimizing standard deviation of flow in pipes does not result in the best distribution, and therefore minimum cost, neither for systems with uniform flows or those with large variations in discharge at hydrants. [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]

The water distribution system (WDS) design problem is defined here as a multiobjective optimization problem under uncertainty. The two objectives are (1) minimize the total WDS design cost and (2) maximize WDS robustness. The WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. Decision variables are the alternative design options for each pipe in the network. The sources of uncertainty are future water consumption and pipe roughness coefficients. Uncertain variables are modeled using probability density functions (PDFs) assigned in the problem formulation phase. The corresponding PDFs of the analyzed nodal heads are calculated using the Latin hypercube sampling technique. The optimal design problem is solved using the newly developed RNSGAII method based on the nondominated sorting genetic algorithm II (NSGAII). In RNSGAII a small number of samples are used for each fitness evaluation, leading to significant computational savings when compared to the full sampling approach. Chromosome fitness is defined here in the same way as in the NSGAII optimization methodology. The new methodology is tested on several cases, all based on the New York tunnels reinforcement problem. The results obtained demonstrate that the new methodology is capable of identifying robust Pareto optimal solutions despite significantly reduced computational effort. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Genetic algorithm (GA) optimization is well suited for optimizing the operation of water distribution systems, especially large and complex systems. GAs have good initial convergence characteristics, but slow down considerably once the region of optimal solution has been identified. In this study the efficiency of GA operational optimization was improved through a hybrid method which combines the GA method with a hillclimber search strategy. Hillclimber strategies complement GAs by being efficient in finding a local optimum. Two hillclimber strategies, the Hooke and Jeeves and Fibonacci methods, were investigated. The hybrid method proved to be superior to the pure GA in finding a good solution quickly, both when applied to a test problem and to a large existing water distribution system. [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]

A methodology is presented for the optimal design and scheduling of investment for the rehabilitation of water distribution networks. Based on the evolutionary programming technique known as Structured Messy Genetic Algorithms, the methodology utilizes a multi-objective formulation which improves the evolutionary process and provides nondominated optimal solutions over a range of costs and benefits. The model is applied to an example--a small artificial network of fifteen pipes. The effects on the optimal solutions of varying parameters such as interest rate and inflation rate are also investigated. [ABSTRACT FROM AUTHOR]

Describes the development of a computer model GANET that involves the application of genetic algorithms to the problem of least-cost design of water distribution networks. Inconsistencies in predictions of network performance caused by different interpretations of the Hazen-Williams pipe flow equation; Potential as a tool for water distribution network planning and management.

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]

This paper presents a novel multi-objective genetic algorithm (MOGA) based on the NSGA-II algorithm, which uses metamodels to determine optimal sampling locations for installing pressure loggers in a water distribution system (WDS) when parameter uncertainty is considered. The new algorithm combines the multi-objective genetic algorithm with adaptive neural networks (MOGA–ANN) to locate pressure loggers. The purpose of pressure logger installation is to collect data for hydraulic model calibration. Sampling design is formulated as a two-objective optimization problem in this study. The objectives are to maximize the calibrated model accuracy and to minimize the number of sampling devices as a surrogate of sampling design cost. Calibrated model accuracy is defined as the average of normalized traces of model prediction covariance matrices, each of which is constructed from a randomly generated sampling set of calibration parameter values. This method of calculating model accuracy is called the ‘full’ fitness model. Within the genetic algorithm search process, the full fitness model is progressively replaced with the periodically (re)trained adaptive neural network metamodel where (re)training is done using the data collected by calling the full model. The methodology was first tested on a hypothetical (benchmark) problem to configure the setting requirement. Then the model was applied to a real case study. The results show that significant computational savings can be achieved by using the MOGA–ANN when compared to the approach where MOGA is linked to the full fitness model. When applied to the real case study, optimal solutions identified by MOGA–ANN are obtained 25 times faster than those identified by the full model without significant decrease in the accuracy of the final solution. [Copyright &y& Elsevier]