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Fresh water availability is essential for the economic development in small communities in remote areas. In desert climate, where naturally occurring fresh water is scarce, seawater or brackish water from wells is often more abundant. Since water desalination approaches are energy intensive, a strong motivation exists for the design of cost-effective desalination systems that utilize the abundant renewable energy resource; solar energy. This paper presents an optimization model of a solar-powered reverse osmosis (RO) desalination system. RO systems rely on pumping salty water at high pressure through semi-permeable membrane modules. Under sufficient pressure, water molecules will flow through the membranes, leaving salt ions behind, and are collected in a fresh water stream. Since RO system are primarily powered via electricity, the system model incorporates photovoltaic (PTO panels, and battery storage for smoothing out fluctuations in the PV power output, as well as allowing system operation for a number of hours after sunset. Design variables include sizing of the PV solar collectors, battery storage capacity, as well as the sizing of the RO system membrane module and power elements. The objective is to minimize the cost of unit volume produced fresh water, subject to constraints on production capacity. A genetic algorithm is used to generate and compare optimal designs for two different locations near the Red Sea and Sinai.