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• A metaheuristic-driven method is proposed to optimally design off-grid micro-grids. • A data compression-directed model reduction preserves the computational tractability. • The moth-flame optimizer is superior to the well-established algorithms in this area. • A direct load control-demand response program delivers cost savings of up to 7.2%. • The system's levelized cost of energy of $0.15/kWh is well below the existing cost. 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. 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 within the context of the proposed method. Accordingly, the performance of the moth-flame optimization algorithm is compared with the most preferred and up-to-date meta -heuristics employed for solving the optimal equipment capacity planning problems of renewable and sustainable energy systems, and is confirmed as superior 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. 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 energy 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%, suggest that the realization of the conceptualized micro-grid on this island is not only technically feasible, but also economically viable. Furthermore, the results obtained by applying the proposed micro-grid equipment capacity planning method are analyzed and validated through comparisons with those of the state-of-the-art methods. [ABSTRACT FROM AUTHOR]