In this study, a comprehensive thermodynamic modeling of a dual pressure combined cycle power plant is modeled. Also, to ensure the developed code, results are compared with an actual data taken from one of the Iranian power plant. The combined cycle power plant is equipped with a duct burner. In second part, by considering number of decision variables, the objective function is optimized. To have a better understanding and optimal design of the system, an optimization is performed. In our multi-objective optimization, first objective function comprises a set of component costs, the fuel cost injected into the combustion chamber, duct burner cost and the cost of exergy destruction. Second objective function is cycle exergy efficiency. Therefore, multi-objective optimization of this cycle is carried out using a computer simulation code written by using the genetic algorithm approach. Finally, the effect of cycle key parameters on these two objective functions is investigated. The results show that gas turbine temperature, compressor pressure ratio and pinch point temperatures are significant design parameters. It means that any changes in these design parameters lead to a drastic change in objective functions. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.