A microbial fuel cell (MFC) is a novel promising technology for simultaneous renewable electricity generation and wastewater treatment. Three non-comparable objectives, i.e. power density, attainable current density and waste removal ratio, are often conflicting. A thorough understanding of the relationship among these three conflicting objectives can be greatly helpful to assist in optimal operation of MFC system. In this study, a mult-iobjective genetic algorithm is used to simultaneously maximizing power density, attainable current density and waste removal ratio based on a mathematical model for an acetate two-chamber MFC. Moreover, the level diagrams method is utilized to aid in graphical visualization of Pareto front and decision making. Three bi-objective optimization problems and one three-objective optimization problem are thoroughly investigated. The obtained Pareto fronts illustrate the complex relationships among these three objectives, which is helpful for final decision support. Therefore, the integrated methodology of a multi-objective genetic algorithm and a graphical visualization technique provides a promising tool for the optimal operation of MFCs by simultaneously considering multiple conflicting objectives. (C) 2017 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.