Abstract
The models used in the design of water distribution networks networks can be quite varied, depending on the objective to be attained. This Ph. Degree focuses primarily on hydraulic sizing water distribution networks, so as to meet certain service requirements, including minimum conditions of pressure, velocity, etc.
The design of water distribution networks is extremely complex.  It is well-known that when the diameters of the conductions are chosen as decision variables, the restrictions are implied functions of these variables of decision, so the space’s region of solutions is a no convex type and the objective function becomes multimodal. At this point, traditional methods based on mathematical techniques are limited to the location of local minima of the objective function, which depends on the starting point of convergence.
Traditionally, water distribution network design, upgrade, or rehabilitation has been based on engineering judgement. Howewer, in the last three decades a significant amount of research has focused on the optimal design of water distribution networks.
The application of heuristic techniques of optimization allows the search beyond these local minimums, which generally ample the field search and with it the capacity to obtain better solutions. The evolutionary algorithms are methods of search of solutions that are based in the natural beginning of the evolution. 
The different evolutionary techniques are numerous. In the literature one can find many optimization models applied to the design of water distribution networks using these techniques. Regrettably, there are no valid criteria for comparing them beyond the minimum cost design for a given network obtained. Inside the evolutionary algorithms, we can find Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Harmony Search and so on
The aim is to minimize the necessary costs of investment for the implantation of a certain system, starting from the topological layout and the demands and requirements of pressure in the nodes. The proposed method develops a code based on the use of numerical particles instead of binary particles. It is also introduced the optimization of the different parameters associated with each methodology.
This doctoral thesis compares the results obtained by some of these techniques applied to optimal design of water networks. Thus, from simulations, the thesis focuses on how to improve the results, for which statistical analysis is performed not only on the results obtained by each of the optimization models, but also the influence adjusting the various parameters of each technique in the good work of it.
In order to do this, we define an efficiency ratio of the algorithm that allows us to relate the quality of the solution obtained with the computational effort that performs an algorithm to find the final solution. Efficiency is a new concept in the application of heuristic methods to solve complex problems. In this case, it represents the relationship between solution quality and speed of resolution of the algorithm
The efficiency (E) gives an idea of the quality of the simulation performed, so that the greater this number the better the relationship between solution quality and resources used to obtain it. This efficiency rating is a neutral to compare optimization algorithms based on different criteria.