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Recent studies show quantum-dot cellular automata (QCA) as one of the promising alternatives to CMOS technology. Optimization plays an important role in circuit design despite the used technology. One possibility is the minimization of the number of basic building blocks usually resulting in less energy consumption and fewer delays in processing. The principles of evolutionary computation have already been successfully used for logic optimization of majority gate-based nano electronic circuits. The realm was to reduce the number of the basic building blocks (majority gates) required for computing Boolean functions. Our study is focused on the space complexity optimization of simple and also more complex QCA devices by means of the minimization of the number of employed QCA cells.