To meet the raising demands for energy and potable water, integration of power plants and desalination systems for large-scale coproduction have been widely used in the world. However, in remote and rural locations with no infrastructures such as power grids, integration of large-scale systems is not financially viable. This paper presents a conceptual design and a methodology based on the GPU-3 Stirling engine in upstream as prime mover, coupled with three configurations of multi-effect evaporation desalination (MED) unit in downstream to address the power-water demands for areas with lower population. A multi-objective optimization technique is employed to find the optimal design parameters of the proposed hybrid system. Three objective functions namely maximizing power and water production and minimizing the cost of products are considered. Decision-making tools are implemented on the optimal points of each configuration to select the optimized configurations for each cogeneration system. The most effective system is then introduced by implementing Analytical Hierarchy Process (AHP) technique. It is found that the final selected system is capable of delivering 2.58 kW of electricity and 19.92 m3 fresh water per day with 2.07 $ ∙ hr−1 cost of products which can be divided into 0.29 $ ∙ kWhr−1 and 1.6 $ ∙ m3 for power and water, respectively.