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Optimization methodologies based on the Brigham Young University OPTDES code are used to determine the minimum per capita crop area required for Controlled Environmental Life Support Systems (CELSS) needed for self-sustaining space colonies and long duration space flights. Various food crop productivity values and nutritional requirements are integrated with numerical optimization algorithms to determine the types of crops which best meet nutritional needs, subject to various constraints, and have minimum growing area. Eleven candidate crops, selected from NASA and other sources, are combined with a nutritional code and selected nutritional requirements.