The present paper aims to study the effect of cooling air inlet methods on gas turbine compressors on increasing their efficiency. After modeling gas turbine cycles with absorption and compression systems in the EES software, these cycles' performance is investigated for all equipment of the cycle from thermodynamic, exergy, and exergoeconomic aspects. In the absorption system, the conventional solution of lithium bromide-water is used as a two-component fluid, and in the compression cycle, the R134a operating fluid is used. According to the results, with the rise in the system's inlet air temperature, the total output work of the gas turbine decreases. Based on the exergoeconomic analysis, the exergy destruction cost dominates the initial cost, resulting in the exergoeconomic factor's decline. Relationship predicted by Group Method of Data Handling (GMDH) to reduce the computation time of optimization. The studied systems are then subjected to two-objective optimization by the Particle Swarm algorithm using MATLAB software. The objective functions are related to the exergy efficiency and total cost rate. The results reveal contradictory behavior in these two objective functions so that with the increase in the exergy efficiency, the total cost rate increases.