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In islanded microgrid design, a proper Distributed Energy Resource (DER) selection, sizing and effective coordination between resources are important and challenging optimization tasks. The types and sizes of renewable energy sources such as wind turbines, photovoltaic panels, the capacities of battery bank and the other distributed generators must be optimized in islanded microgrid design. In this paper, the problem is formulated as a nonlinear integer minimization problem which minimizes the sum of the total capital, operational and maintenance cost of DERs, subject to constraints such as energy limits and emission limits of each DER and Loss of Power Supply Probability (LPSP) of the microgrid. This paper proposes an Evolutionary Strategy (ES) for solving this minimization problem. LPSP of each individual of ES's population is calculated by simulation of 8760 hours in a year. The proposed methodology was used to design microgrids for MODERN project. The simulation studies have shown that the proposed methodology provides excellent convergence and feasible optimum solution for sizing of islanded microgrids using evolutionary strategy.