*Ottimizzazione delle reti di distribuzione idrica tramite algoritmi genetici multi-obiettivo*, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Ingegneria idraulica: scienze e tecnologie dell'acqua, 21 Ciclo.

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## Abstract

Water distribution networks optimization is a challenging problem due to the dimension and the complexity of these systems. Since the last half of the twentieth century this field has been investigated by many authors. Recently, to overcome discrete nature of variables and non linearity of equations, the research has been focused on the development of heuristic algorithms. This algorithms do not require continuity and linearity of the problem functions because they are linked to an external hydraulic simulator that solve equations of mass continuity and of energy conservation of the network. In this work, a NSGA-II (Non-dominating Sorting Genetic Algorithm) has been used. This is a heuristic multi-objective genetic algorithm based on the analogy of evolution in nature. Starting from an initial random set of solutions, called population, it evolves them towards a front of solutions that minimize, separately and contemporaneously, all the objectives. This can be very useful in practical problems where multiple and discordant goals are common. Usually, one of the main drawback of these algorithms is related to time consuming: being a stochastic research, a lot of solutions must be analized before good ones are found. Results of this thesis about the classical optimal design problem shows that is possible to improve results modifying the mathematical definition of objective functions and the survival criterion, inserting good solutions created by a Cellular Automata and using rules created by classifier algorithm (C4.5). This part has been tested using the version of NSGA-II supplied by Centre for Water Systems (University of Exeter, UK) in MATLAB® environment. Even if orientating the research can constrain the algorithm with the risk of not finding the optimal set of solutions, it can greatly improve the results. Subsequently, thanks to CINECA help, a version of NSGA-II has been implemented in C language and parallelized: results about the global parallelization show the speed up, while results about the island parallelization show that communication among islands can improve the optimization. Finally, some tests about the optimization of pump scheduling have been carried out. In this case, good results are found for a small network, while the solutions of a big problem are affected by the lack of constraints on the number of pump switches. Possible future research is about the insertion of further constraints and the evolution guide. In the end, the optimization of water distribution systems is still far from a definitive solution, but the improvement in this field can be very useful in reducing the solutions cost of practical problems, where the high number of variables makes their management very difficult from human point of view.