The binary-coded elitist non-dominated sorting genetic algorithm with the modified jumping gene operator (NSGA-II-mJG) is used to obtain global optimal solutions of flotation circuits. Several single-objective and multi-objective optimization problems are solved using the interconnecting cell linkage parameters (fraction flow rates) and the mean cell residence times as the decision variables. In the single-objective problem, the overall recovery of the concentrate stream is maximized for a desired grade of the concentrate. Two two-objective optimization problems are then solved. In one, the number of non-linking streams and the overall recovery of the concentrate are maximized simultaneously. This gives several simple circuits in a systematic manner with only marginally lower recoveries. In the other two-objective optimization problem, the overall recovery of the concentrate is maximized while the total cell volume is minimized. A three-objective problem (maximization of the overall recovery of the concentrate, maximization of the number of non-linking streams and minimization of the total cell volume) is then solved. All the problems constrain the grade of the product to lie at a fixed value. Finally, a complex and computationally intensive four-objective optimization problem is solved. The solution of several practical optimization problems in this study helps develop useful insights into the optimal solutions. (c) 2006 Published by Elsevier B.V.