Many studies have attempted to optimize integrated Solid Oxide Fuel Cell-Gas Turbine (SOFC-GT), although different and somehow conflicting results are reported employing various algorithms. In this study, Multi-Objective Optimization (MOO) is employed to approach the optimal design of SOFC-GT considering all prevailing factors. The emphasis is placed on the evaluation of the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) performance as two effective approaches for solving the multi-objective and non-linear optimization problems. Multi- objective optimization is carried out on two vital objectives; the electrical efficiency and the overall output power of the system. The considerable achievements are the set of optimal points that aim to identify the system optimal performance which provides a practical basis for the decision-makers to choose the appropriate target functions. For the studied conditions, the two algorithms nearly exhibit similar performance, while the PSO is faster and more efficient in terms of computational effort. The PSO appears to achieve its ultimate parameter values in fewer generations compared to the GA algorithm under the examined circumstances. It is found that the maximum power of 410 kW is accomplished employing the GA optimization method with an efficiency of 64%, while PSO method yields the maximum power of 419.19 kW at the efficiency of 58.9%. The results stress that PSO offers more satisfactory convergence and fidelity of the solution for the SOFC-GT MOO problems.