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Optimization of large and hydraulically complex water distribution systems (WDSs) is computationally expensive as simulation models are required to evaluate the performance of solutions to the problem at hand. Metamodels can act as a surrogate or substitute for these simulation models and provide significant speed-ups in the optimization process. The application of metamodels in the field of WDS optimization has been limited to date, and little guidance has been given in terms of constructing metamodels for hydraulically complex systems. While it is relatively straightforward to obtain satisfactory metamodel approximations to simulation models of simple WDSs, this is not necessarily the case for more complex networks. In order to reduce the complexity of the relationship that is to be approximated by the metamodels, a number of factors have to be considered, including the complexity of the hydraulic simulation model, the complexity of the decision space, and the locations at which outputs are required from the hydraulic simulation model. This research presents a systematic methodology for dealing with these factors and demonstrates the effectiveness of the approach by applying it to an actual WDS. A system in Wallan, Victoria, Australia, is selected for demonstration purposes. Four different metamodelling scenarios are presented here. The results show that, for this case study, some skeletonization of the model is required to achieve suitably accurate metamodels. The optimization results show a reduction in the average daily pumping costs from $457 to $363; a saving of 21%. The net present value (NPV) over 25 years is used as the objective function, which includes both pumping and chlorine costs. The current operating regime corresponds to an NPV of $1.56 million, while the optimized solution has an NPV of $1.34 million; a saving of 14%. In addition to these economic benefits, the optimized solution achieves adequate disinfection throughout the system, whereas the current operating regime results in deficits in chlorine residuals at several locations in the system. DOI: 10.1061/(ASCE)WR.1943-5452.0000052 CE Database subject headings: Optimization; Water distribution systems; Computation; Neural networks; Water quality. Author keywords: Optimization; Water distribution; Evolutionary computation; Neural networks; Water quality.

The suitability of genetic algorithms (GAs) tbr the optimization of water distribution systems (WDSs) has been demonstrated extensively. However, despite many years of application in many different fields, the selection of the GA parameters remains a difficult and time consuming task. In this paper, two methodologies that do not require trial-and-error GA parameter calibration have been tested on a WDS optimization problem to determine their suitability for application in the water resources field and to assess their ability in locating near-optimal solutions. The results indicate that both approaches located solutions that were significantly better than a GA using typical parameter values, while the methodology based on convergence of the GA population located the best solutions overall. This method can be easily applied to assist GA users in identifying suitable GA parameters without requiting a time consuming trial-and-error approach. DOI: 10.1061/(ASCE)WR.1943-5452.0000033 CE Database subject headings: Calibration: Chlorine; Algorithms; Computation; Optimization; Water distribution systems; Pipe networks; Water supply. Author keywords: Calibration; Genetic algorithms; Evolutionary computation; Optimization; Algorithms; Water distribution systems; Pipe networks; Water supply.

Two of the main performance criteria of a water distribution system are that it is inexpensive to construct, operate, and maintain and that it operates in a reliable manner. These two criteria are often conflicting, thus implying that the decision maker needs to reach a compromise in scheduling mains for replacement. One way to facilitate this decision is to generate a trade-off surface that represents the compromise between the two objectives. This paper demonstrates the use of genetic algorithms to generate trade-off curves between cost and reliability for pipe replacement decisions. Curves for two planning scenarios are generated. The first identifies the trade-offs necessary for the current conditions. The second allows the water authority to determine the required levels of future expenditure, given funding constraints, to meet a specified level of service over the entire planning horizon. Alternatively, it provides an estimate of the impact on performance of delaying expenditure. DOI: 10.1061/(ASCE)0733-9496(2006) 132:2(79) CE Database subject headings: Costs; Reliability; Water distribution systems; Retrofitting.

Genetic algorithms (GAs) have been shown to apply well to optimizing the design and operations of water distribution systems (WDSs). The objective has usually been to minimize cost, subject to hydraulic constraints such as satisfying minimum pressure. More recently, the focus of optimization has expanded to include water quality concerns. This added complexity significantly increases the computational requirements of optimization. Considerable savings in computer time can be achieved by using a technique known as metamodeling. A metamodel is a surrogate or substitute for a complex simulation model. This research uses a metamodeling approach to optimize a water distribution design problem that includes water quality. The type of metamodels used are artificial neural networks (ANNs), as they are capable of approximating the nonlinear functions that govern flow and chlorine decay in a WDS. The ANNs were calibrated to provide a good approximation to the simulation model. In addition, two techniques are presented to improve the ability of metamodels to find the same optimal solution as the simulation model. Large savings in computer time occurred from training the ANNs to approximate chlorine concentrations (approximately 700 times faster than the simulation model) while still finding the optimal solution. DOI: 10.1061/(ASCE)0733-9496(2005)131:3(172) CE Database subject headings: Optimization: Water distribution: Evolutionary computation: Neural networks; Water quality, Design.

This paper compares four different methods for estimating the yield of a multiple reservoir system. These include simulation, a combined simulation-optimization model (WATHNET), a full optimization model, and a simplified optimization model called the yield model. Simulation is used widely in practice and provides a good approximation of the behavior of the system but requires a set of operating rules to be specified. The optimization methods automatically determine operating rules and are therefore quite useful in estimating the yield of a new system that has not yet been operated. The four methods are used to estimate the safe historical yield of the Canberra water supply system (Australia). It was found that the full optimization model and the yield model provide high estimates of the system yield because they assume perfect knowledge of future inflows. WATHNET presents a reasonable compromise in estimating the system yield using implied operating rules that are achievable in practice.

A nonlinear model for the optimum design and operation of drip irrigation systems on flat terrain is presented in this paper. The analysis is based on dividing a field into subunits and evaluating various shift patterns and the corresponding pipe and pump sizes in order to identify a minimum cost solution. The decision variables are the lengths of two given pipe sizes for the laterals, the diameters of all other pipes, the size of pump, the area and dimensions of subunits, as well as the shift patterns and the irrigation time for each shift and set of subunits irrigated simultaneously. The optimization procedure involves a complete enumeration approach, which minimizes the sum of the capital cost of the system and the present value of operating costs. The model is applied to a case study of a level rectangular field supplied from a ground-water source at its center. The results obtained indicate that one shift operation is the most cost-effective provided the emitter flow rate is above a defined minimum level.