Islands face limitations in producing and transporting energy due to their geographical constraints. To address this issue, the ROBINSON project, funded by the EU, aims to create a flexible, self-sufficient, and environmentally friendly energy system that can be used on isolated islands. The feasibility of renewable electrification and heating system decarbonization of Eigerøy in Norway is described in this article. A mixed-integer linear programming framework was used for modelling. The optimization method is designed to be versatile and adaptable to suit individual scenarios, with a flexible and modular formulation that can accommodate boundary conditions specific to each case. Onshore and offshore wind farms and utility-scale photovoltaic (PV) were considered to generate renewable electricity. Each option was found to be feasible under certain conditions. The heating system, composed of a biomass gasifier, a combined heat and power system with a gas boiler as backup unit, was also analyzed. Parameters were identified in which the combination of all three thermal units represented the best system option. In addition, the possibility of green hydrogen production based on the excess electricity from each scenario was evaluated.