Multi-objective optimization of the operation of a two-fixed-bed, four-stage pressure swing adsorber (PSA) unit for the separation of air is studied using the newly developed multi-objective optimization technique, the modified MOSA-aJG. The rigorous model developed for a single fixed-bed adsorption column is applicable to PSA units provided different and appropriate boundary and initial conditions are used for the four stages, namely, pressurization, adsorption, blowdown, and purge. Seven of the nine model parameters are the same as obtained earlier for a single-bed O-2-N-2-Zeolite 5A unit. The remaining two parameters are tuned using one set of experimental data on a PSA unit with the same system. Reasonably good agreement is observed between simulation and experimental results. Two two-objective optimization problems and a four-objective problem are formulated for the operation of a PSA. These are solved to obtain optimal values of the adsorption pressure, desorption pressure, adsorption and purge times, and input flow rates during the adsorption and purge stages. The effects of different decision variables on the several objective functions are discussed in detail.