Application of genetic algorithms in the reliability-based optimal design of water distribution networks

Application of genetic algorithm (GA) in reliability-based optimal design of waterdistribution networks (WDNs) is presented in this study. Expected water shortage(EWS) was applied for a surrogate measure of reliability. This can be expressed as thedifference between water demand under normal operation and the supplied water underthe partially failed conditions in a WDN. The expected water shortage was computedfrom the pressure-driven analysis (PDA) using the EPANET hydraulic solver (Ozger etal., 2004; Yoo, 2005). This analysis produces much more realistic results insimulations of partially failed conditions than the demand-driven approach andappeared to be suitable for reliability-based optimization.The expected water shortage was furthermore converted into a function of costobjective, called expected water shortage costs (EWSC), for the application of geneticalgorithm. The expected water shortage cost represents the reduced benefit resultingfrom the decrease of water supply to the customers during irregular conditions. Thiscost can be calculated as the product of the unit water cost and the expected watershortage, over the design life of WDN.A reliability-based optimal design model was finally developed combining a multiobjectiveproblem into a single objective problem, based on the application of geneticalgorithms (GAs). In other words, the reliability, assessed by the expected watershortage in this study, was converted into a cost objective to enable combining withnetwork investment costs. The algorithm was programmed using EPANET Toolkitfunctions and Visual Studio 6.0. C++ programming language.The results obtained from the model simulation is a network layout with not onlyoptimized investment costs but also an appropriate level of reliability in terms ofbenefit which can be derived from minimizing the reduction of water supplied tocustomer during abnormal operating conditions.The optimization model was tested on two sample case networks known in literature,one taken from the research paper of Khomsi et al. (1996) and the other is a Hanoinetwork which has been applied by several researchers.Additionally, the real case network of city of Nonsan, the first local government watersupply system to be taken over by Korea Water Resources Corporation (KOWACO),was analyzed to estimate the optimal pipe size of the network under the considerationof reliability. Several what-if scenarios were analyzed for different conditions of pipe break rates,unit water costs and design life. The study also compares the correlation between thesingle optimal designs while only considering the network cost, and the reliabilitybasedoptimal designs.Those results show that the application of genetic algorithm in reliability-basedoptimal design of WDN is useful to determine the level of reliability based oneconomical grounds. The study also suggests that the optimal layout of WDN candiffer depending on the level of reliability which can be set as a requirement