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Electromagnetic shields play a very significant role in the modern power and electrical industry. Efficient shields are also used in medicine, physics, and when making high-sensitivity electric and magnetic measurements to shield them from electromagnetic interference. Unfortunately, complete, unperforated shells cannot be used in real applications. In this paper, we show a new optimization technique which, by coupling the finite-element method with a genetic algorithm and Bezier curves, supports the design of efficient and esthetic shields.