Currently, gas turbine is one of the most widely-used power generating technologies. The race to achieve higher efficiency from gas turbines is gathering momentum with most of the major manufacturers. Cogeneration with advanced engines has the prospect of attaining thermal efficiencies around 60 in the future. In this condition, further development of gas turbine design optimization in order to obtain higher thermal efficiency seems to be beneficial. In the current work, the design of a single shaft gas turbine in a cogeneration plant is optimized based on the model established using thermodynamic theory. The overall thermal efficiency of the engine is tried to be optimized by adjusting the compressor efficiency, turbine efficiency, compression pressure ratio, and turbine inlet temperatures. A feasible solution should satisfy two physical constraints, namely a desired gas turbine power and a suitable limit of engine exhaust temperature. An evolutionary model using Simulated Annealing algorithm is developed to find the sets of optimal solutions in the space defined by user experience and literature. A number of case studies have been performed and an optimal solution and their corresponding performance are discussed. © 2018 The Authors, published by EDP Sciences.