Cost-based design of wastewater network optimal topology

An optimal water network is an oriented graph, starting with the inlet contaminant free unit operations. When the supply water is available from diverse sources and, accordingly, has different level of pollutants contamination, the associated graph remains oriented, but the starting unit operations are lumped and assigned to proper water source based upon their input concentration restrictions. A cost-based optimisation criterion is used to find the optimum water network topology which reduces both the investment (piping network cost, built using the optimum pipes’ diameter) and operating (pumping) costs, when water sources with or without multiple contaminants are used jointly. This topology is compared against the best topology found using supply water minimization as optimisation criterion. In both cases, the optimisation is carried out using an improved genetic algorithm (GA) variant, which guarantees the observation, in the same time, of both the minimum cost and the overall restrictions. Finding the optimal solution is not simple, since the unknowns’ number outcomes the equations’ number. The GA works with chromosomes based upon all internal flows coded as genes. The restrictions are handled during the population generation, simply eliminating the genes outside the feasible domain. The individuals are selected for interbreeding according to their frequency of selection, using one-point crossover method, and then mutation is applied to randomly selected ones.