The off-grid electrification of remote communities by utilizing renewable energy technologies through the development of smart micro-grids is necessary to realize the sustainable development goals. Optimal sizing of an isolated micro-grid is challenging as it needs to satisfy the electricity demand of the customers from a long-term perspective, whilst adhering to constraints in terms of power supply reliability and system operation without losing computational tractability. This paper proposes a novel method for the optimal sizing process, subject to satisfying a reliability index for meeting the loads. The proposed method also incorporates a direct load control demand response program, and utilizes a data compression-based model reduction technique to flatten the load curve and reduce the computational effort. Furthermore, a conceptual micro-grid model incorporating photovoltaic panels, wind turbines, a battery bank, a DC/AC converter, and an electric vehicle parking lot is used as a test-case system to evaluate the performance of the proposed optimal sizing method. Moreover, a maiden attempt is made to investigate and confirm the effective application of the moth-flame optimization algorithm (MFOA) within the context of the proposed methodology. Accordingly, the performance of the MFOA is compared with the most preferred and up-todate meta-heuristics employed for solving the optimal equipment capacity planning problems of renewable and sustainable energy systems, which has confirmed its superiority in terms of nearing the optimal solutions. In addition, the simulation results demonstrate that implementing a demand response program, by scheduling the charging of electric vehicles, together with directly controlling the domestic deferrable loads, can avoid overloading. This improves the utilization of the available components, which, in turn, reduces the size of some of the components and the life-cycle cost of the system. Moreover, Hengam Island, Iran is used as a representative case study site to demonstrate the applicability and effectiveness of both the proposed method and the conceptualized micro-grid system: the calculated levelized cost of electricity of $0.15/kWh, the discounted payback period of 10.53 years, the profitability index of 2.09%, and the internal rate of return of 11.28%, offer incontrovertible proof that the realization of the conceptualized micro-grid on this island is not only technically feasible, but also economically viable.