A microgrid is a small-scale smart network that contains distributed resources and loads and serves several technical, economic, and environmental aims. In this kind of power system, the energy generated by different sources is often collected in an adequate bus system (ac or dc busses) and transported to loads across a distribution system. In case of islanding operation of a microgrid, each production insufficiency or distribution system fault can cause a partial or total interruption of power supply required by loads of the microgrid. This unavailability can last longer because of the randomness and intermittent behavior of renewable sources and the importance of the maintenance actions of the distribution system. To guarantee high availability of power supply, microgrid must be able to produce and to transfer the power energy requested by loads. The sizing of distributed sources and the design of the distribution system present an important challenge to achieve this goal. This paper offers a new global methodology carried out in two steps: in the first, it aims to optimize the source sizing by adding some microsources for ensuring the balance between sources production and loads requirement, then, in a second step, it aims to enhance the distribution system design by the creation of new paths of power transmission for transferring the produced energy from sources to loads. The proposed optimization methodology aims to achieve the requested availability rate requested by each load (considering their priorities) by taking into account some technical and economic factors. In this methodology based on genetic algorithms, objective functions are defined, and several electrical and economic constraints are formulated. The graph theory is used to represent the architecture of the microgrid distribution system, and Matpower tool of MATLAB is used to model it. An application and implementation of the proposed optimization methodology in a Tunisian petroleum platform indicate that the proposed solution is efficient in optimizing of power supply availability in its microgrid.