“> In the present work a 50 MW Gas Turbine cycle is considered. The optimization procedure is Genetic Algorithm which is a new method in optimizing problems. The plant is comprised of a gas turbine, air compressor, combustion chamber. The design Parameters of the plant, were chosen as: compressor pressure ratio (rcomp), compressor isentropic efficiency (ηcomp), gas turbine isentropic efficiency (ηGT), gas turbine inlet temperature (TC). In order to optimally find the design parameters a thermo-economic approach has been followed