Evolutionary Multi-Objective Optimization of an Activated Sludge Process

Abstract

Abstract Many real problems involve multiple objectives that are often conflicting and non comparable. Rare are the problems in which the objectives to be achieved (maximized or minimized) are single. Such problems are not adequately solved by using single objective function optimization techniques. Non comparable solutions are associated to the multi-objective optimization problems that represent the tradeoff among objectives. These solutions are named Pareto optimal solutions. In this work, a general review about different methods that deal with multi-objective optimization problems is presented. Special attention is given to evolutionary methods, detailing the NSGA II algorithm. This algorithm was implemented in Matlab to deal with crossover and mutation applied directly to real variables and constrained optimization problems. This method of evolutionary multi-objective optimization was applied in an activated sludge wastewater treatment system, in which effluent quality and operational cost are optimized. For this purpose, set-points of nitrate and dissolved oxygen concentrations were used as decision variables. The Pareto curves obtained at the end of 50 generations were analyzed. Finally, for illustration, one point in the Pareto curve was chosen to demonstrate the optimal set of values. In this study, the results obtained show the ability of the algorithm to achieve Pareto optimal solutions.