A self organizing map based hybrid multi-objective optimization of water distribution networks

Water Distribution Networks (WDNs) are an essential infrastructure of every civilization. In the past decades, there has been a lot of work on the optimization of WDNs. This paper presents a hybrid NSGA-II for multi-objective optimization of combinatorial WDN design, utilizing the SOM network as a tool to find the genotypic or phenotypic similarities. SOM is a versatile unsupervised Artificial Neural Network (ANN) that can be used to extract the similarities and find the related vectors with the use of a proper similarity measure. The proposed method, SOM-NSGA-II, derives subpopulations or virtual islands for inbreeding similar individuals to speed up the convergence process of the optimization. The cross-over operation between similar individuals of the subpopulations at the constraint dominated region of the solution space showed a faster convergence and a wider Pareto front for the test problems considered. An added advantage of the method is the application of genotypic sorting of the population by SOM for visual representation of the structure of the Pareto front. The resulted maps showed the extent of variation of the decision variables and their relative importance. This method may be utilized to speed up optimization of large scale WDNs and as an important visual aid for decision makers and designers of WDNs.