In this research study, a 40 MW gas turbine power plant, which is coupled with a multi-effect desalination system with thermal vapor compression, is investigated. The energy, exergy and exergoeconomic analyses of the integrated plant are presented. As the number of effects in a desalination system is a key parameter, the effect of number of effects on the system performance is investigated. The genetic algorithm-based multi-objective optimization is applied to determine the best decision variables. To achieve the best optimization states, different scenarios of multi objective optimization based on the total exergy destruction rate, unit electricity price, total cost rate, gain output ratio, distilled water cost, and total exergy efficiency are examined. Additionally, seven decision variables are compressor pressure ratio (), combustion temperature (), compressor isentropic efficiency (), gas turbine isentropic efficiency (), top brain temperature (TBT), last effect temperature (LET), and ejector compression ratio (Cr). The parametric analysis results indicated that although increasing the number of effect enhance the distilled water production rate, it increases the total cost rate of the system. With motive steam flow rate of 14 kg/s, results showed that distilled water production rate is 12294. Additionally, with three different scenarios the optimal states of integrated system are introduced. The results of optimization scenarios suggested different optimal states that are best guide for designer to select the best system configuration.